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 twoprojects?

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%

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