chap 18 risk management & capital budgeting

Risk Management & Capital Budgeting

Prof. Vijay Karkhanis 1

Concept of Risk• Risk exists when there is a range of possible

outcomes associated with a decision and the probabilities of those outcomes occurring are known . If those possibilities are not known, the decision maker is said to face uncertainty.

• A strategy is a plan or course of action designed to achieve a management goal.

• A state of nature refers to a condition that may exist in the future that will have a significant effect on the success of a strategy.

• An outcome is the gain or loss associated with a particular combination of strategy and state of nature.

• A payoff matrix lists the outcomes associated with each strategy-state of nature combination



Sample Payoff Matrix

Payoff Matrix : Profits ( Rs, Crores) for Each Strategy – State of Nature (Economic Condition) Combination

Strategy Recession Normal Boom

New Plant - 40 25 40

New Marketing Programme - 20 35 70

New Product Design - 15 30 60



Risk and Decision MakingPeople respond to the same risky choices in different

ways as per their attitude. Rational decision making requires that the expected return be determined and the risk be measured.

Risk – Return Evaluation Statistics :Given a set of outcomes Xi, and the probability of

each occurence, Pi, these statistics are : nExpected value or Mean (Expected Return): = Pi(Xi) i=1 ---------------------------- nStandard Deviation (Measure of Risk): Pi(Xi- )2 i=1

Coefficient of Variation (Risk per rupee of Return): v =



Probability Distribution for Two Investment Alternatives

Probability Distribution for Two Investment AlternativesState of Nature Probability (Pi) Outcome (Xi)

Investment I

No Inflation 0.20 100

Moderate Inflation 0.50 200

Rapid Inflation 0.30 400Investment I

No Inflation 0.20 150

Moderate Inflation 0.50 200

Rapid Inflation 0.30 250



Investment - I

v1 Investment -II

v2



Risk PreferencesIn general , investment that offer higher expected

returns also involve greater risk.• Behavior is said to be :

– Risk averse, if the certainty equivalent of gamble is less than the expected value of the gamble.

– Risk neutral, if the certainty equivalent of gamble is equal to the expected value of the gamble.

– Risk seeking, if the certainty equivalent of gamble is greater than the expected value of the gamble.

• Equivalently, behavior is :– Risk averse, if the utility of expected wealth is greater

than the expected utility of wealth– Risk neutral, if the utility of expected wealth is equal to

the expected utility of wealth– Risk averse, if the utility of expected wealth is less than

the expected utility of wealth



Risk ManagementDecision makers manage risk in four fundamental ways :• Insurance – purchase insurance to protect against losses

associated e.g. fire, theft, accident, natural disasters like flood or hurricane etc.

• Hedging – Buying various contracts in the financial markets against financial risks such as a crop failure, stock market decline, currency fluctuations.

• Diversifying – reduce risk by diversifying its activity so that a decline in one market may be offset by better conditions in another market.

• Discounting - differential risk associated with various actions being contemplated by the firm can be adjusted for by adding a risk premium to the interest rate used to discount projected cash flows as the basis for comparison.



Risk Management• Insurance :

– The market for insurance exists because many people are Risk Averse. Market for gambling exists because some people are Risk Seekers.

– Some people exhibit risk-seeking and risk-averse behaviour at the same time.

• Discount Rate – To adjust for risk is to use a risk adjusted discount rate in determining the Net Present Value of the future profits associated with an Investment. Given the stream of future profits, pt, the basic evaluation formula is, n

NPV = t(1 + r) t t =1

Where, r = risk adjusted discount rate or interest rate.t =time period from 1 to n years.



Evaluating Capital project

Payback Period : It is the Number of Years that it takes for the Net Cash Flows (undiscounted) to equal the cost of project is defined as the Payback Period. Default rule is to select the project that has shortest payback period.

Example :Initial Payback

Project Cost 1 2 3 4 5 Period--------- ---------- -------- -------- -------- -------- -------- ------------ A 1,000 500 500 1,000 1,000 1,000 2 B 1,000 250 250 500 5,000 10,000 3

Note : As per payback period rule, Project A would be selected, but Project B should be preferred because it has much larger cash flows in periods four and five. The Net Present Value for Project B will be higher than Project A. Thus Payback period method failsbecause it does not consider all cash flows.



Risk Management

• Hedging :– Purchasing of forward and/or

futures contracts that guarantee a specified price.

• Diversification – firm can reduce risk by diversification of its assets i.e. it can invest in a variety of activities so that a decline in one area of business might be offset by an expansion of another.



Capital BudgetingCapital projects are those that are expected to

generate returns for more than one year. Capital Budgeting refers to the process of planning capital projects, raising funds and efficiently allocating resources to those capital projects include new factories, machinery, automobiles, computers, outlay for R & D, Advertising etc. if returns on those projects will flow for more than one year.

