Risk, Npv and Irr

8/2/2019 Risk, Npv and Irr

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Finance and Growth Strategies

QUESTION 1

a) Distinguish between systematic and unsystematic risk. Which is often regardedas the only relevant risk and why?

b) In the context of the Capital Asset Pricing Model how would you define beta?How are betas determined and where can they be obtained? What are the

limitations of betas?

c) What information does beta give to a financial manager?

QUESTION 2

a) What is the time value of money? Why is it important to discount future cashflows?

b) What factors need to be taken into account when choosing an appropriatediscount rate?

c) What do you understand by the terms (i) net present value (NPV) and (ii)internal rate of return (IRR)?

d) Compare and contrast the NPV and IRR.

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CONTENTS

PART ONE: QUESTION 1

1. INTRODUCTION . . . . . . . . . . . . 32. RISK . . . . . . . . . . . . . . 3

2.1 Systematic Risk and Unsystematic Risk . . . . . . 4

2.2 Why Systematic Risk is OftenRegarded?. . . . . . . 5

3. BETA () . . . . . . . . . . . . . 63.1 Definition of Beta . . . . . . . . . . 6

3.2 How to Determine Betas . . . . . . . . . . 7

3.3 Limitations of Betas . . . . . . . . . . 7

3.4 Information Given to a Financial Manager. .. . . . . . 8

4. CONCLUSION . . . . . . . . . . . . 10PART TWO: QUESTION 2

5. INTRODUCTION . . . . . . . . . . . . 116. UNDERSTANDING THE TIME VALUE OF MONEY? . . . . 127. THE IMPORTANT OF DISCOUNT FUTURE CASH FLOWS . . 138. FACTORS OF CHOOSING A DISCOUNT RATE . . . . . 159. NET PRESENT VALUE AND INTERNAL RATE RETURN . . . 16

9.1 Definition of Net Present Value(NPV) . . . . . . . 18

9.2 Definition of Internal Rate Return.(IRR). . .. . . . . 18

9.3 Contradiction between NPV and IRR . . . . . . . 19

10. CONCLUSION . . . . . . . . . . . . 2011. REFERENCES . . . . . . . . . . . .

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1. INTRODUCTIONWhat is the ultimate goal in a diversification strategy? Most investors must say it is to

improve the investment performance by reducing the risk. Certainly, everyone knows

risk is an essential element of strategic management and often appears as on an element of

empirical studies reported in the strategic management literature. It figures prominently

in both management and many empirical studies of industry, firm and business unit

performance (Bettis and Mahajan, 1990).

Two measures of risk have predominated in the strategic management literature: one or

both of the parameters (alpha or beta ) derived from the Capital Asset Pricing Model

(CAPM), including risk-adjusted returns from the CAPM, and variance or its derivatives,

for instance, standard deviation.

Thereinafter, this assignment will concentrate on categorizing risk and evaluating its

relationship with betas from an asset pricing perspective.

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2. RISK

One way to categorize risk is to distinguish between systematic risk and unsystematic risk.

Total risk is the sum of systematic (market) risk and unsystematic (non-market or specific)

risk. Simply, systematic risk is non-diversifiable component of total risk and

unsystematic risk is the diversifiable component of total risk.

Here below is the methods to represent total risk.

Total risk = Systematic risk + Unsystematic risk

= Undiversifiable risk + Diversifiable risk

= Market risk + Issuer risk

2.1Systematic and Unsystematic Risk

William Sharpe (1964) and John Lintner (1965) developed the CAPM to mark the birth of

asset pricing theory. The CAPM extend the model of portfolio choice developed by

Harry Markowitz (1959). In the portfolio theory, Harry Markowitz (1952) introduced the

notions of systematic and specific (unsystematic) risk.

Systematic risk is the risk of holding the market portfolio. As the market moves, each

individual asset is more or less affected. To the extent that an asset participates in such

general market moves, it entails systematic risk. This is a risk that can affect all

companies at the same times, including such occurrences as inflation, fluctuating interest

rates, recession and wars. All those of sources are inherent to the entire market or a broad

range of securiteis.. As a result, it is also known as market risk (Hertz, 1964) or

undiversifiable risk, which is not able to be avoided through diverfication.

