Consider the following cash flows on two mutually exclusive projects for the Bah

Question

Consider the following cash flows on two mutually exclusive projects for the Bahamas Recreation Corporation. Both projects require an annual return of 16 percent.

a-1. Compute the IRR for both projects. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

a-2. Based on the IRR, which project should you choose?

Submarine Ride

Deepwater Fishing

b-1. Calculate the incremental IRR for the cash flows. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Incremental IRR             %

b-2. Based on the incremental IRR, which project should you choose?

Deepwater Fishing

Submarine Ride

c-1. Compute the NPV for both projects. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

c-2. Based on the NPV, which project should you choose?

Deepwater Fishing

Submarine Ride

c-3. Is the NPV rule consistent with the incremental IRR rule?

No

Yes

Year Deepwater Fishing New Submarine Ride 0 $ 980,000 $ 1,910,000 1 400,000 960,000 2 534,000 830,000 3 450,000 810,000

Explanation / Answer

Explanation:

a.

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR for each project is:

   

Deepwater Fishing IRR:

    

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3

0 = –$980,000 + $400,000 / (1 + IRR) + $534,000 / (1 + IRR)2 + $450,000 / (1 + IRR)3

    

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

  

IRR = 19.00%

  

Submarine Ride IRR:

    

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3

0 = –$1,910,000 + $960,000 / (1 + IRR) + $830,000 / (1 + IRR)2 + $810,000 / (1 + IRR)3

    

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

  

IRR = 18.00%

  

Based on the IRR rule, the deepwater fishing project should be chosen because it has the higher IRR.

  
b.

To calculate the incremental IRR, we subtract the smaller project’s cash flows from the larger project’s cash flows. In this case, we subtract the deepwater fishing cash flows from the submarine ride cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the submarine ride are:

    

Year 0

Year 1

Year 2

Year 3

  Submarine Ride

–$

1,910,000

$ 960,000

$ 830,000

$ 810,000

  Deepwater Fishing

–980,000

400,000

534,000

450,000

  Submarine – Fishing

–$

930,000

$ 560,000

$ 296,000

$ 360,000

  

Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:

    

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3

0 = –$930,000 + $560,000 / (1 + IRR) + $296,000 / (1 + IRR)2 + $360,000 / (1 + IRR)3

  

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

  

Incremental IRR = 16.00%

  

For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 16.00%, is equal the required rate of return of 16 percent, choose the submarine ride project. Note that this is not the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem. That is, the submarine ride has a greater initial investment than does the deepwater fishing project. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.

  
c.

The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be:

    

Deepwater fishing:

    

NPV = –$980,000 + $400,000 / 1.16 + $534,000 / 1.162 + $450,000 / 1.163

NPV = $56148.90

    

Submarine ride:

    

NPV = –$1,910,000 + $960,000 / 1.16 + $830,000 / 1.162 + $810,000 / 1.163

NPV = $108852.50

  

Since the NPV of the submarine ride project is greater than the NPV of the deepwater fishing project, choose the submarine ride project. The incremental IRR rule is always consistent with the NPV rule.

  

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

  
a.

Deepwater fishing

Submarine ride

CFo

–$980,000

CFo

–$1,910,000

C01

$400,000

C01

$960,000

F01

1

F01

1

C02

$534,000

C02

$830,000

F02

1

F02

1

C03

$450,000

C03

$810,000

F03

1

F03

1

  IRR CPT

  IRR CPT

19.00%

  18.00%

  
b.

CFo

–$930,000

C01

$560,000

F01

1

C02

$296,000

F02

1

C03

$360,000

F03

1

  IRR CPT

  16.00%

  
c.   

Deepwater fishing

Submarine ride

CFo

–$980,000

CFo

–$1,910,000

C01

$400,000

C01

$960,000

F01

1

F01

1

C02

$534,000

C02

$830,000

F02

1

F02

1

C03

$450,000

C03

$810,000

F03

1

F03

1

  I = 16%

  I = 16%

  NPV CPT

  NPV CPT

$56148.90

$108852.50

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR for each project is:

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