INTRODUCTION TO FINANCIAL MATHEMATICS: INTEREST THEORY

INTRODUCTION TO FINANCIAL MATHEMATICS: INTEREST THEORY Stephen ARO-GORDON, PhD Baze University Nigeria Department of Financial Mathematics Email: [email protected] / [email protected]

CLASS NOTES

September – October 2015 @ SDMIMD, Mysore, India

1

Session I – Module introduction & overview

Agenda:  The big picture – some global / emerging markets background perspectives  Course essence, outline, scope and general methodology  Introducing groups, course projects, etc. September – October 2015 @ SDMIMD, Mysore, India

Asia–Africa: Biggish geography for global growth  Global population – 7.1 billion  Asia and Africa are areas where the majority of poor peoples of the world live.  Poverty headcount ratio at $1.25 a day (PPP) (% of population) in sub-Saharan Africa is 46.8% compared to global average of 14.5%

September – October 2015 @ SDMIMD, Mysore, India

3

India ….

India’s 7.5% growth rate makes it the fastest growing major economy in the world. September – October 2015 @ SDMIMD, Mysore, India

Investors’ appetite for Africa Africa’s perceived attractiveness relative to other regions has improved dramatically over the past few years. Africa has moved from the third-from-last position in 2011 to become today the second-most attractive investment destination in the world. Last year, only North America ranks ahead of Africa in terms of investment attractiveness Share of SSA in FDI projects in Africa reached an alltime high of 83% in 2013 - [http://www.ey.com/Publication/vwLUAssets/EYattractiveness-africa-2014/$FILE/EY-attractiveness-africa-2014.pdf - 19/09/2015]

September – October 2015 @ SDMIMD, Mysore, India

The Big Six – Key hub economies of Africa 1. Nigeria 2. South Africa 3. Kenya 4. Angola 5. Morocco 6. Egypt - [http://www.ey.com/Publication/vwLUAssets/EY-attractiveness-africa-2014/$FILE/EY-attractiveness-africa-2014.pdf 19/09/2015]

September – October 2015 @ SDMIMD, Mysore, India

India & Nigeria: Emerging markets Dimensions

India

Nigeria

Population

1.276 billion (2015)

182.2 million (2015)

Total Area

3,287,590 km2

923,768 km2

Economy

US$2.3 trillion nominal GDP

US$0.57 trillion

7th largest economy

20th largest economy

$1,808

$3,298

States

29

36

Union territories

7

7

World’s Per capita

Source: https://en.wikipedia.org

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Why Nigeria?

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

“When you change Nigeria, you also change Africa.” - Ban Ki-Moon [www.dailytrust.com.ng -25/08/2015]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Nicer Nigeria… Nigeria is believed to have become more politically stable with the peaceful, credible, and successful election of March 28, 2015. UNCTAD classifies Nigeria as the most preferred investment destination in Africa. The country with 4th highest returns on investment in the world. - [http://www.vanguardngr.com/2015/09/paris-to-abuja-we-are-happy-with-the-visit-is-your-presidenthappy/ - 19/09/2015]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

But the biggest challenge remains… 63% of Nigeria’s huge population is made up of mostly unemployed youths

.

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Some global financial perspectives

September – October 2015 @ SDMIMD, Mysore, India

Quizzes: Some global financial perspectives i. What is the current size of global financial assets in US$? ii. What do you guess may be the current average composition of super-rich’s portfolios? iii. What are the recent trends in international debt securities? iv. What are the trends in the average deposit interest rates in emerging economies? v. Any ideas about the current yields on 10-year government bonds in India, Nigeria, and other emerging markets? vi. Is pension funds’ relatively strong appetite for fixed-income assets justified?

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Global Financial Assets US$’ trillion (2014) S/NO

ASSETS

VALUE

1

Debt

90

% OF TOTAL 10%

2

Stocks

66

7%

3

Securitized products

44

5%

4

OTC derivatives

693

78%

TOTAL

893

100%

 Source: Business Insider India (March 25, 2014) http://www.businessinsider.in/CHART-OFTHE-DAY-The-Rise-Of-The-156-Trillion-Market-For-Global-FinancialAssets/articleshow/32681342.cms [18/09/2015]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Derivatives – an overview)  A financial derivative is a contract which derives its value from the performance of another (called “underlying”) entity such as an asset, index, interest rate, etc. (Examples: futures, swaps, forwards, options, caps, floors, collars)  Derivatives are one of the three main groups of financial instruments – the others being: - Equities (i.e. stocks) - Debt (i.e. bonds and mortgages)  Derivatives are traded over-the-counter or on an exchange (e.g. Chicago Mercantile Exchange) COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Global-Asia-Middle East-Africa: How the super-rich invest their assets (2015) S/NO

ASSETS

GLOBAL

ASIA-MIDDLE EAST -AFRICA

1

Alternative investments

13.1%

14.7%

2

Fixed-income

16.9%

19.1%

3

Real Estate

17.6%

22.3%

4

Cash and Cash equivalents

25.6%

23.0%

5

Equities

26.8%

20.9%

TOTAL

100%

100%

Source: Business Insider India (March 25, 2014) http://www.businessinsider.in/CHART-OFTHE-DAY-The-Rise-Of-The-156-Trillion-Market-For-Global-FinancialAssets/articleshow/32681342.cms [18/09/2015]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Emerging markets’ international debt securities outstanding ($’billion) 2014 - 2015 S/NO

Country

Q4 2014

Q2 2015

1

Mexico

195.4

209.5

2

Brazil

161.5

152.9

3

Russia

113.4

110.1

4

China

77.0

78.6

5

South Africa

29.9

32.9

6

India

27.8

31.2

7

Nigeria

6.4

7.6

Source: Bank for International Settlements. http://www.bis.org/statistics [18/09/2015]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Deposit Interest rates in selected countries (2010 – 2014) S/NO

Country

2010

2011

2012

2013

2014

1

Japan

0.5

0.5

0.5

0.5

0.4

2

Brazil

8.9

11.0

7.9

7.8

10.0

3

Russia

6.0

4.4

5.5

5.6

6.0

4

China

2.8

3.5

3.0

3.0

2.8

5

South Africa

6.5

5.7

5.4

5.2

5.8

6

India

???

???

???

???

???

7

Nigeria

6.5

5.7

8.4

7.9

9.3

Source: data.worldbank.org[18/09/2015]

COM201 Programming 1: September 19, 2015 @ SDMIMD, Mysore, IndiaL01 – Introduction

Selected 10-year Government bond yields [18.09.2015] S/NO

Country

Yield

1

Japan

0.34%

2

Brazil

5.51%

3

Greece

8.10%

4

Mexico

3.55%

5

US

2.16%

6

India

7.71%

7

*Nigeria

14.82%

Source: http://www.bloomberg.com/markets/rates-bonds & http://www.cenbank.org/rates/govtsecurities.asp

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Flight to safety? Most of Nigeria’s US$ 25.4 billion pension funds currently tied to FGN Bonds S/NO

Assets

% of pensions funds invested

1

FGN Bonds

70%

2

Equities

12%

3

Money market

15%

4

Others

3%

Total

100% Source: http://www.punchng.com [18/09/2015]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Introduction to Financial Mathematics: Interest Theory

Course Overview

September – October 2015 @ SDMIMD, Mysore, India

Introduction: Some background information Financial Mathematics (FMT), often variously named as financial engineering, mathematical finance, computational finance, analytical finance, or quantitative finance, is one of the fascinating areas of business management studies. It is a multidisciplinary field that draws tools not only from theoretical mathematics, but also from other disciplines, such as statistics, computer science, finance, and economic theory, to deliver sustainable solutions in the financial services industry. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Financial Mathematics: Interest Theory •

Aim

 The aim of this course is to provide us with further application perspectives in Financial Mathematics with focus on fixed-income instruments in the world of academia, industry and government.

•

An Overview of the Course

 This course focuses on real-world cases in finance, business, and economics, where attempts are made to apply mathematical concepts of interest theory as an important

field of management studies. You will be introduced to key concepts that are applied in calculating present and accumulated values for various streams of cash flows as a basis for use in sound asset/liability management and capital budgeting in modern financial systems.

 We will also revisit in application terms some of the commonly used financial market instruments especially bonds as it relates to the world of finance, business, and economics.

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Key learning objectives  To expand knowledge of diverse application areas of mathematical finance, give a basic understanding of mathematical knowledge of time value of money, compounding and discounting interest techniques, term structure of interest rates, and to get an understanding of key return and risk characteristics of different types of financial assets available for investment and financial management purposes.  To assist in developing further ability to apply a generalized discounted cash flow model as a basis use in effective decision-making, capital budgeting, asset pricing or valuation.  To emphasize imperative of skills in presenting and evaluating basic finance and investment proposals using statistical / computational finance technology products such as MS-Excel and HP12c calculator.

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Linkage with mission statement objectives 

Business leadership:

•

This course gives an overall perspective of applied mathematical / statistical finance and deals with the key dimensions of financial and investment analysis needed for informed decision-making in a competitive environment. Efficient and effective financial management across the whole spectrum of financial markets, money, capital, and derivatives, can help modern organisations to move into a leadership position in their chosen businesses.

•



Organizational excellence:

•

While dealing with financial capital interest and capital budgeting dynamics, course discusses how organizations and investors can be guided to ensure value-added decision making in project / investment portfolio choices. Continuously stressing on fundamental investment parameters, namely, cash flows, risk, return, time value, in turns leads to organizational excellence in an environment of rapid changes and uncertainty.

•

 Value creation: •

•

Course deals with increasing the utility to all the stakeholders through continuous optimal wealthgeneration by learning and applying various quantitative tools and techniques that have significant impact in the emerging financial services industry. Higher utility level automatically leads to highervalue creation for all the stakeholders in the system.

 Dealing with change: •

Course applies mathematics of change for making informed investment decisions and thus exposes and equips students with tools, techniques and frameworks on how to effectively and efficiently measure risk and return in a dynamic financial system. By so doing we can gain further insights into how we can help our organisations to operate sustainably, adapting as necessary, and remaining relevant in today’s fast-pace and increasingly unpredictable business environment.

September – October 2015 @ SDMIMD, Mysore, India

Methodology Each session comprises lectures and problem-solving workshops: –Lectures and classes, 1 hour

–Problem-solving workshops, 30 minutes COM201 September – October 2015 @ SDMIMD, Mysore, India Programming 1: L01 – Introduction

LEARNING AND TEACHING ACTIVITIES • Lectures: Introduce and explain major ideas, concepts or theories and to illustrate their wide-ranging applications. • Interactive lectures: Review materials by encouraging student active participation inviting questions, working through examples, giving short quizzes, discussing case studies, etc. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

LEARNING AND TEACHING ACTIVITIES (cont’d) Classes (smaller-size groups where possible) These encourage to apply the knowledge gained to real or hypothetical cases, and to gain confidence in presenting and defending our own ideas. Classes will usually require us to read some material in advance for discussion, or prepare answers, give some presentations, research a topic, take part in a debate, etc. Active participation will gain you great altitude in your career. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

LEARNING & TEACHING ACTIVITIES (cont’d)  Homework: Homework may be assigned regularly and will usually be discussed in-class. The homework will help us to understand more materials and you will get feedback.  Our suggested solutions should be clear, concise and robust (well-thought / justified). Note the examples in textbooks and the explanations that accompany the calculations.  While we are encouraged to collaborate with our classmates, copying the solution from another student is FORBIDDEN. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Group activities  Projects: We may be given some exercises to accomplish over an extended period of time, say, one month, or even an entire term. This is aimed at:  Helping us to learn together as a team through more problemsolving and skills acquisition.  Providing us a basis for assessing our learning originality, creativity, thoroughness, perseverance, cooperation, and endurance.     

Group projects (when introduced) will follow the following process: Forming the teams and brief project description Progress report Final report Presentation COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Course outline and session plan 1. Overview of interest theory: income, capital, spending, investing; review of the financial system; markets, institutions, and products; further applications of basic mathematics of finance, future and present value, risk and return analysis, annuity, sinking funds, amortization schedules, lease financing and similar financial transactions and economic issues. 2. Further applications of fixed-income mathematics, particularly, principles and problem-solving applications on bond pricing, yields, interest rate parity, covered interest arbitrage. 3. Further cases in capital budgeting, NPV, IRR, DCF methods and common variants. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Scope of the course Time value of money [r, t]

Capital Budgeting Techniques (CBTs)

Creating / Maximizing Value through further applications

Fixed-Income Mathematics (FIMs)

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Sessions plan Sessions

Date

Agenda

1

Saturday, September 19

Course introduction / overview / methodology

2&3

Monday, September 28

Review and further applications of time value concepts

4

Friday, October 16

Review of Fixed-Income Mathematics (FIMs)

5

Monday, October 19

Further applications of FIMs

6

Tuesday, October 20

Review of Capital Budgeting Techniques (CBTs)

7

Wednesday, October 21

Further applications of CBTs

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Course Text & Resources  Financial management: A step- • The Basics of Financial by-step approach by Mathematics. By Bass, R. F. Parasuraman, N. R. (2014). (2003). Department of Delhi: Centage Learning India Mathematics, University of Pvt Ltd. Connecticut. http://homepages.uconn.edu/~rib0  Principles of Corporate 2005/finlmath.pdf Finance (2014) by R. A. Brealey, S.C. Myers, & F. Allen • The Theory of Interest as (11th Edition). Determined by Impatience to Spend Income and Opportunity to  Course Manual on Corporate Invest it by Irving Fisher (1930). Finance (2010) by https://www.unc.edu/~salemi/Eco International Learning Platform n006/Irving_Fisher_Chaper_1.pdf for Investment Professionals (ILPIP). AZEK / ILPIP, Geneva. September – October 2015 @ SDMIMD, Mysore, India

Additional Resources…  How the Bond Market Works by New York Institute of Finance (1988). New Delhi:

 Fundamentals of Financial Derivatives by N. R. Parasuraman, (2014). 3rd Ed. New Delhi: Prentice Hall.  The theory of interest by Irving Wiley India Pvt. Ltd. Fisher (1977). Philadelphia: Porcupine Press. ISBN: 0-87991 Financial Mathematics 864-0 Primary source edition (2014) by Richardson C.  Corporate Finance (Distance Learning Pack) by E. I. John H. & Isaiah, L. M. (2012). Lagos: Accountancy Training and Publication Ltd. September – October 2015 @ SDMIMD, Mysore, India

Further advice…  Spend time to explore and understand worked examples  Practise with clear, concise examples  Continuously improve your problemsolving skills

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

First Steps…  Financial Mathematics (FMT) is a field of management studies that deals with mathematic methods that are mostly used in financial markets, which greatly help to improve the quality of decision-

making in a random and uncertain environment.  FMT is also a professional activity focused on the formulation and study of mathematical models to solve practical business

problems, especially in the financial services industry  FMT thus basically deals with modelling of financial markets and instruments / products.

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Synonyms…  Financial Mathematics  FINANCIAL ENGINEERING  FINANCIAL RISK MANAGEMENT

 QUANTITATIVE FINANCE  MATHEMATICAL FINANCE  COMPUTATIONAL FINANCE QUESTION: What term is common to all the above synonyms? NOTE: Despite its name, Financial Mathematics does not belong to any of the field of traditional mathematics. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Nomenclatures – some perspectives from users FINANCIAL ANALYSIS

FINANCIAL ECONOMICS

FINANCIAL MATHEMATICS

 FA’s assess the viability, stability and profitability of a business or project, usually based on information taken from financial statements.

 FE’s study the structural reasons why a company may have a certain share price.

FMTs are basically modellers – they take the share price as a given and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock market movements.  Quantitative finance applications: - Market movements - Portfolio returns/risk - Optimization - Corporate / capital structuring, etc.

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

“Rate of Interest” revisited…  “Interest” (rate of return on capital) measures the yield

on capital typically over the course of a year expressed as a percentage of the value of capital invested.

 Often denoted, r, ‘interest’ remains a central concept in many economic theories.

