In: Finance
You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of
$ 10.3 million
Investment A will generate
$ 2.01
million per year (starting at the end of the first year) in perpetuity. Investment B will generate
$ 1.49
million at the end of the first year, and its revenues will grow at
2.9 %
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
7.5 %
c. In this case, when does picking the higher IRR give the correct answer as to which investment is the best opportunity?
A) IRR is the rate at which projects NPV =0
Investment A: NPV = ($ 2.01 million / r) - $10.3 million
0 =(2.01/IRR) – 10.3
IRR = 0.1951 or 19.51 %
Investment B: NPV = ($ 1.49 million / (r- 0.029) - $10.3million
0 = (1.49 / (IRR- 0.029)) – 10.3
IRR = O.1691 or 16.91%
Investment a gas a higher IRR of 19.51 % so, we can take investment A based on IRR
B) Investment A: NPV = ($2.1 million / r) - $ 10.3 million
= (2.1 / 0.075) – 10.3
= 17. 7 million
Investment B: NPV = ($1.49 million / (r- 0.029)) - $ 10.3 million
= (1.49 / (O.O75 – 0.029)) – 10.3
= (1.49 / 0.046) – 10.3
= 22.O9 million
Investment B has a higher NPV of 22.09 million when cost of capital is 7.5 %. So, we can take investment B based on NPV
C) Here we will find the cost of capital at which NPV of both the project is equal
NPV A = NPV B
($2.1 million / r) - $ 10.3 million = ($1.49 million / (r- 0.029)) - $ 10.3 million
(2.1 / r) = (1.49 / (r- 0.029))
2.1 r – 0.058 = 1.49 r
0.61 r = 0.058
r = 0.095 or 9.5 %
Based on this we can say that the IRR will give the correct answer for cost of capital grater than 9.5 % as to which investment is the best opportunity.