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Unsystematic risk affects a very specific group of security or an individual security, and

will often relate to unexpected pieces of good news and bad news relating either to the

company concerned. This is not correlated with general market moves and considered

highly diversifiable (Wanger and Lau, 1971). Also, there is no specific formula to

calculate it and it can be eliminated by a perfectly diversified portfolio. Conversely,

systematic risk cannot be eliminated by diversification, even though the investor has a

portfolio of well diversified assets, but cannot be mitigated by being hedged.

Systematic risk can be measured by using beta. In CAPM approach, this theory suggests

that the expected return of a security equals the risk free rate plus a risk premium (KmRf),

see below CAPM formula. Also, investors will often focus on the impact of systematic

risk.

r = Rf + x (KmRf)

where r is the expected return rate on a security;

Rfis the rate of a risk-free investment, i.e. cash and Treasury bill

Km is the return rate of the appropriate asset class.

2.2Why Systematic Risk is Often Regarded?

According to CAPM, the market compensates investors for taking systematic risk but not

for taking unsystematic risk (Peansell, 1986). This is because specific risk can be

diversified away by investing in several companies operating in many different industries,

leaving only the systematic risk relating to the market as a whole.

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Therefore, finance theory suggests that, when assessing an individual company for your

portfolio, you need only yourself with the effect that the market as a whole will have on

that business. Some companies will be more sensitive to market forces than others and

will, therefore, have a higher systematic risk.

When an investor holds the market portfolio, each individual asset in that portfolio

encompasses specific risk, but through diversification, the investors net exposure is just

the systematic risk.

3. BETA ()

Although investors understand that the risk is tied into the market, which can never go

away. However, it can be measured so that investors can make better decisions.

According to the CAPM approach, beta is a key component, which is used to calculate cost

of equity.

3.1.Definition of BetaAs Fama and French (1992) summarized, the central prediction of CAPM is that the market

portfolio of invested wealth is mean-variance efficient in the sense of Markowitz (1959).

The efficiency of the market portfolio implies that expected returns on securities are a

positive linear function of their market betas (the slope in the regression of a securitys

return on the market return), and market betas suffice to describe the cross-section of

expected returns.

In terms of finance and investing, beta is a measure of a portfolios volatility in relation to

the rest of the market. Also, it is a measure of co-movement, not risk. Instead, it is a

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relative risk measurement tool in the CAPM. Stock analysts use this measure all the time

to get a sense of stocks risk profiles.

The formula for Beta is:

= [Cov (r, Km)] / [Standard Deviation (Km)]

where r is the expected return rate of investment;

Km is the return rate of the appropriate asset class.

The measure of risk for a particular company against the market as a whole is called its

beta, where a beta of 1.0 indicates that firm will react exactly as the market does. A more

sensitive company has a beta of more than 1.0 and a less sensitive company will have a

beta of less than 1.0. Company with high beta is supposed to be riskier but provide a

potential for higher returns; conversely, low-beta company pose less risk but also lower

returns.

3.2.How to Determine BetasThere are several factors to determine the Beta Coefficient: (1) the variability of the

individual stock return, (2) the variability of the market return, and (3) the correlation

between the return on the security and the return on the market.

The reason is that beta is based on the historical performance of a stock. It should not be

used as an indication of how the stock may perform in the future.

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3.3.Limitations of Betas

Unfortunately, betas have limitations. There is uncertainty about CAPM beta. The

CAPM beta is derived from estimation procedures and is subject to error. It may not be

constant through time.

In particular that time-statistic for the estimated beta appearing in a CAPM regression

output should be statistically significant, and the regression should be reasonably high

before we draw any conclusions about beta.

While beta does say something about price risk, it does have its limits for financial

manager looking for fundamental risk factors. Beta says nothing about the price paid for

the stock in relation to its future cash flows. For example, a value investor would argue

that a company represents a lower-risk investment after it falls in value. Investors can get

the same stock at a lower price despite the rise in the stocks beta following its decline.

3.4.Information Given to a Financial ManagerIf the financial manager is the follower of CAPM, beta is a useful measure. Financial

manager can utilize beta to assess the risk, which is important to be considered for the

stocks price variability. Also, beta offers a clear, quantifiable measure of its systematic

risk. Surely, there are variations on beta depending on things, such as the market index

used and the time period measured, but broadly speaking, the notion of beta is fairly easy to

understand.