[Read Capital in the Twenty-First Century by Thomas Picketty (2014)]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Financial System revisited… Money market vs. Capital market Short-term vs. longterm Debt – Equity – Derivatives Primary market vs. Secondary market

Public vs. Private Retail vs. Institutional markets UBs / CBs / IBs / MFBs / MBs / Discount houses / other specialized financial institutions, customers, investors & market regulators Domestic markets vs. International markets

September – October 2015 @ SDMIMD, Mysore, India

Financial Markets…  Financial market is a market in which people and entities can trade financial securities, commodities, and other fungible items of value at low transaction costs and at prices that reflect supply and demand.  Securities = stocks and bonds

 Commodities = precious metals and agricultural goods  Fungible items = goods of such nature or kind as to be freely exchangeable or replaceable wholly or partly. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Fundamental roles of financial markets 1. The raising of capital (capital markets)

2. The transfer of liquidity (money markets) 3. The transfer of risks (insurance and derivative markets)

4. Price discovery 5. Global transactions with integration of financial markets

6. Facilitating international trade (currency markets)

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Two broad sides of FMT A.DERIVATIVES B.RISK/PORTFOLIO PRICING MANAGEMENT

Sell-side of business

Buy-side of business

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On widely used models in finance  Stochastic calculus – It𝑜 calculus – partial differential equations  Capital Asset Pricing Model  Sharpe model

 Monte Carlo methods  Brownian motion model  Martingale pricing

 Probability theory, time value, DCF, VAR, time series, econometrics, game theory  Black-Scholes model, numerical analysis, object-oriented computer

programming, etc. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Some key issues in Financial Mathematics Understanding how Evaluating portfolio prices are set in financial performance. markets. Valuation – determining Determining prices, ‘expensive’ and ‘cheap’ manage risk, and identify stocks. profitable opportunities. Portfolio risk modelling Finding fair prices for and validation. options and numerous Higher-speed solutions – other derivative algorithmic trading / securities used by statistical arbitrage to investors as risk-hedging achieve ultra low latency. devices. September – October 2015 @ SDMIMD, Mysore, India

A word about Financial Modelling…  Financial modelling involves building an abstract representation (a model) of a real world financial situation.  A financial model is anything (from simple formulae to complex software package) that is used to compute, forecast or estimate financial numbers, or to represent a financial asset / portfolio / project / or any other investment

 Key contribution to management:  Basically, to assist decision-making, planning and control processes.

Limitations:  Watch for unrealistic / unfounded assumptions.  Models may not fully explain or predict behaviour of people.  Model’s complexity may yield error.  Experience, skills, judgment / common sense are often needed to complement mathematical sophistications.

September – October 2015 @ SDMIMD, Mysore, India

FMT – Beyond the transactionary…

Traditional transaction processing work is fast getting automated.

The real deal is in delivering outcomes: i. Increase in revenue ii. Decrease cost

September – October 2015 @ SDMIMD, Mysore, India

On work opportunities 1. Role as Quantitative analysts in public and private organizations 2. Data analysis, structuring and transaction advisory 3. Credit analysis / scoring /provisioning 4. Investment banking/ Corporate finance / trading 5. Asset management / portfolio optimization / trading strategy development 6. Credit cards

7. Risk management 8. Mortgage banks 9. Management Consulting 10. Derivatives pricing and hedging 11. Business/asset valuation 12. Venture capital 13. Foreign exchange services, etc. 14. Operations management 15. Research / academia

September – October 2015 @ SDMIMD, Mysore, India

On work opportunities (continued) • • • • • • • • •

Historical analysis of an organization Projecting an organization’s financial performance Project finance Real estate Oil and Gas projects Banking & Financial Institutions Personal finances Non-profit organizations / NGOs Government – at Federal/central/national, State/Regional, local council • Investment Banking • Academia - research and educational centres

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

FMT as a mandatory activity Anybody dealing with any decision related to money (is there somebody out there who doesn’t that?). If you are involved in financial decision making/ planning related to large corporate, then you would definitely need FMT day in and day out. FMT is a mandatory activity for business / economic managers/planners, bankers, project finance persons, equity researchers, Private Equity, Venture Capital, and the like. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Multiple job options…

Opt for a job with steady income

Join the academia

Become an entrepreneur

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall: Scope of the Course Time value of money [r, t]

Capital Budgeting Techniques (CBTs)

Creating / Maximizing Value through further applications

Fixed-Income Mathematics (FIMs)

September 19, 2015 @ SDMIMD, Mysore, IndiaCOM201 Programming 1:

L01 – Introduction

Key words Basic mathematics of finance, Bonds, Emerging markets, Financial assets, Financial system, Interest rate, Money, Portfolio, Time, Value COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Feedback …

Any Q & A, Comments & Suggestions? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

PROJECT I & Self-study Project I: Groups W, X, Y, & Z to discuss and agree on a specific area of the course that they will like to present an applied problemsolving project.  Deadline: In-class on Monday, September 28

(b) Self-study:

Let us study and familiarize ourselves with current deposit interest rates and bond yields for various tenors in the global financial markets, particularly in emerging markets.

September – October 2015 @ SDMIMD, Mysore, India

Remember …

“Those who serve are typically the winners in the economic sense.” - Thomas J. Stanley

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Introduction to Financial Mathematics: Interest Theory

Session 2 – Review of Time Value of Money Concept Stephen ARO-GORDON, PhD Department of Financial Mathematics Baze University Abuja Nigeria Email: [email protected] / [email protected]

September – October 2015 @ SDMIMD, Mysore, India

Feedback from the previous session…

Any Q, Comments & Suggestions? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recalling PROJECT I & Self-study… Project I: Groups W, X, Y, & Z to discuss and agree on a specific area of the course that they will like to present an applied problemsolving project.  Deadline: In-class on Monday, September 28

(b) Self-study:

Let us study and familiarize ourselves with current deposit interest rates and bond yields for various tenors in the global financial markets, particularly in emerging markets.

September – October 2015 @ SDMIMD, Mysore, India

Multiple job options revisited

Opt for a job with steady income

Join the academia

Become an entrepreneur

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall: Scope of the Course Time value of money [r, t]

Capital Budgeting Techniques (CBTs)

Creating / Maximizing Value through further applications

Fixed-Income Mathematics (FIMs)

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Workshop sessions plan Sessions

Date

Agenda

1

Saturday, September 19

Course introduction / overview / methodology

2&3

Monday, September 28

Review and further applications of time value of money concept

4

Friday, October 16

Review of Fixed-Income Mathematics (FIMs)

5

Monday, October 19

Further applications of FIMs

6

Tuesday, October 20

Review of Capital Budgeting Techniques (CBTs)

7

Wednesday, October 21

Further applications of CBTs

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Session 2 Learning Agenda…

General introduction. Overview of the Time Value of Money Concept (TVM)

September – October 2015 @ SDMIMD, Mysore, India

“Rate of Interest” revisited…  “Interest” (rate of return on capital) measures the

yield on capital typically over the course of a year expressed as a percentage of the value of capital invested.  Often denoted, r, or, i, ‘interest’ remains a central concept in many economic theories. [Read Capital in the Twenty-First Century by Thomas Picketty (2014)] COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

India ….

India’s 7.5% growth rate makes it the fastest growing major economy in the world. September – October 2015 @ SDMIMD, Mysore, India

Deposit Interest rates in selected countries (2010 – 2014) S/NO

Country

2010

2011

2012

2013

2014

1

Japan

0.5

0.5

0.5

0.5

0.4

2

Brazil

8.9

11.0

7.9

7.8

10.0

3

Russia

6.0

4.4

5.5

5.6

6.0

4

China

2.8

3.5

3.0

3.0

2.8

5

South Africa

6.5

5.7

5.4

5.2

5.8

6

India

???

???

???

???

???

7

Nigeria

6.5

5.7

8.4

7.9

9.3

Source: data.worldbank.org[18/09/2015]

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

1-year fixed deposit interest rate in selected Indian Banks S/N O

1 2 3 4

Bank

RBL Bank DCB Bank Pnb Housing Hudco

Compou Quarterl nd y yearly compou nding 8.75% 8.15% 8.25% 9.15%

https://www.bankbazaar.com/fixed-deposit-rate.html [29/09/2015]

COM201 Programming 1: L01 – Introduction September – October 2015 @ SDMIMD, Mysore, India

Introduction to Financial Mathematics: Interest Theory

Session 2 – Review of Time Value of Money Concept

September – October 2015 @ SDMIMD, Mysore, India

Session 2 – Review of Time Value of Money (TVM) Concept TVM provides a basis for comparing the value of cash inflows and cash outflows received and paid at various points of time. This generally covers: Valuation of rights to receive various sums of money at various points of time. Valuation of obligations to pay various sums of money at various points of time. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Common timelines… Yearly Half-yearly Quarterly Monthly Daily

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Scope of TVM Concept

Future Values (FVs) Present Values (PVs) Perpetuity

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

How relevant are these factors in TVM? Inflation? Foreign exchange value of the local currency?

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Under TVM concept… Inflation, and foreign exchange value of the local currency are not usually factored-in. We take interest rate as a ‘given’ in our computations, whether for PV or FV. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Key aspects of TVM concept I.

II. III. IV. V.

FVL – Future Value of a Lump Sum FVA – Future Value of Annuity PVL - Present Value of a Lump Sum PVA – Present value of Annuity Perpetuity. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Note common computational tools

I. Valuation tables. II. HP12c financial calculator. III. MS Excel, etc

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type I) FVL – Future Value of a Lump Sum Illustration 2.1: PV: $1,000 t: 4 years ***(compounding yearly) r: 10% Required: Find the FV of $1,000.

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

FVL – Future Value of a Lump Sum Solution 2.1: PV: $1,000 t: 4 years r: 10% Ans.: FV = $1,464.10

COM201 Programming 1: September –28, October @ SDMIMD, Mysore, India 2015 @2015 SDMIMD, Mysore, IndiaL01 – Introduction

Frequency of Compounding is very key …. Note: If compounding is more frequent than yearly, the final value will be higher. Illustration 2.2: Recall Illustration 2.1: PV: $1,000 t: 4 years ***(compounding monthly) r: 10% Required: Find the FV of $1,000. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

FVL – Future Value of a Lump Sum Solution 2.1: PV: $1,000 t: 4 years (compound monthly) r: 10% Ans.: FV = $1,489.35 (compare with yearly compounding: $1,464.10). Why the difference? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type II) FVA – Future Value of Annuity Future value is the final value of series of payments called annuity Note: Periodicity: Key condition for annuity  Payments and periods must be in sync, that is, uniform. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type II) FVA – Illustration 2.3 PMT: Yearly deposit of $2000 ***(at the end of each year) t: 10 years r: 6% Required: Find the FV of the annuity COM201 Programming 1: September 28, 2015 @ SDMIMD, Mysore, IndiaL01 – Introduction

(Type II) FVA – Solution 2.3 PMT: Yearly deposit of $2000 (end-ofperiod) t: 10 years r: 6% Ans: FV of the annuity = $26,361.59

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Regular Annuity vs. Annuity due The last illustration (2.3) deals with regular annuity (end-of-period).

Illustration 2.4: PMT: Yearly deposit of $2000 ***(at the beginning of each year) t: 10 years r: 6% Required: Find the FV of the annuity COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type II) FVA – Solution 2.4 PMT: Yearly deposit of $2000 (start-ofperiod) t: 10 years r: 6% Ans: FV of the annuity = $27,943.29 (compare: end-of-period: $26,361.59). Again, why the difference? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

TVM technology helps…

On annuity computations, if you are using MS Excel, you have to indicate annuity type. Type 1 is for annuity due (start-of-period). For HP12c, select BEG function. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On time required for money to accumulate… Illustration 2.5 (FV Lump sum case):

Required: How many years will be required for $1000 to become $1500 at 8%? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On time required for money to accumulate… Solution 2.5 Using Excel NPER function, we input the data r: 8% PV: -1000 FV: 1500 Ans.: t = 5.268446 years Note: One of PV and FV must be input in the negative. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Still on time required for money to accumulate…

Illustration 2.6 (FV Annuity case):

Required: How many years will be required for equal annual instalment of $1000 to become $15000 at 6%? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On time required for money to accumulate…

Solution 2.6 (FV annuity case): Also, using Excel NPER function, we input the data r: 6% PMT: -1000 (note here that this is PMT, not PV) FV: 15000 Ans.: t = 11.01 years Note: One of PMT and FV must be input in the negative. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On the implied interest for a given investment Illustration 2.7 (FV Lump sum case):

Required: Find the implied interest rate for an investment of $1000 today that will accumulate to $5000 in 12 years. COM201 Programming 1: September 28, 2015 @ SDMIMD, Mysore, IndiaL01 – Introduction

On the implied interest for a given investment - Solution 2.7

Using Excel RATE function, we input the data as follows: PV: -1000 FV: 5000 NPER: 12 Ans.: r = 0.143529836, i.e. 14.35% Note: Again, one of PV and FV must be input in the negative. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Still on the implied interest for a given investment Illustration 2.8 (FV Annuity case):

Required: Find the implied interest rate for a regular instalment of $2000 for 5 years growing to $15000 at the end of five years, the first instalment being now. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On the implied interest for a given investment Solution 2.8 (FV annuity case): Again, using Excel RATE function, we input the data as follows: NPER: 5 years PMT: -2000 (note here that this is PMT, not PV and a TYPE 1 annuity) FV: 15000 Ans.: r = 0.138348363, i.e. 13.83% Note: One of PMT and FV must be input in the negative. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Note: Compounding Vs. Discounting

Maturity Value vs. Discounted Value Future Value (FV) vs. Present Value (PV)  PV is the inverse of FV COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

‘Present Value’ generally… Present Value is the value today – that is what future receipts mean in terms of today’s money Is that venture worth investing at all? Is that asset, property, stock, or business worth buying-into at all? Is that a good deal? Is that a good price?... COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type III) PVL – Present Value of a Lump Sum

Illustration 2.9: Suppose you have a credible promissory note for $15,000 maturing in 5 years at interest rate of 10%. What is its PV? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type III) PVL – Solution 2.9 FV: $15,000 t: 5 years r: 10%

Ans.: PV = $9,313.82 Q: Why didn’t you consider annuity type in this case? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Designing a special financial package for that wedding - Present Value of a Lump Sum (Continued)…

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type III) PVL – Present Value of a Lump Sum (Continued)

Illustration 2.10: Suppose you want to have $100000 for your sister’s wedding in 3 years. Assuming an interest rate of 10%, how much do you need to invest today to grow to $100000? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type III) PVL – Solution 2.10

FV: $100000 t: 3 years r: 10%

Ans.: PV = $75,131.48 COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Present Value of Annuity

PVA deals with the present value of series of payments over a number of periods in the future. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Present Value of Annuity (Continued)

Illustration 2.11: Recall the last illustration (2.10). Suppose you still want to have $100000 for your sister’s wedding in 3 years. Assuming an interest rate of 10%, how much do you need to invest yearly to grow to $100000? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Solution 2.11 We use PMT function (annuity due type 1) in Excel: FV: -100000 t: 3 years r: 10%

Ans.: PMT = $27,464.98 COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Present Value of Annuity

Illustration 2.12: What is the PV of series of $1000 received at the end of each year for 4 years? Assume 10% interest rate. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Solution 2.12 PMT: $1000 (end-of-period) t: 4 years r: 10%

Ans.: PV = $3,169.87

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Again, consider Regular Annuity vs. Annuity due… The last illustration (2.12) deals with regular annuity (end-of-period).

Illustration 2.13: PMT: Yearly receipts of $1000 ***(at the beginning of each year) t: 4 years r: 10% Required: Find the PV of the annuity. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Considering Regular Annuity vs. Annuity due… Solution 2.13:

PMT: Yearly receipts of $1000 ***(at the beginning of each year) t: 4 years r: 10% Ans.: PV = $3,486.85 (compare: $3,169.87 for end-of-period) COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Present Value of Annuity (Continued)

Illustration 2.14: Your finance house is approached for a loan of $500000 at 12% interest. What is the equated annual instalments over 4 years assuming the first instalment starts one year from now? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Solution 2.14 Here, we still use PMT function (annuity due type 0) in Excel: PV: -500000 t: 4 years r: 12%

Ans.: PMT = $164617.22 COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Further perspectives on periodicity… Note: NPERY means Number of compounding periods per year S/NO

Periodicity

Required adjustments in computation

1

Half-yearly compounding

NPERY: 1 x 2 = 2 Divide nominal interest rate by: 2

2

Quarterly compounding

NPERY: 1 x 4 = 4 Divide nominal interest rate by: 4

3

Monthly compounding

NPERY: 1 x 12 =12 Divide nominal interest rate by: 12

4

Daily compounding

NPERY: 1 x 365 = 365 Divide nominal interest rate by: 365

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Present Value of Annuity – Ascertaining more frequent instalments

Illustration 2.15: A development bank is considering an application for a term loan of $2000000 at 10% interest. What is the equated monthly instalments (EMIs) over 10 years assuming the first instalment starts one year from now? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Solution 2.15 Here, we still use PMT function (annuity due type 0) in Excel: PV: -2000000 t: 10 years r: 10%

Ans.: PMT = $26430.15 COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Equipment Lease Financing - Self-study

What is the difference between ‘Operating Lease’ and ‘Financial Lease’? What do you understand by ‘Residual Value’? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

(Type IV) PVA – Present Value of Annuity – Equipment lease finance application

Illustration 2.16: Z. Leasing Corporation Plc gives an agroprocessing equipment worth $20000 to G. Ltd on a 5-year financial lease. If instalments are to be paid at the end of each year for five years, find the lease rental payable assuming the in-built interest rate is 13%. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On financial lease– Solution 2.16

We use the PMT function: PV: -20000 t: 5 years r: 13% Ans.: $5,686.29 p.a. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Effective interest rate, k… The nominal interest rate is normally taken to be the yearly rate. But what happens if the compounding period is more frequent? That is, what is the effective interest rate in such situations?