Categories of Capital Projects :– Cost Reduction– Output Expansion– Expansion by Developing New Products / Markets– Government Regulation



Capital BudgetingKey Concepts :• Capital Budgeting refers to the process of planning

capital projects, raising funds, and efficiently allocating those funds to Capital Projects.

• Capital Expenditures are made in order to reduce cost, increase output, expand into new products or markets, and / or meet government regulations.

• In general, capital expenditures are made until the rate of return on the last rupee invested equals the marginal cost of capital.

• The demand for capital function shows the amount of capital spending that will be made at each cost of capital.



Capital Budgeting Process

Year 1 Year 2 Year 3 Year 4 Year 5Sales 1,00,00,000 1,10,00,000 1,21,00,000 1,33,10,000 1,46,41,000

Less: Variable Cost

40,00,000 44,00,000 48,40,000 53,24,000 58,56,400

Less : Fixed Cost

1,00,000 1,00,000 1,00,000 1,00,000 1,00,000

Less : Depreciation

30,00,000 30,00,000 30,00,000 30,00,000 30,00,000

Profit Before Tax

29,00,000 35,00,000 41,60,,000 48,86,000 56,84,600

Less : Income Tax

11,60,000 14,00,000 16,64,000 19,54,400 22,73,840

Profit After Tax 17,40,000 21,00,000 24,96,000 29,31,600 34,10,760

Plus : Depreciation

30,00,000 30,00,000 30,00,000 30,00,000 30,00,000

Net Cash Flow 47,40,000 51,00,000 54,96,000 59,31,600 64,10,760Plus : Salvage value of machinery 40,00,000

Recapture of Working Capital 30,00,000Net Cash Flow (Year 5) 1,34,10,760

• Projecting the Cash Flows : Initial Cost of Project = Machinery Rs. 1.5 Cr.+ Reorg. Rs. 0.2 Cr. + WC Rs. 0.3 Cr. i.e. Total Rs. 2.0 Cr.



Capital Budgeting Process (contd.)

Evaluating the Capital Project :1. Consider all Relevant Cash flows.2. Discount cash flows using the firm’s opportunity cost

of capital.3. Select the one project from a set of mutually exclusive

projects that maximizes the value of the firm.4. Allow each project to be evaluated independently of all

others being considered.Three evaluation techniques will be considered :a) Payback Period, b) Internal Rate of Return, and c) Net

Present Value.




Payback Period : It is the Number of Years that it takes for the Net Cash Flows (undiscounted) to equal the cost of project is defined as the Payback Period. Default rule is to select the project that has shortest payback period.

Example :Initial Payback

Project Cost 1 2 3 4 5 Period--------- ---------- -------- -------- -------- -------- -------- ------------ A 1,000 500 500 1,000 1,000 1,000 2 B 1,000 250 250 500 5,000 10,000 3

Note : As per payback period rule, Project A would be selected, but Project B should be preferred because it has much larger cash flows in periods four and five. The Net Present Value for Project B will be higher than Project A. Thus Payback period method failsbecause it does not consider all cash flows.




Internal Rate of Return : It is the discount rate that equates the present value of the cash flows with the initial investment cost. The formula is,

n C = t(1 + r*) t

t =1Where, At = Net Cash Flow in Year ‘t’, C = Initial Cost of

Project, and n = life of the project.Thus solving previous example,

47,40,000 51,00,000 54,96,000 59,31,600 1,34,10,760------------ + ------------ + ------------- + ------------- + ----------------- + = Rs. 2,00,00,000

(1+ r*)1 (1+ r*)2 (1+ r*)3 (1+ r*)4 (1+ r*)5

Solving for r* we get r* = 0.179 or 17.9 percent. The decision rule is that if “r*” is greater than the Cost of Capital, the investment should be made.




Net Present Value : It consists, of comparing the present value of all Net Cash Flows ( approximately discounted using the firm’s Cost of capital as discount rate ) to the initial investment cost. If NPV > 0 i.e.

n NPV = t(1 + r*) t) – C > 0

t =1Where, At = Net Cash Flow in Year ‘t’, C = Initial Cost of

Project, and n = life of the project.Thus solving previous example,

47,40,000 51,00,000 54,96,000 59,31,600 1,34,10,760NPV = ------------ + ------------ + ------------- + ------------- + ----------------- - 2,00,00,000 =

35,89,004 (1.12)1 (1.12)2 (1.12)3 (1.12)4 (1.12)5

The value of NPV is > 0, the proposal passes the test , so it is a feasible project.




Comparison of NPV & IRR Methods : While evaluating single project both methods give consistent results i.e. if NPV is positive then IRR will be greater than firm’s cost of capital.

