Problem 7-13 NPV versus IRR
Consider the following cash flows on two mutually exclusive
projects for the Bahamas Recreation Corporation. Both projects
require an annual return of 16 percent.
Year | Deepwater Fishing | New Submarine Ride | ||||
0 | −$ | 990,000 | −$ | 1,930,000 | ||
1 | 410,000 | 980,000 | ||||
2 | 542,000 | 840,000 | ||||
3 | 460,000 | 830,000 | ||||
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.)
IRR | |
Deepwater Fishing | % |
Submarine Ride | % |
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?
Submarine Ride
Deepwater Fishing
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.)
NPV | |
Deepwater Fishing | $ |
Submarine Ride | $ |
c-2. Based on the NPV, which project should you
choose?
Submarine Ride
Deepwater Fishing
c-3. Is the NPV rule consistent with the
incremental IRR rule?
No
Yes
a-1 The IRR of the projects are :
The IRR of deep water fishing can be calculated as ,
(Initial investment ) + present value of cash flows = 0
($9,90,000) + $410,000/ (1 + IRR) + $542,000/ ( 1+ IRR)^2 + $4,60,000/ (1 + IRR)^3 = 0
So, the IRR is = 19.6379 %
Similarly for project New submarine ride , the IRR is
= 18.2984%
On the basis of IRR, project Deep water fishing should be accepted due to the higher IRR. The IRR rule states that the project with the higher IRR should be accepted.
b- 1 The incremental IRR is the difference between the cash flows of the two projects. The project with the smaller cash flows is subtracted from the project with the higher cash flows .
So, the incremental IRR is :
CF0 = ($940,000)
CF1 = $5,70,000
CF2= $2,98,000
CF3= $3,70,000
The incremental IRR is 16.7035%. On the basis of incremental IRR, if the incremental IRR > the cost of capital then the project with the higher investment should be chosen.
b- 2 So, the new submarine ride project should be chosen.
c - 1 The NPV of Deep water fishing is :
($9,90,000) + $410,000/1.16 + $5,42,000/1.16^2 + $4,60,000/1.16^3
= $60,945.0982
Similarly the NPV , for project deep water fishing is ,
= $70,830.2923
c-2. On the basis of NPV, the project with the higher NPV should be chosen. So, project New submarine ride should be chosen.
c-3. Yes, the NPV rule is consistent with the incremental IRR.
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