Advanced Capital Budgeting-raw

7/31/2019 Advanced Capital Budgeting-raw

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Copyright 2000 Prentice Hall

CHAPTER

2Advanced Capital

budgeting


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The possibility that an actual return will

differ from our expected return.

Uncertainty..

Differences between Risk & Uncertainty

Probability is known-Risk

Probability is not known- Uncertainty

What is Risk & Uncertainty?


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The Economy in general

Technological factors

Competition

Political factors Inflation

Consumers preference

Internal factors of business enterprise

Financial risk

Natural uncertainty

Human factor

Factors Creating Risk/Sources of risk


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Business Risk

General Economical condition, Technological change, Competitive

market, Political situation, Inflation, Consumers behavior change,

Internal factors of business enterprise may create risk for business

enterprize.

Financial Risk

Financial risk is that part of total risk that management introduces

through debt financing.

According to John. J. Hampton, Financial risk is the chance that

investment will not generate sufficient cash flows to cover interest

payment of money borrowed to finance it or principal repayments on

the debt to provide profits to the firm.

Classification of Risk


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Some risk can be diversified away

and some can not.

Market Risk is also calledNondiversifiable

risk. This type of risk can not bediversified away.

Firm-Specific risk is also calleddiversifiablerisk/ Avoidable risk. This type of risk can

be reduced through diversification.


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Market Risk

Unexpected changes in interest rates.

Unexpected changes in cash flows

due to tax rate changes, foreign

competition, and the overall businesscycle.


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Firm-Specific Risk

A companys labour force goes on strike.

A companys top management dies in aplane crash.

A huge oil tank bursts and floods a

companys production area.


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Capital Budgeting & Uncertainty/Evaluating

risky investment projects

Expected cash flows from an investment

project are not certain. There may be

uncertainty which creates risk.

So, it is needed to consider risk in case oftaking decision through Capital Budgeting.


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State of Probability Return

Economy (P) A B

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%


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Individual Securities

The characteristics of individual securities

that are of interest are the:

Expected Return

Variance and Standard Deviation

Covariance and Correlation


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Proposal A Proposal B

Probability Cash Inflow Probability Cash Inflow

.10

.20

.40

.20

.10

13,00013,50014,00014,50015,000

.10

.25

.30

.25

.10

12,00013,00014,00015,00016,000

From the following information of two investments proposals each costingTk. 40,000 for each project.

You are required to calculate the riskiness of theproposals.


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Formula of Expected Return

For the firm, the expected return of each ofthe project is just a weighted average:

R =

R = P1*R1 + P2*R2 + ........+ Pn*Rn

n

i

RiPi

1

.

Or,


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Calculation of Expected Return

For Project A,

Expected return, R(A) = (.10 *13,000) + (.20 *13,500) +

(.40 *14,000) + (.20 *14,500) + (.10 *15,000)

= Tk. 14,000

For Project B,

Expected return, R(B) = (.10 *12,000) + (.25 *13,000) +

(.30 *14,000) + (.25 *15,000) + (.10 *16,000)

= Tk. 14,000


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Based only on your

expected return

calculations, whichProject would you

prefer?


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RISK?

Have you considered


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How to measure risk

Variance,

Standard Deviation (S.D),

Co-efficient of Variation (COV)

Risk


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A more scientific approach is to examine

the shares STANDARD DEVIATION of

returns.

Standard deviation is a measure of the

dispersion of possible outcomes.

The greater the standard deviation, thegreater the uncertainty, and therefore ,

the greater the RISK.

How do we Measure

Risk?


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Formula of Standard Deviation

=

Pi)(1

2

n

i

RRi

=

(R1-R)2* P1 + (R2-R)

2* P2 + ........+ (Rn-R)2* Pn =

Or,


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Proposal A Proposal B

Probability Cash Inflow Probability Cash Inflow

.10

.20

.40

.20

.10

13,000

13,50014,00014,50015,000

.10

.25

.30

.25

.10

12,000

13,00014,00015,00016,000

From the following information of two investments proposals each costing

Tk. 40,000 for each project.

You are required to calculate the riskiness of theproposals.


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For Project A,

(A) = (13,000-14000)2 * .10 + (13,500-14000)2 * .20 +

(14,000-14000)2 * .40 + (14,500-14000)2 * .20 +

(15,000-14000)2 * .10 = Tk. 548

For Project B,

(B) = (12,000-14000)2 * .10 + (13,000-14000)2 * .25 +

(14,000-14000)2 * .30 + (15,000-14000)2 * .25 +

(16,000-14000)2 * .10 = Tk. 1140

Calculation of Standard

Deviation


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Formula of Co-efficient of

Variation

Standard Deviation

COV = * 100

Expected Value


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Calculation of Co-efficient of

Variation

For Project A,

COV(A) = (548/14000) *100 = 3.91%

For Project B,

COV(B) = (1140/14000) *100 = 8.14%


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Which Project would you prefer?