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For example, to estimate the cost of equity (Ke) we can use the following formula of

CAPM in a Company ABC:

Ke = Rf + x (KmRf)

where Rfis the rate of a risk-free investment, i.e. cash and Treasury bill

Km is the return rate on the market portfolio.

is the Company ABCs beta

The Company ABCs beta is a measure of its systematic risk. This risk is function of the

sensitivity of a company ABCs share price to micro-economic factors, such as inflation

and interest rates. The more sensitive a Company ABCs share price to these factors the

higher beta. An average company will have a beta of one. A company with more

systematic risk than average will have a beta in excess of one and a company with less

systematic risk than the average will have a beta of less than one.

If Company ABC has a beta 1.5, the risk free rate of return is 5% and the market return is

10%, the required rate of return according to the CAPM is:

Ke = 5% + 1.5 x (10% 5%)

= 12.5%

Besides, on the individual asset level, measuring beta can give clues to volatility and

liquidity in the marketplace. For example, Company ABC has a beta 1.5. A beta of 1.5

implies that an investments returns will likely be 1.5 times as volatile as that of the market.

While Company ABCs beta drop down to 0.75, which less than 1.0, it means the security

moves in the same direction as the market, but not as far as the market. Besides, a beta of

0.75 means the security is 25% less volatile than the market.

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Based on the betas, there are the clues given to financial manager to well understand the

volatility and liquidity in the marketplace. Also, the cost of capital represents the discount

rate used to arrive at the present value of a companys future cash flows. All things being

equal, the higher a companys beta is, the higher its cost of capital discount rate. The

higher the discount rate, the lower the present value placed on the companys future cash

flows. In short, beta can impact a companys share valuation.

4. CONCLUSIONNo matter you are a value investor or fundamental investor, risk will be always a cause for

concern. It is important to clearly make the distinction between systematic risk and

unsystematic risk, although there is always a fear of unknown.

How to measure the risk and volatility on a portfolio level? Beta is an useful tool, even

though it goes to some lengths but also deal with the limitations as mentioned in the above

paragraphs. Please remember that beta is based on the historical performance of a stock.

High betas may mean price volality over the near term, but they do not always rule out

long-term opportunity. Also, we should not confused the beta with the attractiveness of

the investment.

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5. INTRODUCTION

We all know that money deposited in a savings account will earn interest. Because of this

universal fact, everyone would prefer to receive money today rather than the same amount

in the future. The concern is whether the money available at the present time is worth

more than the same amount in the future or not.

But how do we know if it is worth or not? In financial, there are a variety of measures

evolved over time for analyzing a capital budgeting proposal. One of older methods is the

payback period, which has the deficiency of not using time value techniques and will

eventually fall by the wayside. However, they are replaced in companies by the newer,

superior methods of evaluation. The newer methods use time value of money (TVM)

concept. (Gallager and Andrew, 1996).

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6. UNDERSTANDING THE TIME VALUE OF MONEY

One of the most fundamental concepts in finance is that money has a time value.

According to time value of money (TVM), money in hand today is worth more than

money you expected to be received in the future. The reason is straightforward: A

dollar you receive today can be invested such that you will have more than a dollar at some

future time. You could use this money to pay off an all or part of a loan, or invest this

money in an interest-bearing account and earn interest on it.

To summarize the concept of time value, it is A dollar today is worth more than a dollar

tomorrow. This explains in part why the value of money is related to time, Also, it

refers to as present discount value.

Besides, TVM is related to another concept called opportunity cost. The cost of any

decision includes the cost of the best-forgone opportunity. Applying this concept, if you

spend your $500 on any other use, it will endure you with opportunity cost and lose the

value of initial money ($500) would grow over time.

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7. THE IMPORTANT OF DISCOUNTED FUTURE CASH FLOWS

Using the TVM concept, discounted future cash flow (DCF) analysis is widely used to

value a project, company, or asset, and is the process of finding the present value of

amount of cash generated in future period. All future cash flows are estimated and

discounted to give their present values. The discount rate used is normally equivalent to

the appropriate cost of capital.

To calculate for only one future cash flow in one future period, mathematically it is

expressed as:

FV

DPV=

(1 +r )n

where DPVis the discounted present value of the future cash flow (FV)

FVis the nominal value of a cash flow amount in a future period;

ris the discount rate

n is the time in years before the future cash flow occurs.