𝑘 =

1 +

𝑖 𝑛 𝑛

−1

Where, i is the nominal interest rate n is the number of compounding periods. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On effective interest rate, k…

Illustration 2.17: If nominal interest rate is 12%, what is the effective yield if the compounding period is halfyearly? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

On effective interest rate, k… Solution 2.17: Ans.: If nominal interest rate is 12%, the effective yield if the compounding period is half-yearly is 12.36%. Hint: Use MS Excel ‘EFFECT’ function. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

What happens if you are not given a nominal interest rate?

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Effective yields of T-Bills…

 Effective T-bill yields are not usually quoted in the financial press.  With information on the face value, sale price, and tenure, we can calculate the effective yield, given generally as:

=

𝑨𝒎𝒐𝒖𝒏𝒕 𝒆𝒂𝒓𝒏𝒆𝒅 𝑨𝒎𝒐𝒖𝒏𝒕 𝒊𝒏𝒗𝒆𝒔𝒕𝒆𝒅

× 100 (%)

Effective yield = 400 9600

× 100 (%)

≈ 8.33% (annualized)

ILLUSTRATION: Assume that a Rs10000 par value Tbill was sold for Rs 9600 with a maturity of a half-a-year (or 182 days). Calculate the effective yield. September – October 2015 @ SDMIMD, Mysore, India

Rule of 72 – an intuitive rule To compute the time, t, it will take for an investment to double, we use the Rule of 72 as follows: 𝒕 =

𝟕𝟐 𝒀𝒆𝒂𝒓𝒍𝒚 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒓𝒂𝒕𝒆

To compute the implied interest rate r, it will take for an investment to double, we use the Rule of 72 as follows:  r=

𝟕𝟐 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒚𝒆𝒂𝒓𝒔 𝒕𝒐 𝒅𝒐𝒖𝒃𝒍𝒆

September – October 2015 @ SDMIMD, Mysore, India

(Type V) Perpetuity

Perpetuity refers to the state of continuing for a long time or indefinitely. A key TVM assumption here is that the interest rate will remain constant, but receipt or payment can also show sustainable growth rate. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

TVM on perpetuities Illustration 2.18 (Constant growth assumption):

Suppose you inherit a real estate portfolio generating $1000 fixed yearly income in perpetuity. If the interest rate is 10%, what is the present value of the inheritance? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

TVM on perpetuities Solution 2.18: Recall: PMT: $1000 (fixed) R = 10% PV in perp. is given by 𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑓𝑙𝑜𝑤 𝑃𝑉 𝑖𝑛 𝑝𝑒𝑟𝑝 = 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 Ans.:Simply $10000! COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Determining growth rate, g...

Recall that a key TVM assumption is that the interest rate will remain constant, but receipt or payment can also show sustainable growth rate.  So, how do we obtain a g in some situations such as when we need to estimate stocks, property prices, and GDP growth rates. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Determining growth rate, g...  Illustration 2.19: Assume the following historical pattern of residential rental values. S/ NO

Year

Rent per annum

1

2006

$10,000

2

2007

$15,000

3

2008

$20,000

4

2009

$21,500

5

2010

$25,000

Required: Determine the annual rental growth rate over the period. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Determining growth rate, g...  Solution 2.19:  The growth rate, g, is given by 𝑔 =

𝑛 − 1√

𝐿𝑎𝑡𝑒𝑠𝑡 𝑟𝑒𝑛𝑡𝑎𝑙 𝐸𝑎𝑟𝑙𝑖𝑒𝑠𝑡 𝑟𝑒𝑛𝑡𝑎𝑙

-1

Where n refers to the number of periods. Hence, we obtain 𝑔 =

4√

25000 10000

- 1 = 1.2574 – 1= 0.2574.

Ans.: The growth rate is 25.74% COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Growing perpetuity  A growing perpetuity refers to a perpetuity that keeps increasing at a constant rate period indefinitely.  The value of a growing perpetuity is given by 𝐹1 𝑃𝑉 𝑖𝑛 𝑝𝑒𝑟𝑝 = (𝑟 − 𝑔) Where, F1 refers to the cash flow one year from now r is the discount rate g is the constant sustainable growth rate. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Growing perpetuity (continued) Illustration 2.20: Suppose the real estate inheritance mentioned earlier (illustration 2.18) generating $1000 income in perpetuity with a 2% growth rate and the applicable discount rate is 8%. What is the present value of the inheritance?

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Growing perpetuity (continued) Solution 2.20: Given F1 = 1000 r = 8% g = 2% The value of the perpetuity is given by 𝑃𝑉 𝑖𝑛 𝑝𝑒𝑟𝑝 =

1000 (0.08 − 0.02)

= 1000/0.06

Ans.: $16666.67 COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Key words Annuity, Annuity due, Cash flow, Compounding, Discounting, Effective yield, Financial Lease, Future Value, Growth rate, Interest rate, Loan amortization schedule, Money, Nominal yield, Operating Lease, Perpetuity, Present Value, Residual value, Time, Periodicity, Perpetuity, Regular annuity, Sinking fund. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Feedback …

Any Q & A, Comments & Suggestions? COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Session 3 Learning Agenda…

Further Applications of the Time Value of Money Concept

September – October 2015 @ SDMIMD, Mysore, India

Recall some basic TVM formulae S/NO

TYPE

1

Future Value of a Lump Sum (FVL)

2

Future Value of Annuity(FVA)

3

Present Value of a Lump Sum (PVL)

4

Present Value of Annuity (PVA)

5

Present Value of Perpetuity (constant rate)

6

Growth rate (g)

7

Growing Perpetuity

8

Effective yield (k)

9

Present Value of Annuity (PVA) – Annuity due

FORMULA

(𝟏 + 𝒓)𝒕 (𝟏 + 𝒓)𝒕 − 𝟏 𝒓 𝟏 (𝟏 + 𝒓)𝒕 𝟏 −

𝒈 =

𝒏 − 𝟏√

𝟏 (𝟏 + 𝒓)𝒕 𝒓 𝑪𝑭 𝒓

𝑳𝒂𝒕𝒆𝒔𝒕 𝒗𝒂𝒍𝒖𝒆

-1

𝑬𝒂𝒓𝒍𝒊𝒆𝒔𝒕 𝒗𝒂𝒍𝒖𝒆

𝑷𝑽 𝒊𝒏 𝒑𝒆𝒓𝒑 =

𝒌 =

𝟏 −

𝑪𝑭𝟏 (𝒓 − 𝒈)

𝒊 𝟏 + 𝒏

𝒏

−𝟏

𝟏 (𝟏 + 𝒓)𝒕 −𝟏 𝒓

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall useful MS Excel functions…

FV PV NPER RATE PMT EFFECT… September – October 2015 @ SDMIMD, Mysore, India

CAUTION…  Remember Garbage in, garbage out (GIGO)? That common computer science and mathematics a concept: the quality of output is determined by the quality of the input. [see Goldstein, S. (April 16, 2013). "The spreadsheet error in Reinhart and Rogoff’s famous paper on debt sustainability“]  Guide against unintended, nonsensical, input data ("garbage in"), otherwise the software will yield undesired, often unreasonable, output ("garbage out").  Always double-check to confirm that the output makes sense in the context of the theory and the sought-after solution. September – October 2015 @ SDMIMD, Mysore, India

True or False? 1. The higher the interest rate, the lower the PV 2. ‘Annuity due’ means that a required payment will be made at the end of the contract period. 3. FV will increase if the number of compounding periods goes up. 4. PV will increase if the number of compounding periods comes down. 5. FV of an annuity due is higher than FV of a regular annuity. 6. If compounding is done quarterly, we will get less at the end on a deposit than if compounding is done annually. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Exercises / problems/ cases… 1. Although your client has made up her mind to set up her own business as soon as practicable, she is not yet sure about the nature the business should take and when exactly it is going to take-off. Moreover, from a similar business plan that she has just studied, she feels that she will probably need up to $1.5 million to meaningfully start the enterprise. In the meantime, she has decided to invest her $500,000 share of a family estate in 5-year fixed deposit with an interest rate of 15% payable annually and at the end of each period. Required: i. Determine the FV of your client’s deposit. Is the estimated FV adequate for the anticipated initial capital of the planned enterprise? ii. If not, what extra sum is needed to be invested now in order to meet up with the minimum take-off capitalization in five years?

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Exercises / problems/ cases… 2. Advise your client who is looking for the maximum maturity value from one of these four options: (a) A 3-year $50000 annuity at 15% interest rate. (b) A 3-year $60000 annuity at 14% interest rate. (c) A 3-year $45000 fixed deposit at 25% interest rate compounding monthly. (d) A 3-year $50000 fixed deposit at 20% interest rate payable at the end of each year. 3. K. Ltd has just purchased a machine at a cost of $10 million. The effective life of the machine is estimated to be 8 years. A sinking fund account is to be created for replacing the machine by a new model at the end of its life span when its scrap realizes nil dollar. Machine price is assumed to increase in line with inflation rate currently 14%. Required: How much should K. Ltd set aside every year out of profit into the sinking fund account if the account pays interest at 15% per annum. COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Exercises / problems/ cases… 4. You are the credit analyst for B Bank Ltd. You want to meet your portfolio target, hence you are considering granting a term loan of $1500000 to Kumar Group for a 5-year tenor at 22% interest rate per annum. The collateral property being offered for this loan is a registered title over a landed property worth $50000 per annum in perpetuity. Local brokers say that the rental values for similar properties in the neighbourhood have been growing at 3% on the average over the past 10 years. Required: i. What is the amount of the loan repayment if the facility is to be repaid by equal annual payment at the end of each of the next 5 years? ii. Determine the present value of the collateral property using a discount rate of 12% under the scenarios of (a) constant perpetuity and (b) growing perpetuity. iii. Advise the prospect on the adequacy of the security, bearing in mind your bank’s minimum LTV (Loan-to-Value) requirement of 70% and using the higher-number of the valuations yielded from the scenarios in (ii). COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Exercises / problems/ cases… 5. The management of K. Equipment Leasing Company Ltd is getting concerned about cost of funding its operations. Currently, the company books an average of 200 financial leases to its customers across various sectors and geographies globally. Its standard lease is for $1500000 for a 5-year tenor at in-built interest rate of 22% per annum. As a cost-saving measure, the CFO advised in a recent management retreat that the company’s annuity policy should be changed from ‘regular’ mode to ‘annuity due’. His advice was based on her estimates of the financial implications if rentals continue to be paid at the end of each period compared to when mad payable at the beginning. Some of the business development managers in the company believe that, given the strategic relationship the company currently has with 25% of the lessees, the contemplated ‘change’ cannot be implemented without resistance by its long-established customers. The board of the company is meeting soon to take a final stand on this, and the Chairman wants your advice. Required: How much more revenue realistically do you think the company can make by changing its annuity policy on leases?

COM201 Programming 1: September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Exercises / problems/ cases… 6. In each of the cases (i) and (ii) below, determine exactly how long it will take for the indicated investment to grow to $150000. i. $80000 investment earning interest at 9% per year compounding annually. ii. $80000 investment earning interest at 9% per year compounding biannually. 7. For cases (i) and (ii) below, determine at what interest rate the indicated investment must be made. i. If $300000 is to grow to %750000 over 10-year period, given that interest is compounded annually. ii. If $300000 is to grow to %750000 over 10-year period, given that interest is compounded semi-annually.

COM201 September – October 2015 @ SDMIMD, Mysore, India Programming 1: L01 – Introduction

Exercises / problems/ cases… 8. G. Corporation Ltd wants to establish a sinking fund beginning at the end of this year. Annual deposits will be made at the end of this year and for the following 9 (nine) years. Deposits earn interest at the rate of 8% per annum compounded annually. Required: Determine the amount of money that must be deposited each year in order to have $12000000 at the time of the 10th deposit.

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

An African Case (1) •

While briefing the House of Representatives on the 2013-2015 Medium Term Expenditure Framework and Fiscal Strategy (MTEFF) some years ago, Nigeria’s Director-General of Debt Management Office (DMO), put Nigeria’s total debt profile at $45 billion. He said: “For 2012, Nigeria’s external debt is projected at $9,021.53 million; 2013, $12,165.10 million; 2014, $14,585 million and 2015, $16,765 million,” adding that “a breakdown for domestic debt is projected at 2012 - $6,483.81 million; 2013 - $7,125.93 million; 2014 - $7,792.41 million and 2015 $8,444.86 million.” [www.ngrguardiannews.com - October 26, 2012].

• Required: •

(a) Estimate the annual growth rate of the country’s external debt stock under the MTEFF.

•

(b) Which of the two components of the country’s debt stock is likely to grow faster? Explain.

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

African Case (2) • A former Nigerian President once considered making an annual provision of N100 billion in sinking funds towards offsetting the country’s debt obligations over the next 8 years. If the sinking fund account attracts an interest income at the rate of 12.5 per cent per annum, what could have been the country’s total debt stock?

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Feedback from the previous session…

Any Q, Comments & Suggestions? COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Cases…

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Exercises / problems/ cases… 1.

Although your client has made up her mind to set up her own business as soon as practicable, she is not yet sure about the nature the business should take and when exactly it is going to take-off. Moreover, from a similar business plan that she has just studied, she feels that she will probably need up to $1.5 million to meaningfully start the enterprise. In the meantime, she has decided to invest her $500,000 share of a family estate in 5-year fixed deposit with an interest rate of 15% payable annually and at the end of each period. Required: i. Determine the FV of your client’s deposit. Is the estimated FV adequate for the anticipated initial capital of the planned enterprise? ii. If not, what extra sum is needed to be invested now in order to meet up with the minimum take-off capitalization in five years?

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Exercises / problems/ cases… 2. Advise your client who is looking for the maximum maturity value from one of these four options: (a) A 3-year $50000 annuity at 15% interest rate. (b) A 3-year $60000 annuity at 14% interest rate. (c) A 3-year $45000 fixed deposit at 25% interest rate compounding monthly. (d) A 3-year $50000 fixed deposit at 20% interest rate payable at the end of each year. 3. K. Ltd has just purchased a machine at a cost of $10 million. The effective life of the machine is estimated to be 8 years. A sinking fund account is to be created for replacing the machine by a new model at the end of its life span when its scrap realizes nil dollar. Machine price is assumed to increase in line with inflation rate currently 14%. Required: How much should K. Ltd set aside every year out of profit into the sinking fund account if the account pays interest at 15% per annum.

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Exercises / problems/ cases… 4. You are the credit analyst for B Bank Ltd. You want to meet your portfolio target, hence you are considering granting a term loan of $1500000 to Kumar Group for a 5year tenor at 22% interest rate per annum. The collateral property being offered for this loan is a registered title over a landed property worth $50000 per annum in perpetuity. Local brokers say that the rental values for similar properties in the neighbourhood have been growing at 3% on the average over the past 10 years. Required: i.

What is the amount of the loan repayment if the facility is to be repaid by equal annual payment at the end of each of the next 5 years?

ii.

Determine the present value of the collateral property using a discount rate of 12% under the scenarios of (a) constant perpetuity and (b) growing perpetuity.

iii.

Advise the prospect on the adequacy of the security, bearing in mind your bank’s minimum LTV (Loan-to-Value) requirement of 70% and using the highernumber of the valuations yielded from the scenarios in (ii).

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Exercises / problems/ cases… 5. The management of K. Equipment Leasing Company Ltd is getting concerned about cost of funding its operations. Currently, the company books an average of 200 financial leases to its customers across various sectors and geographies globally. Its standard lease is for $1500000 for a 5-year tenor at in-built interest rate of 22% per annum. As a cost-saving measure, the CFO advised in a recent management retreat that the company’s annuity policy should be changed from ‘regular’ mode to ‘annuity due’. His advice was based on her estimates of the financial implications if rentals continue to be paid at the end of each period compared to when mad payable at the beginning. Some of the business development managers in the company believe that, given the strategic relationship the company currently has with 25% of the lessees, the contemplated ‘change’ cannot be implemented without resistance by its long-established customers. The board of the company is meeting soon to take a final stand on this, and the Chairman wants your advice. Required: How much more revenue realistically do you think the company can make by changing its annuity policy on leases? COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Exercises / problems/ cases… 6. In each of the cases (i) and (ii) below, determine exactly how long it will take for the indicated investment to grow to $150000. i. $80000 investment earning interest at 9% per year compounding annually. ii. $80000 investment earning interest at 9% per year compounding biannually. 7. For cases (i) and (ii) below, determine at what interest rate the indicated investment must be made. i. If $300000 is to grow to %750000 over 10-year period, given that interest is compounded annually. ii. If $300000 is to grow to %750000 over 10-year period, given that interest is compounded semi-annually.

