Question

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $ 10.5 million . Investment A will generate $ 1.92 million per year​ (starting at the end of the first​ year) in perpetuity. Investment B will generate $ 1.46 million at the end of the first​ year, and its revenues will grow at 2.1 % per year for every year after that.

a. The IRR of investment A is

   The IRR of investment B is

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, when does picking the higher IRR give the correct answer as to which investment is the best​ opportunity?

Answer 1

1.
IRR:
Investment A=1.92/10.5=18.286%

Investment B=1.46/10.5+2.1%=16.005%

Investment A has higher IRR

2.
NPV:
Investment A=-10.5+1.92/6.4%=19.5 million

Investment B=-10.5+1.46/(6.4%-2.1%)=23.45348837 million

Investment B has higher NPV

3.
crossover rate:
1.92/r=1.46/(r-2.1%)
=>r=8.76577289030585%

IRR gives the correct answer when cost of capital is more than 8.77%