Cost, Cash Flow, and Evaluation Criteria Data for Two Capital Investments

Project A Project B

Initial Cost 1,000 1,000

Net Cash Flows (Year)1 450 -3002 450 03 450 6004 450 6005 450 2000

Evaluation CriteriaNPV (12% DR) 622 675

IRR 34.9 24.2



Capital Budgeting Process (contd.)Key Concepts of Evaluating the Capital Project :• The Internal Rate of Return is that discount rate that equates

the present value of all future Net cash Flows to the Cost of Investment. If the IRR on investment exceeds the Cost of Capital, the investment will increase profits.

• Using the Net Present Value evaluation technique , if present value of all future Cash Flows ( discounted by the firm’s Cost of Capital) exceeds the initial cost of the project, the investment should be made.

• The use of the NPV technique will always lead to investment decisions that maximize the value of the firm.

• Generally, the NPV and IRR methods yield consistent accept / reject signals. However, when comparing two mutually exclusive projects, the relative ranking of the projects can be different using the two methods because the IRR technique assumes that future cash flows can be reinvested at the Internal Rate of Return for the project being evaluated.



The Cost of CapitalThe us of NPV and IRR methods requires that future cash flows be discounted

by the firm’s cost of the funds used to pay for the cost of the project. The cost of such funds is called as “Cost of Capital”. In general, the cost of capital is the return required by investors in the debt and equity securities of the firm. There are three sources of funds viz. retained earnings, debt and equity. The cost of using retained earnings for capital earnings is approximately the same as the cost of common stock.

Cost of Debt Capital : The cost is the net or after tax interest rate paid on that debt. It is the after tax cost that is important. For a given interest rate (i) and marginal tax rate (t), the after tax cost of debt (rd) is given byrd = i(1 – t)

e.g. if the firm borrows at a 10 % interest rate and faces a 40% marginal tax rate, its after-tax cost of debt capital isrd = 0.10 ( 1 – 0.40) = 0.06 or 6 percent

If firm is not earning profits, the pre-tax and after-tax interest rates will be the same because the marginal tax rate is zero. Firm should be concerned with marginal cost of capital and not the average cost of capital, because the concern is raising new capital.



The Cost of CapitalCost of Equity Capital : Determining cost of equity

capital from retained earnings or sale of common stock is more controversial than determining the cost of debt. Note that dividends are not deductible from income when computing income taxes, so the firm’s tax rate does not play a direct role in determining the cost of equity capital. There are three approaches to estimating this cost. i) Risk-Free Rate Plus Risk Premium, ii) Discounted Cash Flow, iii) Capital Asset Pricing Model (CAPM).We will study only one approach i.e. Discounted Cash Flow in detail.



Discounted Cash FlowAs the value of the firm is the present value of all future profits, the

value of a share of common stock is the present value of all future dividends using the investor’s required rate of return (re ) as the discount rate, i.e. one share of stock entitles the owner to receive a series of payments (dividends) roughly equivalent to an annuity. Thus, the value of share should equal the present value of the annuity. If the current dividend per share (D0) is expected to remain constant, the value or price (P) of a share will be,

P = D0[ t = 1 ( 1 + re )t

It can be shown that the bracketed term reduces to ( 1/ re )So that the value of a share of stock is simply the dividend rate divided by the

required rate of return i.e. P = D0 / re , However, if the dividend is expected to increase over time at an annual rate of g, it can be shown that the price per share will be given by P = D0 / (re – g), solving equation for re yields an equation for the cost of equity capital,re = (D0/P) + g



Composite Cost of CapitalMany firms attempt to maintain a constant or target capital

structure, e.g. the management of a manufacturing business prefer a capital structure that is 30% debt and 70% equity. Capital would be raised periodically both by incurring debt and by selling stock. The differences in capital structure reflect the preference for risk on the part of owners and nature of business. A firm with a target capital structure may maintain two separate ledgers, i) list of capital projects and 2) List of financing plans (borrowing, sale of stock, etc.)

The Composite Cost of Capital (rc) is the weighted average of the after tax cost of debt (rd) and equity (re) capital. The weights are the proportions of debt (wd) and equity (we) in the firm’s capital structure, i.e.rc = wdrd +were



Cost of Capital – Main Points• The Cost of Capital is the return required by investors

in the debt and equity securities of the firm.• The Cost of Debt Capital is the after-tax interest rate

on the firm’s bonds or borrowing.• Three methods of determining the cost of equity

capital are :1. The risk-free rate plus a risk premium2. Discounted Cash Flow3. The Capital Asset Pricing Method (CAPM)

• The Composite Cost of Capital is a weighted average of the cost of debt and equity where weights are the proportions of debt and equity in the firm’s target capital structure.

chap 18 risk management & capital budgeting

Economy & Finance