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Exercises / problems/ cases… 8. G. Corporation Ltd wants to establish a sinking fund beginning at the end of this year. Annual deposits will be made at the end of this year and for the following 9 (nine) years. Deposits earn interest at the rate of 8% per annum compounded annually. Required: Determine the amount of money that must be deposited each year in order to have $12000000 at the time of the 10th deposit.

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Exercises / problems/ cases…  While briefing the House of Representatives on the 2013-2015 Medium Term Expenditure Framework and Fiscal Strategy (MTEFF) some years ago, Nigeria’s Director-General of Debt Management Office (DMO), put Nigeria’s total debt profile at $45 billion. He said: “For 2012, Nigeria’s external debt is projected at $9,021.53 million; 2013, $12,165.10 million; 2014, $14,585 million and 2015, $16,765 million,” adding that “a breakdown for domestic debt is projected at 2012 - $6,483.81 million; 2013 - $7,125.93 million; 2014 - $7,792.41 million and 2015 - $8,444.86 million.” [www.ngrguardiannews.com - October 26, 2012].

• Required: • (a) Estimate the annual growth rate of the country’s external debt stock under the MTEFF. • (b) Which of the two components of the country’s debt stock is likely to grow faster? Explain. COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall TVM Exercises / problems/ cases…

• A former Nigerian President once considered making an annual provision of N100 billion in sinking funds towards offsetting the country’s debt obligations over the next 8 years. If the sinking fund account attracts an interest income at the rate of 12.5 per cent per annum, what could have been the country’s total debt stock? COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Sessions update Sessions

Date

Agenda



Saturday, September 19

Course introduction / overview / methodology



Monday, September 28

Review and further applications of time value of money concept

4&5

Monday, October 19

(i) Introduction to FixedIncome Mathematics (FIMs) (ii) Bond Valuations – Selected Cases and Problems

6

Tuesday, October 20

Review of Capital Budgeting Techniques (CBTs)

7

Wednesday, October 21

Further applications of CBTs COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Recall: Basic portfolio types…

Money market instruments

Fixedincome securities

Stocks and shares

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Session 4 Introduction to Fixed-income Securities (Bonds)

September – October 2015 @ SDMIMD, Mysore, India

Session 4: Introduction to Fixed-income Securities (Bonds)

1. Overview of bond markets and general concepts. 2. Review some key terminologies, such as YTM, YTC, YTP, YTW, current yield, yield curve, etc. 3. Recent developments the global bond markets, with emphasis on the emerging markets. 4. Introduction to bond valuation approaches. September – October 2015 @ SDMIMD, Mysore, India

Fixed-Income Securities Vs. Common stocks

September – October 2015 @ SDMIMD, Mysore, India

Fixed-Income Securities Vs. Common stocks

The returns from bonds are fairly assured and do not depend upon the performance of the company as you will expect in the case of common stocks or equities. In the case of equity, if profits are inadequate, bonds must be serviced first ahead of the equity-holders. September – October 2015 @ SDMIMD, Mysore, India

Fixed-Income Securities Vs. Common stocks…  A fixed-income security is an investment that pays regular income in the form of a coupon payment, interest payment or preferred dividend.  Unlike a variable-income security, the payments of a fixed-income security are known in advance.  Fixed-income securities can be contrasted with equity securities, (stocks and shares) that create no obligation to pay dividends or any other form of income.  If an issuer fixed-income security misses a payment on a fixed income security, the issuer is in default, and depending on the relevant law and the structure of the security, the payees may be able to force the issuer into bankruptcy – i.e. judged legally to be unable to pay off personal debts.

September – October 2015 @ SDMIMD, Mysore, India

Irving Fisher [Feb 27, 1867 – April 29, 1947]

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Still on Interest Rate Interest rate (APR – Annual Percentage Rate) is a charge for the use of capital. Interest rate, denoted, r, is the price paid for borrowed funds. Borrower vs. Lender Recall interest rate implications for low-risk and high-risk investments.

September – October 2015 @ SDMIMD, Mysore, India

Interest rate dynamics Motivating – savings and wealth accumulation Rationing – project selection Law of diminishing returns Competition – financial innovation, technology, etc. September – October 2015 @ SDMIMD, Mysore, India

Fisher Equation The Fisher equation in Financial Mathematics and Economics estimates the relationship between nominal and real interest rates relative to inflation. The Fisher equation is given as

𝒓 = 𝒊 − 𝝅 Where, r denotes the real interest rate i denotes the nominal interest rate π denotes the inflation rate. September – October 2015 @ SDMIMD, Mysore, India

Inflation and Interest rate Generally, when commodity prices are perceived to rise, lenders require higher rates of interest to protect depreciating purchasing power of debts payments, borrowers are willing to repay in cheaper currency at higher nominal rates. September – October 2015 @ SDMIMD, Mysore, India

Utility of the Fisher Equation… The Fisher equation has a wide range of usage, namely: i. Calculations of YTM of bonds. ii. Trading of inflation-indexed bonds. iii. IRR calculations of investments. iv. Cost-benefit analysis of projects. v. Predicting predict nominal and real interest rate behaviour. vi. Describing real purchasing power of a loan September – October 2015 @ SDMIMD, Mysore, India

What’s ‘bond’ all about?

September – October 2015 @ SDMIMD, Mysore, India

What is a bond?  A bond is a long-term debt security; it is a debt because the bond buyer (investor) actually lends the face amount to the bond issuer (borrower) and it is a security because it can be bought and sold in the open market.  Thus, in finance, bond is a certificate issued by a government or company promising to pay back borrowed money at a fixed rate of interest (coupon) on a specified date.  The bond certificate evidences the lender-creditor relationship.

September – October 2015 @ SDMIMD, Mysore, India

Bond as ‘long-term’…  Bonds are for the long-term (>5 years) by definition…(NYIF, 1997).  Fixed-income securities with maturities < 5 years are usually called bills, notes or other terms…  Underlying master loan/bond agreement will normally contain such basic information as:  Amount of the loan – face amount  Rate of interest – coupon/nominal rate  Schedule/form of interest payments – usually half-yearly  Term/tenor/maturity date.  Other features – callable, convertible, etc.

September – October 2015 @ SDMIMD, Mysore, India

Typical bond investors…

September – October 2015 @ SDMIMD, Mysore, India

Bond market participants  Investors in fixed-income securities are typically looking for a constant and secure return on their investment.  Typical examples are retirees who desire regular dependable payments to live on like gratuity, but not consume principal. They can buy a bond with their money, and use the coupon payment (the interest) as that regular dependable payment  The major investors in fixed-income securities are: (i) institutional investors  pension plans  mutual funds  insurance companies, etc. (ii) Governments (iii) Traders (iv) Individuals September – October 2015 @ SDMIMD, Mysore, India

Typical clientele of bond analysts (www.BondsOnline.com)

Public accounting and research firms Government entities Banks and thrifts Investment advisors Insurance companies Corporations Universities and other non-profit entities Individual investors September – October 2015 @ SDMIMD, Mysore, India

Market Regulators…

September – October 2015 @ SDMIMD, Mysore, India

Global bond market size

September – October 2015 @ SDMIMD, Mysore, India

Global bond market size US$ 100 trillion as of March 2012 (compare with global equity market of about US$53 trillion), up from US$82.2 trillion in 2009. 140% of global GDP, up from 119% in 2008; global bond market growth largely driven by increase in issuance by governments to meet socio-economic interventions. Government bonds are often used to compare other bonds to measure credit risk. 70% Domestic bonds; 30% International bonds. Major players: US 33%, followed by Japan 14%.

September – October 2015 @ SDMIMD, Mysore, India

Fixed-income instruments Common types Government bonds Municipal bonds – revenue bonds, industrial development bonds. Corporate bonds – callable, convertible Mortgage bonds

Indexed bonds Certificate of Deposit Commercial Papers Mortgage-Backed Securities Exchange Traded Funds (ETFs) Junk bonds

September – October 2015 @ SDMIMD, Mysore, India

Typical Bond asset classes (www.BondsOnline.com): •

• •

• • •

•

U.S. corporate and government bonds, including investment grade and high-yield bonds and preferred stocks, fixed and floating rate securities, stripped coupon and principal issues; U.S. money market instruments; U.S municipal bonds including taxable and tax-exempt and investment grade and high yield; U.S. convertible securities; U.S commercial mortgage-backed securities (CMBS); U.S collateralized mortgage obligations – agency/government sponsored enterprise (GSE) and nonagency; U.S. asset-backed securities (ABS);

• U.S agency/GSE pass-through securities, including FNMA, FHLMC, GNMA, and SBA securities; • Emerging market debt; • U.S. whole loan residential mortgages; • International corporate and sovereign issues; • International convertible securities; • European money market instruments. • European ABS and MBS.

September – October 2015 @ SDMIMD, Mysore, India

“Junk” bonds  Junk bond is a bond that is rated below investment grade (bonds rated BBB− and higher are called investment grade). Thus, these bonds have a higher default-risk, but typically pay higher yields than better quality bonds in order to make them attractive to investors.  Greece: On 27 April 2010, the Greek debt rating was decreased to "junk" status by Standard & Poor’s (S&P’s) amidst fears of default by the Greek Government.  Portugal: On 5 July 2011, Portugal's rating was decreased to "junk" status by Moody’s (by four notches from Baa1 to Ba2) (www.wikipedia.com).

September – October 2015 @ SDMIMD, Mysore, India

Credit Rating Agencies  A credit rating agency describes the risk of an investment vehicle like bond with a credit rating.  In North America, the five major agencies for long-term debt instruments are Standard and Poor's, Moody's, Fitch Ratings, Dominion Bond Rating Service, and A.M. Best.  Additionally, we have CRISIL in India and AGUSTO & COMPANY in Nigeria.

 Rating scales vary; the most popular scale uses (in order of increasing risk) ratings of AAA, AA, A, BBB, BB, B, CCC, CC, C. Bonds rated BBB− and higher are called investment grade, while bonds rated lower than investment grade on their date of issue are called speculative grade bonds, or colloquially as "junk" bonds.  The lower-rated bond usually offers a higher yield, an attraction to certain types of portfolios and investment strategies. September – October 2015 @ SDMIMD, Mysore, India

Credit Rating Agencies… Visit the following websites for useful information on rating activities and practices:

www.bondsonline.com www.stern.nyuedu/adamodar/pc/rati ngs.xls September – October 2015 @ SDMIMD, Mysore, India

Recall useful MS Excel functions… FV PV NPER RATE PMT EFFECT PRICE YIELD… September – October 2015 @ SDMIMD, Mysore, India

Debenture bonds  Debenture bonds are usually unsecured bonds.  A debenture bond is backed only by the credit standing of the issuer, and is sometimes convertible into stock. September – October 2015 @ SDMIMD, Mysore, India

Bond Pricing – PV approach (i)

Irredeemable bonds:

𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑎𝑡 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑖𝑒𝑙𝑑 = 𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 (ii) Redeemable bonds: 𝟏 −

= PMT (

𝟏 (𝟏 + 𝒓)𝒕

𝒓

) + Pp

1 ( ) (1 + 𝑟)𝑡

Where, PMT is the coupon payments (annually or semi-annually) r is the yield t is the number of period the coupon is paid Pp is the Par Value (i.e. the bond’s Face Value or value at maturity). September – October 2015 @ SDMIMD, Mysore, India

Some important notes on bond pricing…  Basically, the price or value of a bond is simply the PV of the expected cash flows from the investment, hence the utility of the PVA and PV mathematical methods.  Once we know (i) the coupon rate, (ii) the maturity value, and (iii) the marketrequired yield for a bond, bond valuation is relatively easy to perform. September – October 2015 @ SDMIMD, Mysore, India

Coupon Coupon is a certificate of interest on bond, taken to be a detachable / transferable part of a bond that shows a date and the amount of interest paid on that date. The holder must present it in order to receive payment of the interest.  The coupon rate or nominal yield, i, is simply the coupon payment, PMT, as a percentage of the bond’s face value, F, that is: 𝑃𝑀𝑇 𝑖 = ∗ 100 𝐹 September – October 2015 @ SDMIMD, Mysore, India

What is ‘current yield’?

September – October 2015 @ SDMIMD, Mysore, India

Bond’s current yield A bond’s current yield, r, refers to the coupon payment (PMT) as a percentage of current market price, (P) as opposed to its face value, F. This is given as:

r=

𝑃𝑀𝑇 𝑃

∗ 100

September – October 2015 @ SDMIMD, Mysore, India

Bond Yield…  Bond yield is the internal rate of return (IRR) of bonds of a particular level of risk.  The IRR of an investment is the discount rate at which the NPV of costs (negative cash flows) of the investment equals the NPV of the benefits (positive cash flows) of the investment, that is, the rate at which an investment breaks even.  Thus, two bonds that have identical levels of perceived risk should have the same yield (or overall interest rate) even where the coupons, initial payment and final payment differ.

September – October 2015 @ SDMIMD, Mysore, India

Yield to Maturity (YTM)… perhaps the single most important bond measure.  Yield to Maturity is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the price of the bond.  Thus, YTM (or “book yield” or ”redemption yield”) of a bond or other fixed-interest security such as gilts, is the IRR earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.  It is also called “promised yield” because it encompasses all the cash flow benefits (or losses) that would accrue to the investor over the life of the bond. September – October 2015 @ SDMIMD, Mysore, India

Still on YTM… YTM is generally what bond traders refer to when they use the word “yield”, because, of the three bond “yields” (i.e., coupon yield, current yield, YTM), YTM is the one type of yield that evaluates the effect of principal coupon rate and time to maturity on a bond’s actual yield. Note: YTM does not determine bond price. September – October 2015 @ SDMIMD, Mysore, India

Computing YTM…  Approximate YTM can be computed thus: =

𝐶𝑜𝑢𝑝𝑜𝑛 𝑎𝑚𝑜𝑢𝑛𝑡 + 𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑙𝑖𝑛𝑒 𝑎𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛 𝑜𝑟 𝑙𝑜𝑠𝑠 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

𝑷𝒑 − 𝑷𝒎 𝑪𝒊 + 𝒏 = 𝑷𝒑 + 𝑷𝒎 𝟐

Where, Ci refers to annual coupon value of the investment Pp refers to the par value of the bond Pm refers to the current market price of the bond n refers to the number of years to maturity September – October 2015 @ SDMIMD, Mysore, India

What are the key assumptions underlying standard yield measures?

? September – October 2015 @ SDMIMD, Mysore, India

Key assumptions underlying standard yield measures/quotations? 1. The bond will be held to maturity. 2. All coupon and principal payments will be made on schedule – no default. 3. All the coupons are reinvested at an interest rate equal to the yield-to-maturity. 4. No allowance is made for tax paid by the investor on the return, and is then known as "gross redemption yield". 5. No allowance is made for the dealing costs incurred by the purchaser (or seller). September – October 2015 @ SDMIMD, Mysore, India

MS Excel Technology Help for Bond Yield Measures – Yield Function 1.Dates: should be entered by using the DATE function, e.g. use DATE(2015,5,23) for the 23rd day of May, 2015. Problems can occur if dates are entered as text. 2.

Settlement: The settlement date is the date a buyer purchases a coupon/bond, often the date after the issue date when the security is traded to the buyer. For example, suppose a 30-year bond is issued on January 1, 2008, and is purchased by a buyer six months later. The issue date would be January 1, 2008, the settlement date would be July 1, 2008, and the maturity date would be January 1, 2038, which is 30 years after the January 1, 2008, issue date.

3.Maturity: The maturity date is the date when the security expires.

Rate: The security's annual coupon rate. 5. Pr: The security's price per $100 face value. 6. Redemption: The security's redemption value per $100 face value. 7. Frequency: The number of coupon payments per year. For annual payments, frequency = 1; for semiannual, frequency = 2; for quarterly, frequency = 4. 4.

September – October 2015 @ SDMIMD, Mysore, India

Further Notes  Microsoft Excel stores dates as sequential serial numbers so they can be used in calculations.  By default, January 1, 1900 is serial number 1, and January 1, 2008 is serial number 39448 because it is 39,448 days after January 1, 1900.  Using MS Excel, we can also find YTM by using the IRR or RATE functions September – October 2015 @ SDMIMD, Mysore, India

Bond Variants and YTM implications 1. Discount Bond: This refers to a bond whose coupon rate is less than its YTM. 2. Premium Bond: This refers to a bond whose coupon rate is more than its YTM. 3. Par Bond: This refers to a bond whose coupon rate is equal to its YTM.

