Question

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?

Answer 1

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.