Question

1.- You are choosing between two projects. The cash flows for the projects are given in the following table​ ($ million):

Project	Year 0	Year 1	Year 2	Year 3	Year 4
A	−$48	$26	$19	$19	$15
B	−$101	$22	$42	$48	$61

a. What are the IRRs of the two​ projects?

b. If your discount rate is 5.1%​, what are the NPVs of the two​projects?

c. Why do IRR and NPV rank the two projects​ differently?

2.- You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $9.6 million.

Investment A will generate $2.15 million per year​ (starting at the end of the first​ year) in perpetuity. Investment B will generate $1.57

million at the end of the first​ year, and its revenues will grow at 2.8% per year for every year after that.

a. Which investment has the higher IRR​?

investment A___ Investment B___

b. Which investment has the higher NPV when the cost of capital is 5.5%​?

c. In this​ case, when does picking the higher IRR give the correct answer as to which investment is the best​ opportunity?

Answer 1

1.
=IRR({-48;26;19;19;15})=26.0678936512625%

2.
=IRR({-101;22;42;48;61})=21.641707297219%

3.
=NPV(5.1%,{-48;26;19;19;15})*(1+5.1%)=22.5988723131844

4.
=NPV(5.1%,{-101;22;42;48;61})*(1+5.1%)=49.2953103306917

5.
Because of size differences

6.
IRR
A=2.15/9.6=22.40%

B=1.57/9.6+2.8%=19.15%

Investment A has higher IRR

7.
NPV
A=-9.6+2.15/5.5%=29.491 million

B=-9.6+1.57/(5.5%-2.8%)=48.548 million

Investment B has higher NPV

8.
2.15/r=1.57/(r-2.8%)
=>r=10.3792%

If cost of capital is more than 10.3792%