1. When a bond sells at a discount: YTM > r > i 2. When a bond sells at a premium: i > r > YTM 3. When a bond sells at a par: YTM = r = i Where, i is coupon yield r is the current yield YTM is the IRR of the bond

September – October 2015 @ SDMIMD, Mysore, India

Accounting for discount or premium…

Subject to the applicable accounting rules in treatment of liabilities, bond discount or premium is usually amortized over the bond life. Use the applicable TVM formula or MS Excel PMT function. September – October 2015 @ SDMIMD, Mysore, India

What is straight Bond?

September – October 2015 @ SDMIMD, Mysore, India

Zero-Coupon Bond…  A zero-coupon bond (also discount bond or deep discount bond) is purchased at a price lower than its F, with the F repaid at the date of maturity; the bond does not make periodic interest payments, or coupons, hence the term zero-coupon bond.  When the bond reaches maturity, its investor simply receives its par value – “simple maturity”.  In essence, any type of coupon bond that has been stripped of its coupons is zero-coupon bond.

September – October 2015 @ SDMIMD, Mysore, India

YTM Variants 1. Yield to call (YTC): when a bond is callable, that is, it can be repurchased by the issuer before the maturity, so the cash flow is shortened compared to the standard YTM. 2. Yield to put (YTP): same as YTC, except that the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date. 3. Yield to worst (YTW): when a bond is callable, puttable, exchangeable, or has other features, the YTW is the lowest yield of YTM, YTC, YTP, among others.

September – October 2015 @ SDMIMD, Mysore, India

What are the basic features of government bonds?

September – October 2015 @ SDMIMD, Mysore, India

Basic features of government bonds… i. Issued at face value (par value). ii. No default risk as the bonds carry sovereign guarantee iii. Ample liquidity as the investor can sell the security in the secondary market. iv. Coupon payment usually paid half-yearly based on the face value of the bond. v. No tax deducted at source (Note exceptions in some jurisdictions). September – October 2015 @ SDMIMD, Mysore, India

How risky are bonds?  Fixed-income securities yield a steady rate of return, but they also have risk.  Bonds have price risk – their values have inverse relationship with the market yield. September – October 2015 @ SDMIMD, Mysore, India

Bond risks • • • • • •

Inflation risk Interest rate risk Currency risk Default risk Reinvestment risk Liquidity risk

• Convexity risk • Credit quality risk • Political risk • Market risk

September – October 2015 @ SDMIMD, Mysore, India

How to manage Bond risks…

October 19, 2015 @ SDMIMD, Mysore, India

Managing bond risks…  Indexed bonds – pricing bonds relative to a benchmark, usually a government security, inflation, etc.  Credit Rating – assessment of country risk, etc.  Credit spread – better-quality bonds have smaller spread between its required return and the benchmark’s YTM.  The required/adjusted return is then applied in discounting the bond cash flows to obtain the bond price.  The foregoing is referred to as the Relative Pricing Approach.

September – October 2015 @ SDMIMD, Mysore, India

Bond price sensitivity to interest rate (i.e. yield)  Linearity and convexity nature: The sensitivity of a bond’s market price to yield movements is measured by its duration and convexity.  Linearity/duration - %change in price for a given %change in yield or elasticity of the bond’s price w.r.t. discount rates.  But price is not a linear, but rather a convex function of the discount rate, hence the idea of convexity to measure the “curvature” of bond price changes.  There are other price sensitivity measures that form part of the everyday language and thinking of fixed-income investors and investment professionals.  Interested students should consult the details in the notes in http://faculty.darden.virginia.edu/conroyb/valuation/val2002/f-1238.pdf

September – October 2015 @ SDMIMD, Mysore, India

Utility of Convexity measures in bond investing… The pricing aspect of Convexity is much less important now since many people now have access to calculators and computers that can do the pricing.  The more important use of convexity is that it provides insight into how a bond will react to yield changes.

 Empirically, bond price reaction to changes in yield is not symmetric.  For a given change in yield, bond prices drop less for a given increase in yield and increase more for the same decreases in yield.  The downside is less and the upside is more. This is clearly a desirable property.  Thus, the higher the Convexity of a bond the more desirable bonds are; in other words bonds with high convexity are more desirable.

September – October 2015 @ SDMIMD, Mysore, India

Cash pricing vs. clean price Cash price – “full price”, “all-in price” or “dirty price”) is the price of a bond that includes accrued interest, i.e. any interest due to the holder of the bond since the previous coupon date

 A bond’s ‘clean price’ is the price that excludes any interest that has accrued and the basis is generally regarded as more stable over time than cash prices.  Many bond markets make quotations on ‘clean price’ basis, and merely add the accruals to the actual amount to be paid when a purchase is settled.  Each bond market has its own day-count convention. It is thus useful to confirm the ‘day-count convention’ obtaining in the market (see next slide).

September – October 2015 @ SDMIMD, Mysore, India

Day-count convention…  'Day-Count Convention’ is a  Types of day-count system used to determine the number of days between two conventions: coupon dates, which is pivotal to 1. 30/360 day-count convention calculating accrued interest and assumes there are 30 days in PV when the next coupon a month and 360 days in a payment is less than a full coupon period away. year.  'Day-Count Convention’ helps 2. An actual/actual day-count to standardize things in the bond convention uses the actual market so as to much as possible number of days in the month achieve an even playing field and year for a given interest when a bond is sold between coupon dates. period, that is 365 days.

September – October 2015 @ SDMIMD, Mysore, India

Yield curve…  Yield curve is defined as a Utility: curve on a graph in which the yield of fixed-interest Yield curve is used as: securities is plotted against the length of time they have - As a benchmark for other debts in the market, such to run to maturity, that is, to yield-maturity relationship. as mortgage rates and bank lending rates  The most frequently reported yield curve - To make some prediction compares the 3-month, 2regarding changes in year, 5-year and 30-year US economic output and Treasury debt.

growth. September – October 2015 @ SDMIMD, Mysore, India

Yield curves… Yield curves of selected SSA countries (Silkinvest.com)

September – October 2015 @ SDMIMD, Mysore, India

Yield curves… Normal yield curve: Yield rises as maturity lengthens, i.e. the slope of the yield curve is positive. September – October 2015 @ SDMIMD, Mysore, India

Yield curves: Other types 1.Steep yield curve. 2.Flat yield curve – e.g. Nigeria’s 2-12-month fixed-deposits 3.Inverted yield curve – (see right hand side): Yields being lower and lower for each longer term-period, thus lenders can attract long-term borrowing. September – October 2015 @ SDMIMD, Mysore, India

Yield curves (continued) What is the shape of US Treasury Bond Rates as of 15th October 2015?

S/No

Fixed-Income asset

Yield %

1

3-month

-0.3%

2

6-month

-0.05%

3

2-year

0.57%

4

3-year

0.87%

5

5-year

1.31%

6

10-year

2.00%

7

30-year

2.85%

Source: finance.yahoo.com September – October 2015 @ SDMIMD, Mysore, India

Some issues with yield curves… Uncertainty over exactly how and why the curve appears the way it does at any particular moment. The possibility that the shape of the curve can change at any time. All other rate-determining factors are held constant. To overcome this limitation, we can use the ‘duration’ concept. September – October 2015 @ SDMIMD, Mysore, India

Duration… Duration measures the average time it takes for all cash flows from a security to reach the investor. Mathematically, duration is the PV-weighted measure of the maturity of the security or portfolio, that is: Sum of weighted DCF of all returns receivable and redemption value Duration = Current market price

September – October 2015 @ SDMIMD, Mysore, India

Just how safe are these government bonds?  The US had been AAA-rated by S&P since 1941, but the world’s largest economy suffered credit rating humiliation in 2011 when S&P’s stripped it of its AAA rating (www.theguardian.com).

Country

India Nigeria

S&P Rating

BBBB+

Outlook

Positive Stable

Source: Countryeconomy.com [18/10/2015]

September – October 2015 @ SDMIMD, Mysore, India

Indian Bond market (G-SEC)  Asian bond markets currently dominated by India (15%) and China (44%).  Driven by fiscal deficit  Yield is currently around 7.8%  Bonds market growing phenomenally in India (see right-side)  Major investors:  Global credit investors (non-Asians)  Asian life insurers  Mutual Funds  Foreign investors hold about 30% [Wap.business.standard.com – 15/10/2015]

Year

Amount

2008

US$25 billion

2014

US$61 billion

*2018

US$160 billion

*Estimates Source: Wap.business.standard.com [15/10/2015]

September – October 2015 @ SDMIMD, Mysore, India

10-year GOI Bonds Issue Date

Coupon Rate

4th November 2011

7.80%

11th August 2011

8.79%

Source: http://www.rrfinance.com/fixed-income/GSec_Details.aspx [18/10/2015].

September – October 2015 @ SDMIMD, Mysore, India

Why the clamour for African government bonds over the past few years?

September – October 2015 @ SDMIMD, Mysore, India

Emerging markets…. the new sources of good returns

 16 countries in SSA including Nigeria have issued foreign-currency bonds according to the Economist (August 29, 2015, p. 20)  According to Morgan Stanley, foreign investors own 25-50% of the stock of bonds in Brazil, Turkey, South Africa, Indonesia, Malaysia, and Mexico. September – October 2015 @ SDMIMD, Mysore, India

Why the clamour for African government bonds over the past few years?  The region has also become a new  Relatively high yield. Despite some focus for the Islamic finance and lean quarters, a high number of "highbonds market. growth" regional sovereigns have in  In late April, Côte d’Ivoire became recent years issued debt securities: the latest regional sovereign to issue • Ghana an Islamic finance bond, or Sukuk, • Kenya raising $490 million to pay for • Senegal • Côte d’Ivoire infrastructure projects. • Nigeria - yields on Nigerian 10-year  South Africa launched the bonds, just shy of 14% on 30 April 2015. • Ethiopia - the National Bank of Ethiopia continent’s first Shariah-compliant announced plans to launch a secondary bond US-dollar debt facility in September market in 2016 2014  Thought partly pre-emptive of the US  Niger launching its own $258 million Federal Reserve hiking interest Sukuk in February 2015. rates, Sub-Saharan African sovereigns printed paper in record http://www.euromoney.com/Article/3463288/Sub-Saharanvolumes in 2014, issuing $9.17 billion -Source: Africa-2015-Compelling-investment.html [16/10/2015] of bonds, against $6.28 billion in 2013. September – October 2015 @ SDMIMD, Mysore, India

“When you change Nigeria, you also change Africa.” - Ban Ki-Moon [www.dailytrust.com.ng -25/08/2015]

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Emerging markets…. the new sources of good returns  With bond yields depressed in rich countries in the wake of resurgent American growth, investors pile into emerging market bonds on the search for good returns.  However, there is implication for anticipated raising of interest rate by the US following the winding down of QE in 2014. September – October 2015 @ SDMIMD, Mysore, India

Bonds Market in Nigeria  National government bonds and Treasury bills are the dominant instruments in the country’s domestic debt, accounting for over 95% of total domestic debt stock.  FGN bonds account for almost 70% of the total bonds outstanding as at the end of 2014 with average yield of 11.53% (Africaneconomicoutlook.org). September – October 2015 @ SDMIMD, Mysore, India

FGN (Nigeria) Bonds- October 2015

Issue Date

Tenor

Coupon Rate

October 14, 2015

5-year

13.11%

October 14, 2015

10-year

13.87%

September 16, 2015

5-year

15.95%

September 16, 2015

20-year

15.97%

Source: http://www.cenbank.org/rates/GovtSecuritiesDrillDown.asp?market=Bonds[18/10/2015].

September – October 2015 @ SDMIMD, Mysore, India

Analysis of average yields in the Nigerian T-bills and bond markets (January – October, 2015)

Month

T-bills

Bonds

October 2015 January 2015

8.3%

14.2%

Average real ROI 1.7%

14.3%

15.2%

6.1%

Source: Afrinvest

September – October 2015 @ SDMIMD, Mysore, India

Why real ROI is falling…

September – October 2015 @ SDMIMD, Mysore, India

Recent inflation dynamics in Nigeria (2009-2015; Dec-2014-Sept 2015) Inflation rate %

Inflation rate %

18 9.5 16 9

14

12

8.5 10 Inflation rate % 8

Inflation rate % 8

6 7.5

4

2 7 0 2009 2010 2011 2012 2013 2014 2015

September – October 2015 @ SDMIMD, Mysore, India

Recall: Inflation and Interest rate Generally, as noted earlier, when commodity prices are perceived to rise, lenders require higher rates of interest to protect depreciating purchasing power of debts payments, borrowers are willing to repay in cheaper currency at higher nominal rates. September – October 2015 @ SDMIMD, Mysore, India

Comparing India-Nigeria bond markets…

September – October 2015 @ SDMIMD, Mysore, India

Coupon rates on 10-year central government bonds in India & Nigeria: Why the difference?????? 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% India

October 19, 2015 @ SDMIMD, Mysore, India

Nigeria

COM201 Programming 1: L01 – Introduction

GOI bonds attract lower nominal yields compared to FGN bonds, why?

September – October 2015 @ SDMIMD, Mysore, India

80 Corporate Bonds issued so far in Nigeria, 1960 – 2013 (SEC Nigeria, 2015) – *see some current ones below: Company

Coupon Rate

Year of Issue

Year of Maturity

Features

*Sterling Bank Plc

13.00%

2011

2018

Subordinated unsecured nonconvertible Bond

*United Bank for Africa (UBA) Plc

14.00%

2011

2018

Fixed-rate Bond

*Challeram Plc

MPR + 5%

2011

2019

Floating rate Bond

* *Those with the farthest maturity dates Source: http://www.sec.gov.ng/corporate-bonds-issued-in-nigeria.html [18/10/2015].

September – October 2015 @ SDMIMD, Mysore, India

Next session … Introduction to Bond Valuation 1.Deterministic Approaches

i.PV Approach ii.Relative Pricing iii.Arbitrage-free Pricing

2. Stochastic Calculus/PDE Approach - CIR Model - Black-Derman-Toy Model - Hull-White Model - HJM Model - Chen Model - Jamshidian’s trick

September – October 2015 @ SDMIMD, Mysore, India

Introduction to Financial Mathematics: Interest Theory

Session 5 Bond Valuation: Selected Cases and Problems

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

ILLUSTRATION 1: MGY Plc Corporate Bonds

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems Q.1. MGY Plc has two debentures in London bond Market. The quotation for both debentures is at par value of £100.00. The company has a strong tract record of consistent growth and profitability. Additional information on the two bonds are as follows: i. 14% irredeemable debentures ii. 16% debenture redeemable in 5 (five) years’ time at par iii. The current market rate of interest for this type of investment is 18% yearly.

