Consider the following two mutually exclusive projects:

Consider the following two mutually exclusive projects:   

Year	Cash Flow (A)				Cash Flow (B)
0	–$	348,000			–$	51,000
1		47,000				24,200
2		67,000				22,200
3		67,000				19,700
4		442,000				14,800

  

Whichever project you choose, if any, you require a 14 percent return on your investment.

a-1	What is the payback period for each project? (Round your answers to 2 decimal places. (e.g., 32.16))

	Payback period
Project A	years
Project B	years

a-2	If you apply the payback criterion, which investment will you choose?
	Project B

b-1	What is the discounted payback period for each project? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

  

	Discounted payback period
Project A	years
Project B	years

  

b-2	If you apply the discounted payback criterion, which investment will you choose?
	Project B

c-1	What is the NPV for each project? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

  

	NPV
Project A	$
Project B	$

c-2	If you apply the NPV criterion, which investment will you choose?
	Project A

d-1	What is the IRR for each project? (Round your answers to 2 decimal places. (e.g., 32.16))

	IRR
Project A	%
Project B	%

d-2	If you apply the IRR criterion, which investment will you choose?
	Project B

e-1	What is the profitability index for each project? (Do not round intermediate calculations and round your final answers to 3 decimal places. (e.g., 32.161))

  

	Profitability index
Project A
Project B

e-2	If you apply the profitability index criterion, which investment will you choose?
	Project B

f	Based on your answers in (a) through (e), which project will you finally choose?
	Project A

Explanation: a.

The payback period for each project is:
A:	3 + ($167,000/$442,000) = 3.38 years
B:	2 + ($4,600/$19,700) = 2.23 years
The payback criterion implies accepting Project B, because it pays back sooner than project A.

b.

The discounted payback for each project is:
A:	$47,000/1.14 + $67,000/1.142 + $67,000/1.143 = $138,005.49
	$442,000/1.144 = $261,699.48
	Discounted payback = 3 + ($348,000 – 138,005.49)/$261,699.48 = 3.80 years
B:	$24,200/1.14 + $22,200/1.142 = $38,310.25
	$19,700/1.143 = $13,296.94
	Discounted payback = 2 + ($51,000 – 38,310.25)/$13,296.94 = 2.95 years
The discounted payback criterion implies accepting Project B because it pays back sooner than A.

c.

The NPV for each project is:
A:	NPV = –$348,000 + $47,000/1.14 + $67,000/1.142 + $67,000/1.143 + $442,000/1.144
	NPV = $51,704.97
B:	NPV = –$51,000 + $24,200/1.14 + $22,200/1.142 + $19,700/1.143 + $14,800/1.144
	NPV = $9,369.98
NPV criterion implies we accept project A because project A has a higher NPV than project B.

d.

The IRR for each project is:
A:	$348,000 = $47,000/(1+IRR) + $67,000/(1+IRR)2 + $67,000/(1+IRR)3 + $442,000/(1+IRR)4
	Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
	IRR = 18.89%
B:	$51,000 = $24,200/(1+IRR) + $22,200/(1+IRR)2 + $19,700/(1+IRR)3 + $14,800/(1+IRR)4
	Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
	IRR = 23.47%
IRR decision rule implies we accept Project B because IRR for B is greater than IRR for A.

e.

The profitability index for each project is:
A:	PI = ($47,000/1.14 + $67,000/1.142 + $67,000/1.143 + $442,000/1.144) / $348,000 = 1.149
B:	PI = ($24,200/1.14 + $22,200/1.142 + $19,700/1.143 + $14,800/1.144) / $51,000 = 1.184
Profitability index criterion implies accept Project B because its PI is greater than Project A’s.

Calculator Solution:

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

   

CF(A)	c.		d.		e.
	CFo	–$348,000	CFo	–$348,000	CFo	$0
	C01	$47,000	C01	$47,000	C01	$47,000
	F01	1	F01	1	F01	1
	C02	$67,000	C02	$67,000	C02	$67,000
	F02	2	F02	2	F02	2
	C03	$442,000	C03	$442,000	C03	$442,000
	F03	1	F03	1	F03	1
	I = 14%		IRR CPT		I = 14%
	NPV CPT		18.89%		NPV CPT
	$51,704.97				$399,704.97

    

PI = $399,704.97 / $348,000 = 1.149

    

CF(B)	c.		d.		e.
	CFo	–$51,000	CFo	–$51,000	CFo	$0
	C01	$24,200	C01	$24,200	C01	$24,200
	F01	1	F01	1	F01	1
	C02	$22,200	C02	$22,200	C02	$22,200
	F02	1	F02	1	F02	1
	C03	$19,700	C03	$19,700	C03	$19,700
	F03	1	F03	1	F03	1
	C04	$14,800	C04	$14,800	C04	$14,800
	F04	1	F04	1	F04	1
	I = 14%		IRR CPT		I = 14%
	NPV CPT		23.47%		NPV CPT
	$9,369.98				$60,369.98

    

PI = $60,369.98 / $51,000 = 1.184

f.

The final decision should be based on the NPV since it does not have the ranking problem associated with the other capital budgeting techniques.