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For a decision which generates multiple cash flows in multiple time periods, all the cash

flows must be discounted and then summed into a single net present value. For example,

where the investor invests $100,000 in cash (at time 0 = now) to earn the following cash

flow (totally $165,000) and the given discount rate (r) is 15% per year, then:

Year Future Cash Flow

(Future Value $)Calculation Discounted ($)

1 10,000 10,000 / (1.15)1 8,696

2 20,000 20,000 / (1.15)2 15,123

3 40,000 40,000 / (1.15)3 26,301

4 60,000 60,000 / (1.15)4 34,305

5 35,000 35,000 / (1.15)5 17,401

Total Amount of Discounted Cash Flow: 101,826

The new present value (NPV) is (101,826-100,000) = 1,826.

Based on the above calculation, the net present value is positive. This is an importance

that the net present value of the decision after discounting all future cash flows at least be

positive. If negative, it means that the investment decision would actually lose money

even if it appears to generate a nominal profit. For instance, if the expected sales price of

investment in the above example was less than $165,000 in five years, but $130,000 in five

years or 165,000 in six years, then on the above assumptions the investment would actually

cause investor to lose money in present-value terms.

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8. FACTORS OF CHOOSING A DISCOUNT RATE

Discount rate is also a key variable of the DCF analysis. It is often to use the weighted

average cost of capital (after tax) in firm as discount rate. Since the NPV is very sensitive

to changes in the discount rate, the prudent investor will test a range of reasonable discount

rate to get a sense of the range of possible results.

To some extent, the selection of the discount rate is dependent on the rate of return for the

NPV calculation, and the use to which it will be put. If determining whether the

investment will add value to the value to the firm, using the firms weighted average cost

of capital may be appropriate. Besides, the reinvestment rate may be a better choice while

investor is trying to decide between alternative investments in order to maximize the value

of the firm.

There is another approach to choosing the discount rate factor. It is to decide the rate

which reflects the opportunity cost of investment. For example, using reinvestment rate

of the firm, it can be defined as the rate of return for the investment on average. In a

capital constrained environment, it is useful to value the investment by the reinvestment

rate rather than the possibly lower cost of capital as the discount factor.

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9. NET PRESENT VALUE AND INTERNAL RATE RETURN

The two most-used measures for evaluating an investment are the net present value and the

internal rate of return.

Thereinafter, we will discuss these two measures in connection with this income stream of

Project Y:

Year 0 1 2 3 4 5 6

Income $ (10,000) 2,000 2,000 2,000 2,000 2,000 2,000

9.1.Definition of Net Present Value (NPV)The net present value (NPV) is simply the sum of the present value (PV) of a projects cash

flow. The formula of NPV is:

where NPVis the net present value of a whole income stream

Iis income amounts for each year

ris the discount rate

n is the time in years before the future cash flow occurs.



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The given discount rate (r) is 5% per year.

Year 0 1 2 3 4 5 6

Income $ (10,000) 2,000 2,000 2,000 2,000 2,000 2,000

Discount $ 1,905 1,814 1,728 1,645 1,567 1,492

The NPV of Project Y is ($10,151 10,000) = $151.

If the NPV is positive, it says that the company expects to receive benefits that are large

enough to repay the company for (1) the assets cost, (2) the cost of financing the project,

and (3) a rate of return that adequately compensates the company for the risk found in the

cash flow estimates. If the NPV is negative, the benefits are not large enough to cover all

three of the above, and therefore the project should be rejected.

If the project has NPV = $0, then the project generates exactly enough cash flows to

recover the cost of the investment and to enable to company to earn their required

rate of return.

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9.2.Definition of Internal Rate Return (IRR)

The Internal Rate of Return (IRR) is the discount rate that forces the present value of the

benefits to equal the present value of the cost, then, the NPV will be equal to zero. It is

the rate of return the project is expected to generate.

Based on the Project Y example, IRR is found by trial and error.

IRR 4% 5% 5.47% 6%

NPV ($) 485 151 0 (165)

In the example, while setting the discount rate to 0.0547, the NPV becomes zero. This

discount rate, 5.47%, is the internal rate of return for this investment.

The particular discount rate, IRR, forces the projects NPV to equal to zero rather than

using the cost of capital. Thus, these two approaches differ in only one respect. In NPV

method, a discount rate is specified and the equation is solved for NPV. In the IRR

method, the NPV specified to equal zero and the discount rate (IRR) that forces this

equality is found.