Required: Determine the values of the MGY Plc’s two debentures. September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Cases and Problems Solution to Illusration 1: (i) To value 14% irredeemable debenture, we apply PVA in perpetuity formula, thus, we have:

𝑫𝒆𝒃𝒆𝒏𝒕𝒖𝒓𝒆 𝑽𝒂𝒍𝒖𝒆 =

𝑴𝒂𝒓𝒌𝒆𝒕 𝒑𝒓𝒊𝒄𝒆 𝒂𝒕 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒚𝒊𝒆𝒍𝒅 𝑪𝒐𝒖𝒑𝒐𝒏 𝑹𝒂𝒕𝒆

Therefore, we have,

𝑫𝒆𝒃𝒆𝒏𝒕𝒖𝒓𝒆 𝑽𝒂𝒍𝒖𝒆 =

𝟎. 𝟏𝟖 × 𝟏𝟎𝟎 = £𝟏𝟐𝟖. 𝟓𝟕 𝟎. 𝟏𝟒

Observe: The market value of £128.57 > £100.00 par value, hence this is a premium debenture bond. Why? (ii) To value the 16% debenture redeemable in 5 years’ time, we need to use the PV/DCF method. [Use the PV function in MS Excel]

September – October 2015 @ SDMIMD, Mysore, India

Valuation of 16% debenture redeemable in 5 years’ time… (Recall: current r is 18%)

Year

PMT

PV@ 18%

1 2 3 4 5

16 16 16 16 116 PV

£13.56 £11.49 £9.74 £8.25 £50.70 £93.75

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

ILLUSTRATION 2: 25% vs. 15% Par Bonds

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems Q.2. Consider a Rs 1000 par bond with 25% coupon maturing in 10 years’ time. The issuer makes semiannual coupon payments and the market required yield is 15% per annum. Required: (i) Determine the value of the bond. (ii) Determine the bond’s value assuming the coupon rate is now reduced to 15% while the market yield hikes up to 20%.. (iii) Comment on the results of your valuations. September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

Q.2 solution (i): See the MS Excel outputs below: Data items PMT @ 25% coupon rate (semi) NPER Discount rate (coupon) Per Value Discount rate (Maturity) t Bond Valuation: PVA Add: PV (1000) Bond Value

Inputs 125 20 0.075 1000 0.15 10

Outputs

*Note: Semi-annual *Note: Annual

£1,274.31 £247.18 £1,521.50

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems Q.2 solution (ii): See the MS Excel outputs below: Data items PMT @ 15% coupon rate (Semi) NPER Discount rate (coupon) Per Value Discount rate (Maturity) t Bond Valuation: PVA Add: PV (1000)

Inputs 75 20 0.10 1000 0.20 10

Outputs

*Note: Semi-annual

*Note: Annual

Rs638.52 Rs161.51 Rs800.02

Bond Value September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

ILLUSTRATION 3: 15% Par Bond Valuation

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

Q.3. Calculate the market value of a bond with a 15% annual coupon, a 5year time to maturity, and a face value of Rs1000. Hint: Here, you are not given the market yield; so, what are you going to do? September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

Q.3 Solution: See the MS Excel Outputs below: Data items PMT @ 15% coupon rate (annual) NPER Discount rate (coupon) Per Value Discount rate (Maturity) t

Inputs 150 5 0.15 1000 0.15 5

Bond Valuation: PVA Add: PV (1000)

Outputs

*Note: Annual *Note: Annual

Rs502.82 Rs497.18 Rs1000.00

Bond Value October 19, 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

ILLUSTRATION 4: YTM of Rs1000 GOI bond

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

Q.4. Consider a 10% GOI bond RS1000 par value with 5 years remaining to maturity having a current price of Rs900.00. Required: Determine the YTM of the bond September – October 2015 @ SDMIMD, Mysore, India

Recall computing YTM…  Approximate YTM can be computed thus: =

𝐶𝑜𝑢𝑝𝑜𝑛 𝑎𝑚𝑜𝑢𝑛𝑡 + 𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑙𝑖𝑛𝑒 𝑎𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛 𝑜𝑟 𝑙𝑜𝑠𝑠 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

𝑷𝒑 − 𝑷𝒎 𝑪𝒊 + 𝒏 = 𝑷𝒑 + 𝑷𝒎 𝟐

Where, Ci refers to annual coupon value of the investment Pp refers to the par value of the bond Pm refers to the current market price of the bond n refers to the number of years to maturity September – October 2015 @ SDMIMD, Mysore, India

Solution to Illustration 4… Hence, the approximate YTM is estimated thus: =

=

𝐶𝑜𝑢𝑝𝑜𝑛 𝑎𝑚𝑜𝑢𝑛𝑡 + 𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑙𝑖𝑛𝑒 𝑎𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛 𝑜𝑟 𝑙𝑜𝑠𝑠 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

𝟏𝟎𝟎𝟎 −𝟗𝟎𝟎 𝟏𝟎𝟎+ 𝟓 𝟏𝟎𝟎𝟎 + 𝟗𝟎𝟎 𝟐

=

𝟏𝟐𝟎 𝟗𝟓𝟎

= 12.63%

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

ILLUSTRATION 5: Duration of a Treasure Bond

September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems Q.5. Assume a Treasury Certificate (TC) of Rs1000 par value with 5 years tenor and paying Rs80 per year as interest, payable yearly at year-end, and a current market price of Rs900. The market yield of the TC is 10.73%. Required: Determine the bond’s duration.

September – October 2015 @ SDMIMD, Mysore, India

Solution 5… Recall ‘Duration’ measures the average time it takes for all cash flows from a security to reach the investor, that is: Sum of weighted DCF of all returns receivable and redemption value Duration = Current market price

September – October 2015 @ SDMIMD, Mysore, India

Solution 5 continued …  The results of the MS Excel below indicates the TC’s average maturity to be 4 years and 3 months:

Market Price: Rs900.00

1 2 3 4 5

80 80 80 80 1080

Weighted CF

PV/10.73%

80 160 240 320 5400

72.25 130.49 176.77 212.86 3243.90 3836.27

Duration (years)

4.26

September – October 2015 @ SDMIMD, Mysore, India

Keywords… Amortization, Bonds, Arbitrage-free Pricing, Bond Issuer, Bond yields, Convexity measures, Credit rating, Credit spread, Current yield, Day-count convention, Debenture bonds, Discount bonds, Fixed-income securities, Fisher equation, India, IRR, Linearity, Nigeria, Nominal yield, Price sensitivity, Premium bonds, Par bonds, Redemption value, Stochastic Calculus/PDE Approach, Yield curve, YTC, YTM, YTP, YTW. September – October 2015 @ SDMIMD, Mysore, India

Introduction to Financial Mathematics: Interest Theory

Session 6– Review of Capital Budgeting Techniques Stephen ARO-GORDON, PhD FIMC, FCMA, FCAI, ANIVS, RSV, IAQF

Senior Lecturer & Head Department of Financial Mathematics Baze University Abuja Nigeria Email: [email protected] / [email protected] September – October 2015 @ SDMIMD, Mysore, India

Feedback from the previous session…

Any Q, Comments & Suggestions? COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Introduction to Financial Mathematics: Interest Theory

Recall: Session 5 Bond Valuation: Selected Cases and Problems

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems

ILLUSTRATION 1: MGY Plc Corporate Bonds

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems Q.1. MGY Plc has two debentures in London bond Market. The quotation for both debentures is at par value of £100.00. The company has a strong tract record of consistent growth and profitability. Additional information on the two bonds are as follows: i. 14% irredeemable debentures ii. 16% debenture redeemable in 5 (five) years’ time at par iii. The current market rate of interest for this type of investment is 18% yearly.

Required: Determine the values of the MGY Plc’s two debentures. September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Cases and Problems Solution to Illusration 1: (i) To value 14% irredeemable debenture, we apply PVA in perpetuity formula, thus, we have:

𝑫𝒆𝒃𝒆𝒏𝒕𝒖𝒓𝒆 𝑽𝒂𝒍𝒖𝒆 =

𝑴𝒂𝒓𝒌𝒆𝒕 𝒑𝒓𝒊𝒄𝒆 𝒂𝒕 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒚𝒊𝒆𝒍𝒅 𝑪𝒐𝒖𝒑𝒐𝒏 𝑹𝒂𝒕𝒆

Therefore, we have,

𝑫𝒆𝒃𝒆𝒏𝒕𝒖𝒓𝒆 𝑽𝒂𝒍𝒖𝒆 =

𝟎. 𝟏𝟖 × 𝟏𝟎𝟎 = £𝟏𝟐𝟖. 𝟓𝟕 𝟎. 𝟏𝟒

Observe: The market value of £128.57 > £100.00 par value, hence this is a premium debenture bond. Why? (ii) To value the 16% debenture redeemable in 5 years’ time, we need to use the PV/DCF method. [Use the PV function in MS Excel]

September – October 2015 @ SDMIMD, Mysore, India

Valuation of 16% debenture redeemable in 5 years’ time… (Recall: current r is 18%)

Year

PMT

PV@ 18%

1 2 3 4 5

16 16 16 16 116 PV

£13.56 £11.49 £9.74 £8.25 £50.70 £93.75

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems

ILLUSTRATION 2: 25% vs. 15% Par Bonds

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems Q.2. Consider a Rs 1000 par bond with 25% coupon maturing in 10 years’ time. The issuer makes semiannual coupon payments and the market required yield is 15% per annum. Required: (i) Determine the value of the bond. (ii) Determine the bond’s value assuming the coupon rate is now reduced to 15% while the market yield hikes up to 20%.. (iii) Comment on the results of your valuations. September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems

Q.2 solution (i): See the MS Excel outputs below: Data items PMT @ 25% coupon rate (semi) NPER Discount rate (coupon) Per Value Discount rate (Maturity) t Bond Valuation: PVA Add: PV (1000) Bond Value

Inputs 125 20 0.075 1000 0.15 10

Outputs

*Note: Semi-annual *Note: Annual

£1,274.31 £247.18 £1,521.50

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems Q.2 solution (ii): See the MS Excel outputs below: Data items PMT @ 15% coupon rate (Semi) NPER Discount rate (coupon) Per Value Discount rate (Maturity) t Bond Valuation: PVA Add: PV (1000)

Inputs 75 20 0.10 1000 0.20 10

Outputs

*Note: Semi-annual

*Note: Annual

Rs638.52 Rs161.51 Rs800.02

Bond Value September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems

ILLUSTRATION 3: 15% Par Bond Valuation

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems

Q.3. Calculate the market value of a bond with a 15% annual coupon, a 5year time to maturity, and a face value of Rs1000. Hint: Here, you are not given the market yield; so, what are you going to do? September – October 2015 @ SDMIMD, Mysore, India

Bond Valuation – Selected Cases and Problems

Q.3 Solution: See the MS Excel Outputs below: Data items PMT @ 15% coupon rate (annual) NPER Discount rate (coupon) Per Value Discount rate (Maturity) t

Inputs 150 5 0.15 1000 0.15 5

Outputs

*Note: Annual *Note: Annual

Bond Valuation: PVA Add: PV (1000)

Rs502.82 Rs497.18 Rs1000.00

Bond Value September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems

ILLUSTRATION 4: YTM of Rs1000 GOI bond

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond Valuation – Selected Cases and Problems

Q.4. Consider a 10% GOI bond RS1000 par value with 5 years remaining to maturity having a current price of Rs900.00. Required: Determine the YTM of the bond September – October 2015 @ SDMIMD, Mysore, India

Recall computing YTM…  Approximate YTM can be computed thus: =

𝐶𝑜𝑢𝑝𝑜𝑛 𝑎𝑚𝑜𝑢𝑛𝑡 + 𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑙𝑖𝑛𝑒 𝑎𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛 𝑜𝑟 𝑙𝑜𝑠𝑠 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

𝑷𝒑 − 𝑷𝒎 𝑪𝒊 + 𝒏 = 𝑷𝒑 + 𝑷𝒎 𝟐

Where, Ci refers to annual coupon value of the investment Pp refers to the par value of the bond Pm refers to the current market price of the bond n refers to the number of years to maturity September – October 2015 @ SDMIMD, Mysore, India

Recall: Solution to Illustration 4… Hence, the approximate YTM is estimated thus: =

=

𝐶𝑜𝑢𝑝𝑜𝑛 𝑎𝑚𝑜𝑢𝑛𝑡 + 𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑙𝑖𝑛𝑒 𝑎𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛 𝑜𝑟 𝑙𝑜𝑠𝑠 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

𝟏𝟎𝟎𝟎 −𝟗𝟎𝟎 𝟏𝟎𝟎+ 𝟓 𝟏𝟎𝟎𝟎 + 𝟗𝟎𝟎 𝟐

=

𝟏𝟐𝟎 𝟗𝟓𝟎

= 12.63%

September – October 2015 @ SDMIMD, Mysore, India

Recall: Bond valuation keywords… Amortization, Bonds, Arbitrage-free Pricing, Bond Issuer, Bond yields, Convexity measures, Credit rating, Credit spread, Current yield, Day-count convention, Debenture bonds, Discount bonds, Fixed-income securities, Fisher equation, India, IRR, Linearity, Nigeria, Nominal yield, Price sensitivity, Premium bonds, Par bonds, Stochastic Calculus/PDE Approach, Yield curve, YTC, YTM, YTP, YTW. September – October 2015 @ SDMIMD, Mysore, India

Workshop sessions update Sessions

Date

Agenda



Saturday, September 19

Course introduction / overview / methodology



Monday, September 28

Review and further applications of time value of money concept

4&5

Monday, October 19

(i) Introduction to FixedIncome Mathematics (FIMs) (ii) Bond Valuations – Selected Cases and Problems

6

Tuesday, October 20

Review of Capital Budgeting Techniques (CBTs)

7

Wednesday, October 21

Further applications of CBTs COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Session 6: Agenda Review of CBT essence, concepts, capital rationing, hurdle rate, mutually exclusivity, etc. DCF and Non-DCF approaches - NPV, IRR, Profitability Index, ARR / ROI, BEP, Payback period. Despite what may be regarded as their various weaknesses (some are highlighted in this presentation), these CBTs are very popular in global industries for making the right choice of investment proposals. September – October 2015 @ SDMIMD, Mysore, India

What is Capital Budgeting?

September – October 2015 @ SDMIMD, Mysore, India

Capital budgeting: Let’s look at the two terms…

“CAPITAL” = Economic resource(s) that can be used to produce or generate economic wealth. “BUDGET” = Plan for allocating resources in terms of specifying how capital will be spent during a particular period. September – October 2015 @ SDMIMD, Mysore, India

What is Capital Budgeting?  Capital budgeting (also known as investment appraisal, or capital project appraisal) deals with the process by which an organization or investor determines whether projects are worth pursuing.  Such projects may be new R&D, opening a new branch office, replacing a machine, building an estate, providing road infrastructure, etc.  Capital budget is a list of capital investment projects that an organisation has decided to execute.  Generally, a project is worth pursuing if it increases the value of the company, that is, mathematically, if the project earns a rate of return that exceeds the cost of capital (𝒓 > 𝒌). September – October 2015 @ SDMIMD, Mysore, India

Essence of CBT… Dealing with inherent uncertainty from the business environment. Long-term projects are capital intensive. Risk management / risk insurance for corporate sustainability. Performance evaluation – due diligence. Optimal capital structure – long-term investment decision versus short-term investment decision. Capital rationing. September – October 2015 @ SDMIMD, Mysore, India

Cash flow…  In capital budgeting, cash flow is key.  We are interested in the project’s life blood – the actual net amount of cash that flows out of the business as a result of the investment decision (cash out-flow), and the return to the business (cash in-flow) from that project during its life.  Incremental cash flow, not absolute cash flows.  You will need to also consider associated cash flow components such as:  Income tax  Net residual/disposal value at the end of the asset’s useful life  Incidental costs that may need to be capitalized, etc. September – October 2015 @ SDMIMD, Mysore, India

Capital Budgeting: Under certainty & Uncertainty… Certainty

Uncertainty

DCF approaches

The conservative estimate method

Non-DCF methods

The payback method Risk-adjusted discount rate Probability distribution of

cash flow

Certainty equivalent approach

Sensitivity analysis September – October 2015 @ SDMIMD, Mysore, India

Capital budgeting under certainty…

September – October 2015 @ SDMIMD, Mysore, India

Capital rationing… The system of placing restrictions on the amount of new investments or projects that can be undertaken by a company is known as ‘capital rationing’. Capital rationing is usually achieved by imposing a higher cost of capital for investment consideration or by setting a ceiling on the specific sections of the budget.  In the process of doing capital rationing, some projects may be discovered to be mutually exclusive. September – October 2015 @ SDMIMD, Mysore, India

Mutually exclusive projects…  Two projects are mutually exclusive when it is not feasible and viable to execute both of them.  Acceptance of one of the projects means the rejection of the other.  In such situations, usually, projects will be ranked from the highest to lowest NPV, and the project with the highest positive NPV will be selected. September – October 2015 @ SDMIMD, Mysore, India

What is hurdle rate?

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Hurdle rate…. The hurdle rate (opportunity cost of capital) is the expected return that is forgone by investing in a project rather than in comparable financial securities or investment opportunities that have similar risk as the project under consideration. October 20, 2015 @ SDMIMD, Mysore, India

Hurdle rate factors…. i. ii. iii. iv. v. vi. vii.

Current availability and sources of corporate financing The business growth prospects Company tax status The WACC (Weighted Average Cost of Capital) Asset Structure The level of business risk The adequacy of business’s cash flow to service debt. October 20, 2015 @ SDMIMD, Mysore, India

Capital budgeting techniques DCF NPV

IRR PI

Non-DCF Pay-back period ARR / ROI BEP

Discounted Pay-back method

Annual Equivalent Cost September – October 2015 @ SDMIMD, Mysore, India

DCF approaches

September – October 2015 @ SDMIMD, Mysore, India

DCF convention Cash flows occur at the end of the year Initial investment outlay occurs at the beginning of the first year, i.e. Year 0. If it occurs at the beginning of the Year 2, it should be timed (for computational purpose) as occurring in Year 1. However, many lease payments are made in advance (at the beginning of the year), hence due recognition must be given to this timing (annuity due format) in your DCF calculations. September – October 2015 @ SDMIMD, Mysore, India

(1) Recall NPV formula If n is the number of cash flows in the list of values, the formula for NPV is 𝑛

𝑁𝑃𝑉 = 𝑖=1

𝑉𝑎𝑙𝑢𝑒𝑠𝑖 (1 + 𝑟𝑎𝑡𝑒)𝑖

September – October 2015 @ SDMIMD, Mysore, India

NPV decision rules If the NPV is positive, it means that the project’s discounted rate of return is higher than the cost of capital, hence the project is viable and should be accepted. If the NPV is negative, the project should be rejected. If the NPV is zero, it means the project merely breaks even. September – October 2015 @ SDMIMD, Mysore, India

NPV Illustration  Q: Use the NPV approach at 20% hurdle rate to ascertain the viability of a project with the following cash flows:

Year 0 1 2 3 4 5

Cash flow (£) -170000 70000 70000 70000 50000 30000

September – October 2015 @ SDMIMD, Mysore, India

Discuss solution from your MS Excel analysis….