How would you decide?


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Project A Project B

Expected Return Tk. 14000 Tk. 14000

Standard Deviation Tk. 548 Tk. 1140

Co-efficient of Variation 3.91% 8.14%

Summary


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Certainty Equivalent Approach

CF1 CF2 CFn

(1+RF)1 (1+RF)

2 (1+RF)n+ . . . ++ -ICONPV =

CF1 = Expected Net cash inflow * Certain equivalent factor

Where NPV= Net Present Value

CF1 = Certain annual cash inflow in year 1

RF= Risk free rate of return

ICO = initial Cash outlay

n = the projects expected life


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Risk Adjusted Discounting RateApproach

CF1 CF2 CFn

(1+R)1 (1+R)2 (1+R)n+ . . . ++ -ICONPV =


CF1 = annual cash inflow in year 1

R= Discounting Rate



)(F

MiF

i RRRR


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Example:

Suppose the Risk-free rate is 6%, the average return on thestock Market Index is 12%, and Company X has a beta of1.2.According to the CAPM, what should be the required rateof return on Company X shares?

Rj = Rf + (Rm - Rf)

Rj = .06 + 1.2 (.12 - .06)

Rj = .132 = 13.2%

According to the CAPM, Company X shares should bepriced to give a 13.2% return.

The CAPM equation:

Rj = Rf + j (Rm - Rf)

where:

Rj = the Required Return on security j,

Rf= the risk-free rate of interest,

j = the beta of security j, and

Rm = the return on the market index.


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Net Present Value (NPV)

CF1 CF2 CFn

(1+k)1 (1+k)2 (1+k)n+ . . . ++ -ICONPV =

NPV = the total PV of the annual net cash flows - the initial outlay.


CF1 = annual cash flow in year 1

k = appropriate discount rate or required rate of return (cost of capital)




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Evaluating risky investment projects

A company is considering two mutually exclusive investments costing tk. 90,000 each.

Expected life for both projects is 5 years. Cash flows associated with the twoprojects are as follows:

Calculate Expected value for both projects

Calculate Standard Deviation for both projects

Calculate Coefficient of variation for both projects

Which project is more risky? Which project should be accepted and why ?

Probability

Distribution

Period 1 Period 2 Period 3 Period 4 Period 5

NCB (tk.) NCB (tk.) NCB (tk.) NCB (tk.) NCB (tk.)A B A B A B A B A B

0.100.250.300.250.10

3000040000500006000070000

2000040000600005000070000

2000030000400005000060000

5000025000350004500070000

2000030000400005000060000

1000020000500006000050000

1500035000650002500045000

1500055000450003000040000

3000045000550005000040000

2000025000400001000035000


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Evaluating risky investment projects

A company is considering two mutually exclusive investments. Cost of capital is 10% and

the current risk-free rate of return is 7%. Cash flows associated with the twoprojects are as follows:

Project A Project B

Initial Investment Tk. 150,000 Initial Investment Tk. 150,000

Year Certaintyequivalent factors

(Expected Value)Cash inflows (Tk.)

Certaintyequivalent factors

(Expected Value)Cash inflows (Tk.)

123

45

0.950.900.85

0.800.75

50,00045,00055,000

60,00070,000

0.900.850.80

0.750.70

40,00050,00060,000

65,00070,000

Calculate the net present value (ignoring risk) for each project.

Calculate the Certainty equivalent net present value for each project. Which project should be

accepted and why?

Calculate the Risk-adjusted discount rate for both projects. Consider Project A has a RADR

factor of 1.20 and Project B has a RADR factor of 1.80. Market return for both projects is 12%

Calculate the Risk-adjusted NPV for each project. Which project should be accepted andwhy?


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CF1 CF2 CFn

(1+RF)1 (1+RF)2 (1+RF)n+ . . . ++ -ICONPV =

CF1 = Expected Net cash inflow * Certain equivalent factor

CF1 CF2 CFn

(1+R)1

(1+R)2

(1+R)n

+ . . . ++ -ICONPV =

)( FMiFi RRRR

CF1 CF2 CFn

(1+k)1 (1+k)2 (1+k)n+ . . . ++ -ICONPV =

1

2

4

3


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Project A Project B

NPV (Ignoring risk) Tk. 58,559 Tk. 60,772

NPV (certainty equivalent) Tk. 42,279 Tk. 32,076

Risk adjusted discount rate 13% 16%

NPV (risk adjusted discount rate) Tk. 42,728 Tk. 29,307

Summary


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C i ht 2000 P ti H ll

Practice at Home

All examples related the topics

covered

Problems & Solution:1- 5 (Page:69)

Financial Management

- Prof. Shahjahan Mina

Advanced Capital Budgeting-raw

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