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	–$	29,900			–$	29,900
1		15,300				4,750
2		13,200				10,250
3		9,650				16,100
4		5,550				17,700

  

a-1	What is the IRR for each of these projects? (Do not round intermediate calculations and round your final answers 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 final 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 and round your final answer 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 = –$29,900 + $15,300 / (1 + IRR) + $13,200 / (1 + IRR)2 + $9,650 / (1 + IRR)3 + $5,550 / (1 + IRR)4

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

IRR = 20.57%

The equation for the IRR of Project B is

0 = –$29,900 + $4,750 / (1 + IRR) + $10,250 / (1 + IRR)2 + $16,100 / (1 + IRR)3 + $17,700 / (1 + IRR)4

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

IRR = 18.58%

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 = –$29,900 + $15,300 / 1.11 + $13,200 / 1.112 + $9,650 / 1.113 + $5,550 / 1.114

NPVA = $5,309.15

And the NPV of Project B is:

NPVB = –$29,900 + $4,750 / 1.11 + $10,250 / 1.112 + $16,100 / 1.113 + $17,700 / 1.114

NPVB = $6,130.13

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 = $10,550 / (1 + R) + $2,950 / (1 + R)2 – $6,450 / (1 + R)3 – $12,150 / (1 + R)4

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

R = 14.09%

At discount rates above 14.09 percent choose project A; for discount rates below 14.09 percent choose project B; indifferent between A and B at a discount rate of 14.09 percent.

  

Calculator Solution:

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

     

	Project A
	CFo	–$29,900	CFo	–$29,900
	C01	$15,300	C01	$15,300
	F01	1	F01	1
	C02	$13,200	C02	$13,200
	F02	1	F02	1
	C03	$9,650	C03	$9,650
	F03	1	F03	1
	C04	$5,550	C04	$5,550
	F04	1	F04	1
	IRR CPT		I = 11%
	20.57%		NPV CPT
			$5,309.15

  

	Project B
	CFo	–$29,900	CFo	–$29,900
	C01	$4,750	C01	$4,750
	F01	1	F01	1
	C02	$10,250	C02	$10,250
	F02	1	F02	1
	C03	$16,100	C03	$16,100
	F03	1	F03	1
	C04	$17,700	C04	$17,700
	F04	1	F04	1
	IRR CPT		I = 11%
	18.58%		NPV CPT
			$6,130.13

     

	Crossover rate
	CFo	$0
	C01	$10,550
	F01	1
	C02	$2,950
	F02	1
	C03	–$6,450
	F03	1
	CO4	–$12,150
	FO4	1
	IRR CPT
	14.09%