Question

1. A project has an investment cost of CF50m and is expected to produce risky cash flows perpetually and which will, on average, be CF15m per annum but fluctuate with a volatility of 30% per annum. The stock market is expected to have a return of 15% per annum and is likely to experience volatility of 20% per annum. The correlation between the project’s cash flows and the market’s returns is 0.5. The central bank’s treasury bond yield is 300 basis points.

Evaluate the NPV of the project.

Answer 1

Writing down all the information given in the question:

investment on the project= CF 50 Mn

Cash flows expected to generated perpetually on an average= CF 15m

Volatility in cash flows on annual Basis=30%

Expected Stock Market Return=15 %

Volatility in Stock Market Return=20%

correlation between the project’s cash flows and the market’s returns = 0.5

The central bank’s treasury bond yield =3%

From the data given we will forst calculate Beta of cash fo\lows:

Beta=( Variation of Cash flows/Variation of stock MArket)* correlation between project’s cash flows and the market’s returns

Beta=(0.30/0.20) x .5= 0.75

Now we will calculate the cost of equirt/Required rate fof return for the project:

K=Rf+Beta x(Rm-Rf)

Here Rf=Risk free rate( ie retunr on treasury bond)

Rm=Market return

Purtting the values:we get:

K=3%+0.75 x(15%-3%)

K=3%+0.75 x12%

k=3%+9%=12%

Now we will use k as discounting factor to calculate NPV of the Project

NPV=-50+15/(1+0.12)+15/(1.12)2+............................. infinity(Perpetual)

NPV=-50+sum of infinite Geometric progression series

Sum of Geometric progression series = a/(1-r), where a is first number in the series, and r = common difference)

Putting the formula we get:

NPV=-50+15/1.12x(1+1/1.12+1/1.122+............................. perpetual)

NPV=-50+15/12 x 1/(1-1/(1/1.12))

NPV=-50+15/1.12x9.33=-50+125=CF75 Mn

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