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

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

   

Year	Cash Flow (A)				Cash Flow (B)
0	–$	28,300			–$	28,300
1		13,700				3,950
2		11,600				9,450
3		8,850				14,500
4		4,750				16,100

  

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 10 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 = –$28,300 + $13,700 / (1 + IRR) + $11,600 / (1 + IRR)2 + $8,850 / (1 + IRR)3 + $4,750 / (1 + IRR)4

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

IRR = 16.88%

The equation for the IRR of Project B is:

0 = –$28,300 + $3,950 / (1 + IRR) + $9,450 / (1 + IRR)2 + $14,500 / (1 + IRR)3 + $16,100 / (1 + IRR)4

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

IRR = 16.45%

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 = –$28,300 + $13,700 / 1.10 + $11,600 / 1.102 + $8,850 / 1.103 + $4,750 / 1.104

NPVA = $3,634.77

And the NPV of Project B is:

NPVB = –$28,300 + $3,950 / 1.10 + $9,450 / 1.102 + $14,500 / 1.103 + $16,100 / 1.104

NPVB = $4,991.41

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 = $9,750 / (1 + R) + $2,150 / (1 + R)2 – $5,650 / (1 + R)3 – $11,350 / (1 + R)4

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

R = 15.46%

At discount rates above 15.46 percent choose Project A; for discount rates below 15.46 percent choose Project B; indifferent between A and B at a discount rate of 15.46 percent.

  

Calculator Solution:

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

     

Project A
CFo	–$28,300	CFo	–$28,300
C01	$13,700	C01	$13,700
F01	1	F01	1
C02	$11,600	C02	$11,600
F02	1	F02	1
C03	$8,850	C03	$8,850
F03	1	F03	1
C04	$4,750	C04	$4,750
F04	1	F04	1
IRR CPT		I = 10%
16.88%		NPV CPT
		$3,634.77

   
 

Project B
CFo	–$28,300	CFo	–$28,300
C01	$3,950	C01	$3,950
F01	1	F01	1
C02	$9,450	C02	$9,450
F02	1	F02	1
C03	$14,500	C03	$14,500
F03	1	F03	1
C04	$16,100	C04	$16,100
F04	1	F04	1
IRR CPT		I = 10%
16.45%		NPV CPT
		$4,991.41

     

Crossover rate
CFo	$0
C01	$9,750
F01	1
C02	$2,150
F02	1
C03	–$5,650
F03	1
CO4	–$11,350
FO4	1
IRR CPT
15.46%