Risk analysis in capital budgeting

Taken from Financial Management

(Prasanna Chandra)

Sources of risk

• Project specific risk• Competitive risk• Industry specific risk• Market risk• International risk

Perspectives of risk

• Three different perspectives– Standalone risk– Firm risk– Market risk

1. Sensitivity analysis or ‘what if’ analysis

Problem: ABC is considering the risk characteristics of a project . The firm has identified that the following factor, with their respective expected values, have a baring on the NPV of this project

Initial investment 30,000Cost of capital 10%Quantity manufactured and sold (annually) 1,400Price per unit 30 variable cost 20fixed cost 3,000 depreciation 2,000Tax rate 50% Life of the project 5 YearsNet salvage value nil

Assume the underlying variable can take the values as shown belowunderlying variable pessimistic

optimisticQuantity manufactured and sold 800 1800price Rs 20 Rs50Variable cost per unit 15 40

Calculate the sensitivity of net present value to the variations in-1. Sales 2. price 3. variable cost

– Limitations• Possibility of change• Variables (changing)• Subjectivity

2. Scenario analysis

Example: different scenarios1.moderate appeal at modest price2.Strongly appeal at low but price sensitive3.Small segment but high price

n

1jj

2jNCF

2 P)ENCFNCF(

Here, σ2 = variance; σ = standard deviation, NCFj = Net cash flow of jth event;

ENCF = Expected net present value;

Pj = Probability of jth event.

Problem: you are given three scenarios, and the probability of occurrence of NPV

Scenarios probability NPVBest case .25 1,46,180Base case .50 5,809Worst case .25 (37,257)

Calculate expected NPVStandard deviationCoefficient of variation

3. Decision tree Approach

• Delineate – Decision points– Chance points

Incorporating Project Risk into Capital Budgeting Decisions

Modification in the conventional methods

1. Risk adjusted discount rateDiscount rate should be adjusted with level of risk

Rk = i + n + dk i = risk free rate of interest n = adjustment for normal riskdk = adjustment for the differential risk of project

Example: replacement investment cost of capital

expansion investment CoC + 3%investment in related line CoC + 6%investment in new line CoC + 10%

2. Certainty equivalent method

NPV = αtĈt

(1+i)t

αt = Certainty equivalent coefficient (CEC)

Ĉt = expected cash flow for year t

i = risk free interest rateI = initial investment

Σ - I

A project involves an outlay of Rs. 5,00,000. Its expected cash inflow at the end of year 1 is Rs. 2,00,000. Thereafter it decreases every year by Rs 10,000. It has an economic life of 6 years. The certainty equivalent factor is αt = 1 - .05t. Calculate the net present value of the project of the risk free rate of return is 10 percent.

Problem: There is a proposal for manufacturing a new product. The initial investment is estimated to be 50 million and the cash inflows for the year 1 through 3 would have the following distributions.

Year 1 cash flow 15 20 30Probability 0.4 0.3 0.3

Year 2 cash flow 20 25 30Probability 0.4 0.4 0.2

Year 3 cash flow 25 30 40Probability 0.3 0.5 0.2

Calculate expected NPV, standard deviation, and coefficient of variation considering cost of capital to be 10%.