9.3.Contradiction between NPV and IRRTo understand how the NPV and IRR can give seemingly different advice is to use, it can

be found the cues from the net present value curve (NPV curve). The NPV curve shows

the relationship between the discount rate and the net present value for a range of discount

rates.



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The NPV curve, the relationship between the discount rate and the net present value has a

formula that can be written like this:

where NPVis the net present value of a whole income stream

I is income amounts for specific year. The subscripts (which are also the

exponents in the denominators) are the year numbers, starting with 0, which is

this year.

ris the constant discount rate

n is the number of years the investment lasts.

The underlying cause of ranking conflicts between NPV and IRR is the reinvestment rate

assumption. All discounted cash flow methods implicitly assume that cash flows can be

reinvested at some rate, regardless of that actually is done with the cash flows.

The process of discounting is the reverse of compounding. Because compounding

assumes reinvestment, so does discounting. NPV and IRR are both found by discounting,

so they both implicitly assume some discount rate. Inherent in the NPV calculation is the

assumption that cash flows can be reinvested at the required rate of return in project, or

cost of capital, while the IRR calculation assumes reinvestment at the IRR rate.

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10.. CONCLUSION

To do only one investment, we should choose the one with the highest NPV at the discount

rate appropriate to us. A problem with that advice, though, is that discount rates can

change with general economic conditions. Thus, we are more confident about choosing

one investment over another if your chosen investment has a higher NPV over a board

range of possible discount rates.

Regardless of what happens in the future to discount rates, we will be better off with the

higher NPV investment than with the lower NPV investment at all discount rates.

But which capital budgeting methods are better? NPV method or IRR method? The

IRR method seems to be the more popular of the two methods (by a small margin).

However, the NPV method is superior to IRR method. The reason is the cash inflows

generally are used as substitutes for outside capital. That is, cash flows replace outside

capital, and save the firm the cost of outside capital.

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11.. REFERENCES

Baker, Samuel L. (2000). "Perils of the Internal Rate of Return". Retrieved on January 12,

2007.

Bettis, R.A. and V. Mahajian (1990). Risk analysis in corporate performance

measurement, in R. A. Bettis and H. Thomas (eds.), Risk, Stategy and Management, JAI

Press, Greenwich, CT, pp.83-110.

Fama, E. F. and K. R. French (1992). The cross-section of expected stock returns,

Journal of Finance, 67:2, pp.427-465.

Gallager, T and Andrew Jr., J., (1996). Financial Management : Principals and Practices,

Upper Saddle River, NJ: Prentice Hall.

Hertz, D. B. (1964). Risk Analysis in Capital Investment, Harvard Business Review,

January-February 1964.

Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments

in Stock Portfolios and Capital Budgets,Review of Economics and Statistics, 47:1, 13-37.

Markowitz, H. M. (1952). Portfolio selection,Journal of Finance, 7:1, 77-99.

Markowitz, H. M. (1959). Portfolio sections: Efficient Deversification of Investments,

Cowles Foundation Monograph No. 16, New York: John Wiley & Sons, Inc.

Peansell, K. (1986). The Capital Asset Pricing Model, Issues in France, M. Firth 1986,

p.86.

Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under

Conditions of Risk,Journal of Finance, 19:3, pp. 425-442.

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Sharpe, W.F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under

Conditions of Risk,Journal of Finance, 19:3, pp. 425-442.

Wanger, W. H. and S. Lau (1971). The Effects of Diversification on Risk, Financial

Analysts Journal, November-December 1971, pp.107-109.

Websites

Part One

a) http://www.cowlitzbank.com/resources/public/downloads/Reduce%20risk.diversify.pdf

http://findarticles.com/p/articles/mi_qa5386/is_200609?pnum=4&opg=n21399513&tag

=artBody;col1

b) and c)

http://www.investopedia.com/articles/stocks/04/113004.asp

Part Two

a) www.investopedia.com/articles/03/082703.asp

www.12manage.com/methods_npv_zh.html

b) http://www.answers.com/topic/discounted-cash-flow

c) and d)

http://www.realdata.com/ls/alphabet-soup.html

http://www.peoi.org/Courses/finanal/ch/ch10e5.html#anchor2350002
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