You are deciding between two mutually exclusive investment opportunities. Both r

ID: 2822986 • Letter: Y

Question

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of

$ 10.2 million$10.2 million.

Investment A will generate

$ 1.98$1.98

million per year? (starting at the end of the first? year) in perpetuity. Investment B will generate

$ 1.57$1.57

million at the end of the first? year, and its revenues will grow at

2.8 %2.8%

per year for every year after that.

a. Which investment has the higher

IRR??

b. Which investment has the higher NPV when the cost of capital is

6.5 %6.5%??

c. In this? case, when does picking the higher IRR give the correct answer as to which investment is the best? opportunity?

a) For a perpetuity, IRR = Regular Cashflow/Initial investment

Hence, for Project A, IRR = 1.98/10.2 = 19.41%

For a growing perpetuity, IRR = (Regular Cashflow/Initial investment) + Growth rate

Hence, for Project B, IRR = 1.57/10.2 + 2.8% = 18.19%

Hence Investment A has higher IRR

b) NPV = PV of Future Cash flows - Investment

PV of a perpetuity = Regular Cashflow/Cost of capital

So, for A, NPV = (1.98/6.5%) - 10.2 = $30.46

PV of a growing perpetuity = Regular Cashflow/(Cost of capital - Growth Rate)

So, for B, NPV = (1.57/(6.5% - 2.8%)) - 10.2 = $42.43

NPV for Investment B is higher

c. For this, we need to calculate the cost of capital at which

NPV (Investment A) = NPV (Investment B)

(1.98/r) - 10.2 = (1.57/(r - 2.8%)) - 10.2

1.98/r = (1.57/(r - 2.8%))

1.98r - 5.544% = 1.57r

0.41r = 5.544%

r = 13.52%

This implies when cost of capital would be 13.52%, we will be able to say that project with higher IRR is better and choose that.

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