Question

In: Finance

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

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?

Solutions

Expert Solution

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.


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