0

1

-170000 70000

2

3

4

5

70000

70000

50000

30000

NPV= £11,352.24 September – October 2015 @ SDMIMD, Mysore, India

What to you think of the NPV approach?

October 20, 2015 @ SDMIMD, Mysore, India

A critique of the NPV approach… • Advantages:  Accounts for the time value of money.  It is in sync with valuecreation and maximization objectives of firms/shareholders  Ease of project selection as only projects with positive NPV will be selected

• Disadvantages:  The hurdle rate / cost of capital that is applied may be subjective; it difficult to determine the group's appropriate cost of capital.  IRR (project risk) is not measured; this may lead to the rejection of otherwise profitable projects.  Sometimes, results could conflict with IRR’s.

September – October 2015 @ SDMIMD, Mysore, India

(2) Recall IRR Concept  IRR is closely related to NPV, the net present value function.  The rate of return calculated by IRR is the discount rate corresponding to a 0 (zero) net present value. That is the discount rate that gives 𝑁𝑃𝑉 = 0.  Mathematically, we mean: 𝑵

𝑵𝑷𝑽𝑰𝑹𝑹 = 𝒕=𝟏

𝑵𝑪𝑭𝒕 − 𝑵𝑰𝑵𝑽 = 𝟎 𝒕 (𝟏 + 𝑰𝑹𝑹)

Where, NINV is the Net Investment. NCF is the annual net cash flow from the project. September – October 2015 @ SDMIMD, Mysore, India

Finding IRR by Linear interpolation…  Prior to today’s computerization, the IRR can be manually (but tediously) estimated by assuming a linear change in NPV between two discount rates.  In those days, we could find the IRR by Linear Interpolation formula: +𝒗𝒆 𝑵𝑷𝑽 𝑰𝑹𝑹 = 𝑫𝒊𝒔𝒄𝒐𝒖𝒏𝒕 𝒓𝒂𝒕𝒆 𝒐𝒇 + 𝒗𝒆 𝑵𝑷𝑽 + × 𝟏% +𝒗𝒆 𝑵𝑷𝑽 𝒑𝒍𝒖𝒔 − 𝒗𝒆 𝑵𝑷𝑽

 Trial and error method – A rate is assumed and used as a discount factor and if the NPV is not zero, another higher or lower rate is used, on and on, until the NPV is zero or close to zero. September – October 2015 @ SDMIMD, Mysore, India

Technology help….  Today, we can use the IRR function in MS Excel, HP12c calculator or other software to perform our computations.  You can use the IRR function of Excel.  The value of ‘guess’ in the function can be any number such as 0.10 or 10%; it will have no bearing on the answer.  The IRR function will perform normally even if you don’t insert a ‘guess’ as long as one of the cash flows has a sign opposite to the sign of other cash flows.  Usually the NINV (net investment) will be shown as negative number.

September – October 2015 @ SDMIMD, Mysore, India

IRR decision rules…  Accept the project as long as: 𝑰𝑹𝑹 > 𝒉𝒖𝒓𝒅𝒍𝒆 𝒓𝒂𝒕𝒆 (k - WACC)  Reject the project as long as: 𝑰𝑹𝑹 ≤ 𝒉𝒖𝒓𝒅𝒍𝒆 𝒓𝒂𝒕𝒆 (k)  In the case of mutually exclusive projects, accept the project having the highest-ranked IRR, provided that: 𝑰𝑹𝑹 − 𝒉𝒖𝒓𝒅𝒍𝒆 𝒓𝒂𝒕𝒆 > 𝟎 September – October 2015 @ SDMIMD, Mysore, India

Basic rationale behind IRR…  IRR gives us a single number representing the benefits of a project.  IRR is independent of the rate of return prevalent in the capital market, hence, as the name suggests, it is internal or intrinsic to the project. It does not depend on anything except the cash flows of the project.

September – October 2015 @ SDMIMD, Mysore, India

What’s your view about the IRR approach?

September – October 2015 @ SDMIMD, Mysore, India

A critique of the IRR approach… • Advantages:  As applicable to the NPV approach, IRR accounts for the time value of money.  It is comparable to the hurdle rate.  Considered at the best method of Capital Budgeting because it also shows project profitability.

• Disadvantages:  Analysis may at times yield multiple IRRs (In such cases, double-check with NPV).  Output may be affected/dependent on the scale or size of the project.  Decision conflicts may arise when used together with NPV technique (In such cases, double-check with NPV).

September – October 2015 @ SDMIMD, Mysore, India

(3) Profitability Index (PI)  PI [also known as Benefit/Cost Ratio, Profit Investment Ratio (PIR) and Value Investment Ratio (VIR)] measures the PV of future cash flows relative to the initial investment, i.e.: 𝑷𝑽 𝒐𝒇 𝒇𝒖𝒕𝒖𝒓𝒆 𝑪𝒂𝒔𝒉 𝑭𝒍𝒐𝒘𝒔 𝑷𝑰 = 𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝑰𝒏𝒗𝒆𝒔𝒕𝒎𝒆𝒏𝒕

 A PI of 1 indicates breakeven [assuming that the cash flow calculated does not include the investment made in the project]. Any value < 1 would indicate that the project's PV is less than the initial investment. As the value of the PI increases, so does the financial attractiveness of the proposed project. September – October 2015 @ SDMIMD, Mysore, India

A note of caution when computing Profitability Index (PI)

Some students confuse NPV with PV in the PI formula. Note: When computing Profitability Index, use PV not NPV which is a net benefit. September – October 2015 @ SDMIMD, Mysore, India

Profitability Index (PI): Decision rules

PI Rules for selection or rejection of a project: If PI > 1 then accept the project If PI < 1 then reject the project

September – October 2015 @ SDMIMD, Mysore, India

What’s your view about the PI approach?

September – October 2015 @ SDMIMD, Mysore, India

A critique of the PI approach… • Advantages:

PI is relatively easy to understand. Relative ease of computation.

• Disadvantages:

Application to project appraisal is rather limited to situations where there is only a singular constraint (capital). It may not provide the best guide where capital is not the only constraint.

September – October 2015 @ SDMIMD, Mysore, India

(4) Annual Equivalent Cost  In some circumstances, such as in leases and machinery/vehicle replacement policies, we want to ascertain the proposal that has the lowest annual equivalent cost, or the least costly, as opposed to most costly proposals.  This may be useful where investment proposals have unequal time periods and the absolute NPVs will not be comparable because of the unequal lives.  Annual Equivalent is given thus: 𝑺𝒖𝒎 𝒐𝒇 𝑷𝑽𝒔 𝑨𝒏𝒏𝒖𝒂𝒍 𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 = 𝑺𝒖𝒎 𝒐𝒇 𝒅𝒊𝒔𝒄𝒐𝒖𝒏𝒕 𝒇𝒂𝒄𝒕𝒐𝒓𝒔 September – October 2015 @ SDMIMD, Mysore, India

Annual Equivalent Cost…  Where no information is given on cost of capital, you can base your computations on the average cost per year.  In this case, the capital cost is taken as the difference between the price of a new asset (say, vehicle) and the sale price at the end of the appropriate replacement interval.  Maintenance costs are cumulative.  To compute the average cost per year, total cost for each year will be the capital cost + accumulated maintenance cost for each year.

September – October 2015 @ SDMIMD, Mysore, India

Non-DCF approaches

September – October 2015 @ SDMIMD, Mysore, India

(1) Accounting Rate of Return (ARR)  ARR (also known as the ROI method) does not take into account the concept of time value of money.  Rather, ARR calculates the return, generated from net income of the capital investment proposal.  The ARR is a percentage (%) return

• ARR Formula: 𝑨𝑹𝑹 =

𝑵𝒆𝒕 𝑷𝒓𝒐𝒇𝒊𝒕 −𝑨𝒏𝒏𝒖𝒂𝒍 𝑫𝒆𝒑𝒓𝒆𝒄𝒊𝒂𝒕𝒊𝒐𝒏 𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑰𝒏𝒗𝒆𝒔𝒕𝒎𝒆𝒏𝒕

September – October 2015 @ SDMIMD, Mysore, India

* 100

ARR: How can we have a good estimates for the ‘Annual depreciation’ and the ‘Average investment’ ?

September – October 2015 @ SDMIMD, Mysore, India

Computing ARR: Average Investment  You can estimate Average Investment thus: 𝑩𝒐𝒐𝒌 𝑽𝒂𝒍𝒖𝒆 𝑩𝑽 𝒂𝒕 𝒕𝒉𝒆 𝒃𝒆𝒈𝒊𝒏𝒏𝒊𝒏𝒈 𝒐𝒇 𝒀𝒆𝒂𝒓 𝟏 + 𝑩𝑽 𝒂𝒕 𝒕𝒉𝒆 𝒆𝒏𝒅 𝒐𝒇 𝒖𝒔𝒆𝒇𝒖𝒍 𝒍𝒊𝒇𝒆 𝟐

September – October 2015 @ SDMIMD, Mysore, India

What’s your view about the ARR approach?

October 20, 2015 @ SDMIMD, Mysore, India

A critique of the ARR approach… • Advantages:  Relatively easy to understand and calculate.  Ease of expression in % terms.  Uses standard accounting concept (net profit, etc.)

• Disadvantages:  Time value of money / cash flows ignored in its computation.  It adopts a measure of return based on accounting concept which can be open to numerous variants.  Bad debts and depreciation numbers can be manipulated to boost profit / return.  It may give an unrealistic view of performance during periods of inflation.  There is no rational way of ascertaining what the appropriate cut-off ARR should be.

September – October 2015 @ SDMIMD, Mysore, India

(2) Break-even point (BEP) Analysis  BEP is the point where gains cover costs, i.e. the point at which the gain from an economic activity equals the costs incurred in pursuing it.  At BEP, cost or expenses and revenue are equal.  It is shown graphically as the point where the total revenue and total cost curves meet. In the linear case the break-even point is equal to the fixed costs divided by the contribution margin per unit.

• BEP Formula: 𝑸𝑩𝑬𝑷 =

𝑭 𝑷 − 𝑽

Where, 𝑸𝑩𝑬𝑷 is the quantity of sales at break-even F is the total fixed cost. P is the price per unit of quantity. V is the variable cost per unit of quantity

September – October 2015 @ SDMIMD, Mysore, India

What’s your view about the BEP approach?

September – October 2015 @ SDMIMD, Mysore, India

Further notes on BEP technique… Some limitations of the BEP technique:  Linearity / constancy of Fixed cost and Variable Costs may be unrealistic where there has been a change in the production scale.  The implied assumption of 100% sales may also be unrealistic in a highly competitive market. September – October 2015 @ SDMIMD, Mysore, India

(3) Project Pay-back Period  Pay-back period indicates time taken to recover the initial outlay of a project.  Obviously, in this context, projects with the shortest pay-back would be considered favourably.  Q: [What does this tell you about investorbehaviour and finance risk-return theory?]

• Decision Rules: • Pay-back (Project X) < Payback (Standard): Accept • Pay-back (Project Y) > Payback (Standard): Reject  Note: Sometimes, Project A, B, C, D, E, … can be ranked according to their pay-back periods, for necessary consideration.

September – October 2015 @ SDMIMD, Mysore, India

Pay-back Illustration Q: Determine the pay-back period for this project:

Year 0 1 2 3 4 5

Cash flow (£) ‘000 -150 40 50 60 60 60

September – October 2015 @ SDMIMD, Mysore, India

What’s your view about the pay-back approach?

September – October 2015 @ SDMIMD, Mysore, India

A critique of the Pay-back approach… • Advantages:

• Disadvantages:

 Relatively easy to understand.  Easy of computation – uses project cash flows rather than some accounting profit that is open to so many interpretations  Favours quick-return projects  Minimizes risk associated with long-term projects

 Technique does not measure the project’s overall worth  It ignores time value of money concept.  It offers a rather crude approach to timing of projects  It does not explicitly account for investment risk.

September – October 2015 @ SDMIMD, Mysore, India

Capital budgeting under uncertainty…

September – October 2015 @ SDMIMD, Mysore, India

Recall Capital Budgeting: under certainty & Uncertainty… Certainty

Uncertainty

DCF approaches

The conservative estimate method

Non-DCF methods

The payback method Risk-adjusted discount rate Probability distribution of

cash flow

Certainty equivalent approach

Sensitivity analysis September – October 2015 @ SDMIMD, Mysore, India

Capital budgeting under uncertainty…  Projects are subject to a number of risks or threats, or future uncertainty, and this can pose a challenge to financial planning or project appraisal.  Risk management – identification, measurement, and economic control of risk that threaten the assets and earnings of a business or organization – curbing or minimizing the impact.  Insurable risks  Other risks – the project/asset itself, market, management continuity, interest rate risk, credit or default risk, inflation risk, etc. September – October 2015 @ SDMIMD, Mysore, India

Statistical measures of project risk Standard deviation, s, given as: 1 =√ 𝑁 −1

𝑁

(𝑥𝑖 − 𝑥 )2 𝑖=1

 Where projects have different expected cash flows, the relative riskiness should be measured by the coefficient of variation, given as:

=

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑚𝑒𝑎𝑛

=

𝑠 𝑥

September – October 2015 @ SDMIMD, Mysore, India

End of Session 6 Review of Capital Budgeting Techniques

October 20, 2015

September – October 2015 @ SDMIMD, Mysore, India

Introduction to Financial Mathematics: Interest Theory

Session 7 Capital Budgeting: Selected Cases and Problems September – October 2015 @ SDMIMD, Mysore, India

Capital budgeting techniques DCF NPV

IRR PI

Non-DCF Pay-back period ARR / ROI BEP

Discounted Pay-back method

Annual Equivalent Cost September – October 2015 @ SDMIMD, Mysore, India

Capital Budgeting: Selected Cases and Problems

ILLUSTRATION 1: Siemens EUR 9 million Project Appraisal September – October 2015 @ SDMIMD, Mysore, India

Illustration 1… Q.1. Siemens, the German leader of electronics and electrical engineering is considering a project with an initial investment of EUR 9 million. The net operating cash flows from the investment are EUR 1.5 million yearly for the next 15 years. Siemens follows a rule that only projects with a pay-back period of 5 years or less will be accepted. Required: Determine the payback period for this project and advise on project selection by Siemens’ Board. September – October 2015 @ SDMIMD, Mysore, India

Solution 1: Siemens’ EUR 9 million project appraisal  Project pay-back (PP) is determined thus:

9𝑚 𝑃𝑃 = = 6 years 1.5𝑚 Decision: Since Pay-back (6 years) > Pay-back (Standard: 5 years max.), Siemens will not invest in the project.

September – October 2015 @ SDMIMD, Mysore, India

Illustration 2… Still on Siemens EUR 9 million Project Appraisal September – October 2015 @ SDMIMD, Mysore, India

Illustration 2… Q.2. Regarding the same Siemens EUR 9 million project plan, a more detailed analysis of the project shows that the net annual cash flows from the project are not equal but as follows: EUR 3m, EUR 2m, EUR 1.5m, EUR 1.5m, EUR 1.5m, EUR 1.1m, EUR 1.1m, EUR 1m, and EUR 0.8m, respectively . Assume the same rule applies, namely, that only projects with a pay-back period of 5 years or less will be accepted. Required: Determine the payback period for this project and advise on project selection by Siemens’ Board.

September – October 2015 @ SDMIMD, Mysore, India

Solution 2: Siemens’ EUR 9 million project appraisal  Since the cash flows are not equal each year, to calculate the PP, we need to add the cash flows to determine the cumulative cash flows: Year

Cash Flow (EUR million)

Cumulative Cash Flow (EUR million)

1

3

3

2

2

5

3

1.5

6.5

4

1.5

8

5

1.5

9.5

6

1.1

10.6

7

1.1

11.7

8

1.0

12.7

9

0.8

13.5

September – October 2015 @ SDMIMD, Mysore, India

Solution 2 continued….

