Question

Show work and explain how you got your answer, do not just post an excel spreadsheet with answers please.

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

$ 10.3

million. Investment A will generate

$ 2.18

million per year​ (starting at the end of the first​ year) in perpetuity. Investment B will generate

$ 1.51

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

7.8 %

​?

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?

Answer 1

Firstly, lets define some term which we are going to calculate to solve above problem -

Net Present Value (NPV) is the difference of discounted value at cost of capital of all future Cash Inflows and Initial Investment. It indicates the net benefit of Investment in present value terms.

Rule = Higher NPV is better.

Internal rate of return (IRR) is the rate at which present value of all future cash flows equals to the initial investment.

Rule = Higher IRR is better.

Cross over rate is the rate (cost of capital) at which NPV of all projects (Investment) is Same.

Rule = At Cross over rate, Project with Higher IRR is better.

Information Provide -

Investment A

Initial Investment = $10,300,000

Annual perpetual Cash Inflow = $2,180,000

Investment B

Initial Investment = $10,300,000

Annual Growing perpetual Cash Inflow = $1,510,000

Growth rate (g) = 2.2%

a.

Computation of IRR of the Investment -A

where,

r = IRR

putting the values,

Computation of IRR of the Investment -B

Thus, Investment-A is higher IRR.

b.

NPV of Investment - A at 7.8%

where,

k = cost of capital

NPV of Investment - B at 7.8%

Thus, Investment A has higher NPV

c.

Cross over rate of Investment A and Investment B

At Cross over rate,

where,

k = cross over rate

Thus, if Cost of capital is 7.16% then picking the higher IRR give the correct answer because at this rate NPV of both Investment is same.

You may found some difference due to rounding off.