Garage, Inc., has identified the following two mutually exclusive projects:

Problem 9-12 NPV versus IRR [LO1, 5]

Garage, Inc., has identified the following two mutually exclusive projects:

   

Year	Cash Flow (A)				Cash Flow (B)
0	–$	28,500			–$	28,500
1		13,900				4,050
2		11,800				9,550
3		8,950				14,700
4		4,850				16,300

  

a-1	What is the IRR for each of these projects? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	IRR
Project A	%
Project B	%

  

a-2	Using the IRR decision rule, which project should the company accept?
	Project A

a-3	Is this decision necessarily correct?
	No

b-1	If the required return is 11 percent, what is the NPV for each of these projects? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

  

	NPV
Project A	$
Project B	$

b-2	Which project will the company choose if it applies the NPV decision rule?
	Project B

  

c.	At what discount rate would the company be indifferent between these two projects? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Discount rate

%

 

Explanation:

a.

The IRR is the interest rate that makes the NPV of the project equal to zero. The equation for the IRR of Project A is:

  

0 = –$28,500 + $13,900 / (1 + IRR) + $11,800 / (1 + IRR)2 + $8,950 / (1 + IRR)3 + $4,850 / (1 + IRR)4

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

IRR = 17.37%

The equation for the IRR of Project B is:

0 = –$28,500 + $4,050 / (1 + IRR) + $9,550 / (1 + IRR)2 + $14,700 / (1 + IRR)3 + $16,300 / (1 + IRR)4

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

IRR = 16.73%

Examining the IRRs of the projects, we see that the IRRA is greater than the IRRB, so IRR decision rule implies accepting Project A. This may not be a correct decision; however, because the IRR criterion has a ranking problem for mutually exclusive projects. To see if the IRR decision rule is correct or not, we need to evaluate the project NPVs.

b.

The NPV of Project A is:

NPVA = –$28,500 + $13,900 / 1.11 + $11,800 / 1.112 + $8,950 / 1.113 + $4,850 / 1.114

NPVA = $3,338.68

And the NPV of Project B is:

NPVB = –$28,500 + $4,050 / 1.11 + $9,550 / 1.112 + $14,700 / 1.113 + $16,300 / 1.114

NPVB = $4,385.47

The NPVB is greater than the NPVA, so we should accept Project B.

 
c.

To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project. Here, we will subtract the cash flows for Project B from the cash flows of Project A. Once we find these differential cash flows, we find the IRR. The equation for the crossover rate is:

Crossover rate: 0 = $9,850 / (1 + R) + $2,250 / (1 + R)2 – $5,750 / (1 + R)3 – $11,450 / (1 + R)4

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

R = 15.28%

At discount rates above 15.28 percent choose Project A; for discount rates below 15.28 percent choose Project B; indifferent between A and B at a discount rate of 15.28 percent.

  

Calculator Solution:

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

     

Project A
CFo	–$28,500	CFo	–$28,500
C01	$13,900	C01	$13,900
F01	1	F01	1
C02	$11,800	C02	$11,800
F02	1	F02	1
C03	$8,950	C03	$8,950
F03	1	F03	1
C04	$4,850	C04	$4,850
F04	1	F04	1
IRR CPT		I = 11%
17.37%		NPV CPT
		$3,338.68

   
 

Project B
CFo	–$28,500	CFo	–$28,500
C01	$4,050	C01	$4,050
F01	1	F01	1
C02	$9,550	C02	$9,550
F02	1	F02	1
C03	$14,700	C03	$14,700
F03	1	F03	1
C04	$16,300	C04	$16,300
F04	1	F04	1
IRR CPT		I = 11%
16.73%		NPV CPT
		$4,385.47

     

Crossover rate
CFo	$0
C01	$9,850
F01	1
C02	$2,250
F02	1
C03	–$5,750
F03	1
CO4	–$11,450
FO4	1
IRR CPT
15.28%