 Observe: The CCF (cumulative cash flow) in the 4th year is EUR 8 million, while CCF for the 5th year is EUR 9.5m. Since the project has to recover only EUR 9 million, the PP > 4 years but < 5 years.  The exact PP can be computed thus: 1𝑚 𝟐 𝑃𝑃 = 4 + = 𝟒 𝐲𝐞𝐚𝐫𝐬 1.5 𝑚 𝟑 2 (4 3

Decision: Since the computed PP years) < Pay-back (Standard: 5 years max.), Siemens will invest in the project.

September – October 2015 @ SDMIMD, Mysore, India

Illustration 3… Still on Siemens EUR 9 million Project Appraisal September – October 2015 @ SDMIMD, Mysore, India

Illustration 3… Q.3. Siemens’ opportunity cost of capital is 10%. Recall the same Siemens EUR 9 million project plan, where a more detailed analysis of the project shows that the net annual cash flows from the project are not equal but as follows: EUR 3m, EUR 2m, EUR 1.5m, EUR 1.5m, EUR 1.5m, EUR 1.1m, EUR 1.1m, EUR 1m, and EUR 0.8m, respectively . Assume the same rule applies, namely, that only projects with a pay-back period of 5 years or less will be accepted. Required: Compute the discounted payback period for this project and advise on project selection by Siemens’ Board. September – October 2015 @ SDMIMD, Mysore, India

How would you handle a discounted PP case like this one?

September – October 2015 @ SDMIMD, Mysore, India

Solution 3: Siemens’ EUR 9 million project appraisal  To calculate the discounted PP, we need to add the PVs of cash flows to determine the cumulative discounted cash flows: Year

Cash Flow (EUR million)

PV of Cash Flow @ 10% (EUR million)

Cumulative Cash Flow (EUR million)

1

3

2.73

2.73

2

2

1.65

4.38

3

1.5

1.13

5.51

4

1.5

1.02

6.53

5

1.5

0.93

7.46

6

1.1

0.62

8.08

7

1.1

0.56

8.65

8

1.0

0.47

9.11

9

0.8

0.34

9.45

September – October 2015 @ SDMIMD, Mysore, India

Solution 3 continued…  Observe: The discounted CCF (DCCF) in the 7th year is EUR 8.65 million, while DCCF for the 8th year is EUR 9.11m. Since the project has to recover only EUR 9 million, the PP > 7 years but < 8 years.  Again, the exact PP can be computed thus: 0.35 𝑚 𝑃𝑃 = 7 + = 𝟕. 𝟕𝟒 𝐲𝐞𝐚𝐫𝐬 0.47 𝑚 Decision: Since the computed PP (7.74 years) > Pay-back (Standard: 5 years max.), Siemens will NOT invest in the project. September – October 2015 @ SDMIMD, Mysore, India

Illustration 4… Philips EUR 60,000 Project Appraisal September – October 2015 @ SDMIMD, Mysore, India

Illustration 4… Q.4. Philips, one of the world’s biggest electronics companies and Europe’s largest, is a global leader in colour television sets, lighting, and other electronic products. The company is considering a replacement project with a net initial investment of EUR 60,000. The project has a four-year life, and annual net cash flows of EUR 30,000 (1st year), EUR 25,000 (2nd year), EUR 20,000 (3rd year), and EUR 10,000 (4th year). Philips WACC is 16%. Required: Should the project be accepted? Use NPV and IRR methods and comment on whether there is any disparity on the decision reached using the two techniques. September – October 2015 @ SDMIMD, Mysore, India

Solution 4: Philips’ EUR 60,000 project appraisal  The Excel calculation (below) indicates that the precise IRR of the Philips project is 18.71%: 0

1

2

3

4

-60000

30000

25000

20000

10000

IRR

18.71%

NPV/16%

EUR 2,394.14

 Decision: Since the project’s IRR is > the WACC (16%), the firm should accept the project. Also, with the same project providing a positive NPV, there is no disparity between the decision reached using the NPV method and the decision using the IRR method. September – October 2015 @ SDMIMD, Mysore, India

Illustration 5… SNEPCO’s EUR 2.5 billion New Oil Field Project Appraisal

September – October 2015 @ SDMIMD, Mysore, India

Illustration 5… Q.5: The Shell Nigeria Exploration and Production Company (SNEPCo) – which explores for, produces, refines and markets petroleum products etc.) pioneered Nigeria's deep-water oil and gas production at the Bonga field, a project that increased Nigeria's oil capacity by 10% when output began in 2005.At full output, Bonga has the potential to add more than 200,000 barrels of crude oil and 150 million standard cubic feet of gas to Nigeria's daily production. The company’s cost of capital is 15%. SNEPCo is considering a new oil field development project which requires a net initial investment of EUR 2.5 billion. The cash flows from the project over its four-year life will be:

Year

Cash flows (EUR billion)

0

-2.5

1

3.1

2

1.8

3

1.4

4

-4.4

Required: Should the project be accepted? September – October 2015 @ SDMIMD, Mysore, India

Solution 5: SNEPCO’s EUR 2.5 billion project appraisal  The Excel calculation (below) indicates that the precise IRR of the SNEPCo project is 17.8%:

0 -2.5

1 3.1

2 1.8

3 1.4

4 -4.4

IRR

17.8%

NPV/15% -EUR 0.033 bn  Decision: Although the project’s IRR is > the cost of capital (15%), SNEPCo should reject the project because its NPV is negative.

September – October 2015 @ SDMIMD, Mysore, India

Illustration 6…

Production of G. Benguze Pvt Ltd ’s new healthcare product

September – October 2015 @ SDMIMD, Mysore, India

Illustration 6… Q.6: G. Benguze Pvt Ltd (GB), a market leader in the healthcare industry, is considering production and sales of its new product called stevo. Based on a recent feasibility study report, GB’s management estimates the following cost and price patterns associated with product roll-out: Price per unit

Rs 70.00

Variable cost per unit

Rs 50.00

Fixed Cost

Rs 60000

Required:

Determine the BEP output. September – October 2015 @ SDMIMD, Mysore, India

Solution 6… Recall the BEP Formula: 𝑸𝑩𝑬𝑷 =

𝑭 𝑷 − 𝑽

Where, 𝑸𝑩𝑬𝑷 is the quantity of sales at break-even F is the total fixed cost. P is the price per unit of quantity. V is the variable cost per unit of quantity October 21, 2015 @ SDMIMD, Mysore, India

Solution 6 continued … Therefore, the break-even point for production of stevo is determined thus:

𝑄𝐵𝐸𝑃 =

60000 70 − 50

= 𝟑𝟎𝟎𝟎 𝒖𝒏𝒊𝒕𝒔

September – October 2015 @ SDMIMD, Mysore, India

Illustration 7…

Still on production of G. Benguze Pvt Ltd ’s new healthcare product (stevo)

September – October 2015 @ SDMIMD, Mysore, India

Illustration 7… Q.7: Assume that the same form (GB) wants to buy a new machinery whose investment cost is EUR 764,000. The machinery’s useful life is 5 years only when the disposal value is zero. Annual net cash flow from operation is estimated at EUR 250,000. Required:

Determine the machinery’s ROI.

September – October 2015 @ SDMIMD, Mysore, India

Solution 7… Recall the ARR / ROI Formula:

ROI =

𝑁𝑒𝑡 𝑃𝑟𝑜𝑓𝑖𝑡 −𝐴𝑛𝑛𝑢𝑎𝑙 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

* 100

 First, determining the annual depreciation, we have, 𝐴𝐷 =

𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑈𝑠𝑒𝑓𝑢𝑙 𝑙𝑖𝑓𝑒

=

764,000 5

= EUR 152,800 yearly depreciation September – October 2015 @ SDMIMD, Mysore, India

Solution 7 continued … Therefore, the ARR is determined thus:  RO1 =

250000 −152800 764000

* 100 = 12.72%

September – October 2015 @ SDMIMD, Mysore, India

Illustration 8… Still on G. Benguze Pvt Ltd

September – October 2015 @ SDMIMD, Mysore, India

Illustration 8… Q.8: The same company (GB) is considering investment in either of two projects with the following cash flows: Project A (EUR’000)

Project B (EUR’000)

1000

1200

Year 1

50

600

Year 2

200

400

Year 3

1000

1000

Year 4

100

50

Initial Investment

The cost of capital is expected to be 12% for Project A, and 15% for Project B. Required: Compute the NPV of the two projects and advise GB management on the better option. September – October 2015 @ SDMIMD, Mysore, India

Solution 8… Results from the Excel analysis show: Project

Project A Project B

NPV

-EUR 18380 EUR 269830

 Decision: Project B should be accepted since it has positive NPV in comparison to Project A that has a negative NPV September – October 2015 @ SDMIMD, Mysore, India

Illustration 9…

ILLUSTRATION 9: Still on G. Benguze Pvt Ltd September – October 2015 @ SDMIMD, Mysore, India

Illustration 9… Q.9: The same company (GB) is further considering investment in either of two projects with the following cash flows: Project X (EUR)

Project Y (EUR)

Initial Investment

160000

189966

Year 1

68466

70000

Year 2

70000

80000

Year 3

70000

80000

Year 4

70000

75000

Year 5

70000

70000

The cost of capital is expected to be 33% for Project X, and 28% for Project Y. Required: Compute the PI, NPV, and IRR of the two projects. Advise GB management on the possible option(s) based on hurdle rates (i) 25% and (ii) 30%. September – October 2015 @ SDMIMD, Mysore, India

Solution 9…  Results from the Excel analysis show: Project

PI

NPV

IRR

Project X

0.88

-EUR 2.63

33%

Project Y

1.16

-EUR 15.59

28%

 Decisions: i. Based on the above results, Project Y with PI of 1.16 will be ranked ahead of Project X having 0.88. ii. Both projects have negative NPVs and may be rejected. iii. If decision is to be taken purely on the basis of IRR, then both projects will be accepted if the hurdle rate is 25%. But if the hurdle rate is 30%, project Y will be rejected, while Project X having 33% will be considered. September – October 2015 @ SDMIMD, Mysore, India

Further exercise (1)…

G. Kumar Pvt Ltd.'s mutually exclusive projects

September – October 2015 @ SDMIMD, Mysore, India

G. Kumar Pvt Ltd  G. Kumar Pvt. Ltd. is considering projects X and Y which are mutually exclusive. The cash flows of the project are: Project X EUR

Project Y EUR

Capital Cost

13000

30000

2016

12000

3000

2017

6000

3000

2018

3300

41700

The company’s CFO has computed the IRR of the projects as 20% and 18% respectively, and has recommended that Project X be accepted since it has a higher IRR. The company’s cost of capital is 10%.  Required: Do you agree with the CFO’s evaluation? September – October 2015 @ SDMIMD, Mysore, India

Further exercise (2)…

On most cost-efficient car replacement policy

September – October 2015 @ SDMIMD, Mysore, India

On most cost-efficient car replacement policy

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

Further exercise (2)…  A new car costs Rs.3200. Its sale values and maintenance costs at the end of the first and subsequent years are indicated in the table below. Operating costs remain constant. Year

Sale Value

Annual maintenance costs

1

2000

400

2

1320

480

3

800

600

4

440

800

5

240

1200

6

40

2000

 Required: How often should the car be replaced if the goal is to keep the average total cost per period to the barest minimum? September – October 2015 @ SDMIMD, Mysore, India

Further exercise (3)…

G. PAWA Plc: Optimal replacement period for GP196

September – October 2015 @ SDMIMD, Mysore, India

Further exercise (3)…  The Central Technical Services Department (CTSD) of G. PAWA Plc is in charge of procuring certain specialist equipment such as GP196 which processes work for various divisions and branches of the company. The scope of operations in each branch or division does not warrant the purchase of a machine for the exclusive use of any one division or branch office. GP196 works to full capacity (4000 hours) and work is often contracted out at N5 per hour.  The CTSD has always replaced GP196 every 3 years, because after 3 years, there is a significant probability that the equipment will suffer major breakdown requiring major repairs. Hence, its trade-in value diminishes substantially from the 3rd year upwards (continue in the next slide)… September – October 2015 @ SDMIMD, Mysore, India

Re: Central Technical Services Department continued …..

The company’s CFO is the of the view that the 3-yearly replacement policy for GP196 may not be the best one to adopt. Some other members of senior management are proposing 1-year replacement period since it is an equipment put to heavy use and shared by many departments, while other executives suggest that the equipment should be replaced every two years. The company’s cost of capital is 10%. September – October 2015 @ SDMIMD, Mysore, India

Re: Central Technical Services Department continued …..  Additional Information:  A new machine of the type GP196 currently costs Rs.16000 and during the first year of operation, the machine will give the equivalent of 4000 processing hours and a direct processing cost of N10000.  At the end of the first year, it has a trade-in value of N14000.  During the second year of operation, it will give the equivalent of 3900 processing hours for a direct operating cost of N10,500, and at the end of this period, the trade-in value will be N13000.  In the third year, the effective processing hours will be 3600 for a direct operating cost of N12000 and a trade-in value of N12000.

 Required: Advise the Management of G. PAWA Plc regarding the optimal replacement period for GP196.

September – October 2015 @ SDMIMD, Mysore, India

Further exercise (4)…

To buy or lease? September – October 2015 @ SDMIMD, Mysore, India

Further exercise (4)… A company with a cost of capital of 10% is contemplating the acquisition of a machine that will save Rs2400 in cash operating costs annually over its useful life of 4 years. The machine will have no residual value. The machine may be bought outright for Rs6500 cash. The same machine is available on a 4-year lease at Rs2000 per annum. The company’s borrowing rate is 6%. Required: Should the company buy or lease?

September – October 2015 @ SDMIMD, Mysore, India

Further exercise (5)…

Mars Investment Ltd.'s mutually exclusive projects

September – October 2015 @ SDMIMD, Mysore, India

Mars Investment Ltd.'s mutually exclusive projects…  Mars Investment Ltd is considering investing in either of two projects A and B, each costing EUR 40 million. Company income tax is 30% payable on a preceding year basis. The projected cash flows from the two projects are as shown in the table (right).  Required: Appraise the two projects using the NPV method and make appropriate recommendation to the company’s management.

Year Project A Project B (EUR‘000) (EUR‘000) 1 22000 20000 2 3

22000 24000

20000 22000

4 5 6 7

24000 30000 30000 28000

22000 34000 34000 28000

September – October 2015 @ SDMIMD, Mysore, India

Further exercise (6)…

The G. KAPA Plc Capital Rationing challenge

September – October 2015 @ SDMIMD, Mysore, India

Further exercise…  G. KAPA Plc is a global firm specializing in the production of children’s toys. Owing to the liquidity squeeze and credit control in the financial system, the company finds it difficult to access credit for expansion of its operations. The CFO has advised that available projects could be financed through internally generated revenue, but the constraint here is that the available cash resources of EUR 620000 cannot meet all the available projects whose expected net cash flows are in the table below: Project

Year 0 (EUR)

Year 1 (EUR)

Year 2 (EUR)

Year 3 (EUR)

Year 4 (EUR)

Year 5 (EUR)

A

-246000

70000

70000

70000

70000

-

B

-180000

75000

87000

64000

-

-

C

-175000

48000

48000

63000

73000

-

D

-180000

62000

62000

62000

62000

62000

E

-180000

40000

50000

60000

70000

40000

F

-150000

35000

82000

82000

-

-

September – October 2015 @ SDMIMD, Mysore, India

The G. KAPA project capital rationing case continued…  Additional information:  The six projects, A, B, C, D, E, and F, are not divisible and may not be postponed to a future period and all the projects have similar risks to the existing investments.  Projects A and E are mutually exclusive.  G. KAPA’s cost of capital is 12% per annum. Required: i. Estimate the expected NPV for each of the six projects and their respective PIs. ii. Rank the six projects according to the two Capital Budgeting measures. iii. Recommend to G. KAPA board which projects to choose. September – October 2015 @ SDMIMD, Mysore, India

Keywords…  Accounting concepts, Annual depreciation, Annual equivalent cost, ARR, Average investment, Benefit/Cost Ratio, BEP, Book Value, Capital budgeting, Capital project appraisal, Capital rationing, Cost of Capital, DCF, DCF yield, Discount rate, Fixed Cost, Hurdle rate, Mutually exclusive projects, Leasing, NCF, NINV, Non-DCF approaches, NPV, Investment appraisal, IRR, Pay-back period, Profit Investment Ratio, Profitability Index, R&D, Rate of Return, Residual value, ROI, Value Investment Ratio, Variable Cost, WACC.

September – October 2015 @ SDMIMD, Mysore, India

Stephen ARO-GORDON, Ph.D. Baze University Abuja, Nigeria Department of Financial Mathematics Faculty of Computing & Applied Sciences Email: [email protected] / [email protected]

COM201 Programming 1:

September – October 2015 @ SDMIMD, Mysore, India L01 – Introduction

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