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

Question

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $10.4 million. Investment A will generate

$ 1.93 million per year (starting at the end of the first year) in perpetuity. Investment B will generate $1.45 million at the end of the first year, and its revenues will grow at

2.2% 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 6.4%?

c. In this case, for what values of the cost of capital does picking the higher IRR give the correct answer as to which investment is the best opportunity?

Explanation / Answer

A:

0=-10.4+1.93/IRR => IRR=18.56%

NPV=-10.4+1.93/0.064=$19.75625 million

B:

0=-10.4+1.45/(IRR-0.022) =>IRR=16.14%

NPV=-10.4+1.45/(0.064-0.022)=$ 24.123 million

Hence, A has higher IRR and B has higher NPV

Find the crossover rate or the rate at which NPV of both the projects are equal

=>-10.4+1.45/(r-0.022)=-10.4+1.93/r

So,r-0.022=r*1.45/1.93

=>0.2487r=0.022

So, r=0.08845=8.845%

We can say that IRR rule will give correct answer when cost of capital is greater than 8.845%

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