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.

What is the payback period for the following set of cash flows? (Round your answer to 2 decimal places. (e.g., 32.16))

What is the payback period for the following set of cash flows? (Round your answer to 2 decimal places. (e.g., 32.16))

Year	Cash Flow
0	–$	5,600
1		1,325
2		1,525
3		1,925
4		1,425

Payback period

years

Explanation:

To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project has created:

$1,325 + 1,525 + 1,925 = $4,775

in cash flows. The project still needs to create another:

$5,600 – 4,775 = $825

in cash flows. During the fourth year, the cash flows from the project will be $1,425. So, the payback period will be three years, plus what we still need to make divided by what we will make during the fourth year. The payback period is:

Payback = 3 + ($825 / $1,425) = 3.58 years

Compute the payback period for each of these two separate investments: a. A new operating system for an existing machine is expected to cost $270,000 and have a useful life of six years. The system yields an incremental after-tax income of $77,884 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000. b. A machine costs $190,000, has a $14,000 salvage value, is expected to last eleven years, and will generate an after-tax income of $43,000 per year after straight-line depreciation.

Compute the payback period for each of these two separate investments:

a.	A new operating system for an existing machine is expected to cost $270,000 and have a useful life of six years. The system yields an incremental after-tax income of $77,884 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000.
b.	A machine costs $190,000, has a $14,000 salvage value, is expected to last eleven years, and will generate an after-tax income of $43,000 per year after straight-line depreciation.

a.

		Cost of investment		$270,000
Payback period	=		=		=	2.23 years
		Annual net cash flow		$121,217

  Where

Annual after-tax income	$	77,884
Plus depreciation*		43,333
Annual net cash flow	$	121,217

		$270,000 – $10,000
*Annual depreciation	=		=	$43,333
		6

b.

		Cost of investment		$190,000
Payback period	=		=		=	3.22 years
		Annual net cash flow		$59,000

  Where

Annual after-tax income	$	43,000
Plus depreciation*		16,000
Annual net cash flow	$	59,000

		$190,000 – $14,000
*Annual depreciation	=		=	$16,000
		11

Beyer Company is considering the purchase of an asset for $250,000. It is expected to produce the following net cash flows. The cash flows occur evenly throughout each year. Year 1 Year 2 Year 3 Year 4 Year 5 Total Net cash flows $ 50,000 $ 36,000 $ 60,000 $ 130,000 $ 24,000 $ 300,000 Compute the payback period for this investment. (Cumulative net cash outflows must be entered with a minus sign. Round your payback period to 2 decimal places.)

Beyer Company is considering the purchase of an asset for $250,000. It is expected to produce the following net cash flows. The cash flows occur evenly throughout each year.

	Year 1				Year 2				Year 3				Year 4				Year 5				Total
Net cash flows		$	50,000			$	36,000			$	60,000			$	130,000			$	24,000			$	300,000

Compute the payback period for this investment. (Cumulative net cash outflows must be entered with a minus sign. Round your payback period to 2 decimal places.)

	Annual Net Cash Flows				Cumulative Cash Flows
Year 1		$	50,000			$	-200,000
Year 2			36,000				-164,000
Year 3			60,000				-104,000
Year 4			130,000				26,000
Year 5			24,000				50,000

Cost of investment	$	250,000
Paid back in years 1-3		-104,000
Paid back in year 4	$	104,000

		Amount paid back in year 4		$104,000
Part of year	=		=		=	0.80
		Net cash flow in year 4		$130,000

Payback period = 3 + 0.80 = 3.80 years, (or nearly 3 years and 9 months)

Martin Company is considering the purchase of a new piece of equipment. Relevant information concerning the equipment follows: (Ignore income taxes.) Purchase cost $ 195,000 Annual cost savings that will be provided by the equipment $ 38,600 Life of the equipment 13 years Required: 1a. Compute the payback period for the equipment. (Round your answer to 1 decimal place.) Payback period years 1b. If the company requires a payback period of 4 years or less, would the equipment be purchased? No 2a. Use straight-line depreciation based on the equipment's useful life. Compute the simple rate of return on the equipment. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) Simple rate of return % 2b. Would the equipment be purchased if the company's required rate of return is 11%? Yes Explanation: 1a. The payback period is: Payback period = Investment required Net annual cash inflow = $195,000 = 5.1 years $38,600 per year 1b. No, the equipment would not be purchased because the (5.1 years) payback period exceeds the company's maximum (4-years) payback period . 2a. The simple rate of return would be computed as follows: Annual cost savings $ 38,600 Less annual depreciation ($195,000 ÷ 13 years) 15,000 Annual incremental net operating income $ 23,600 Simple rate of return = Annual incremental net operating income Initial investment = $23,600 = 12.1% $195,000 b. The equipment would be purchased since its 12.1% rate of return is greater than the company's 11% required rate of return.

Martin Company is considering the purchase of a new piece of equipment. Relevant information concerning the equipment follows: (Ignore income taxes.)

Purchase cost	$	195,000
Annual cost savings that will be     provided by the equipment	$	38,600
Life of the equipment		13 years

   

Required:

1a.	Compute the payback period for the equipment. (Round your answer to 1 decimal place.)

Payback period

years

  

1b.	If the company requires a payback period of 4 years or less, would the equipment be purchased?
	No

2a.	Use straight-line depreciation based on the equipment's useful life. Compute the simple rate of return on the equipment. (Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Simple rate of return

%

2b.	Would the equipment be purchased if the company's required rate of return is 11%?
	Yes

Explanation:

1a.

The payback period is:

Payback period	=	Investment required
		Net annual cash inflow
	=	$195,000	= 5.1 years
		$38,600 per year

1b.

No, the equipment would not be purchased because the (5.1 years) payback period exceeds the company's maximum (4-years) payback period .

2a.

The simple rate of return would be computed as follows:

   

Annual cost savings	$	38,600
Less annual depreciation ($195,000 ÷ 13 years)		15,000
Annual incremental net operating income	$	23,600

Simple rate of return	=	Annual incremental net operating income
		Initial investment
	=	$23,600	= 12.1%
		$195,000

b.

The equipment would be purchased since its 12.1% rate of return is greater than the company's 11% required rate of return.

Martin Company is considering the purchase of a new piece of equipment. Relevant information concerning the equipment follows: (Ignore income taxes.) Purchase cost $ 231,000 Annual cost savings that will be provided by the equipment $ 37,400 Life of the equipment 11 years Required: 1a. Compute the payback period for the equipment. (Round your answer to 1 decimal place.) Payback period 6.2 correct years 1b. If the company requires a payback period of 5 years or less, would the equipment be purchased? No correct 2a. Use straight-line depreciation based on the equipment's useful life. Compute the simple rate of return on the equipment. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) Simple rate of return 7.1 correct % 2b. Would the equipment be purchased if the company's required rate of return is 8%? No correct

Martin Company is considering the purchase of a new piece of equipment. Relevant information concerning the equipment follows: (Ignore income taxes.)

Purchase cost	$	231,000
Annual cost savings that will be     provided by the equipment	$	37,400
Life of the equipment		11 years

   

Required:

1a.	Compute the payback period for the equipment. (Round your answer to 1 decimal place.)

Payback period

6.2  years

  

1b.	If the company requires a payback period of 5 years or less, would the equipment be purchased?
	No

2a.	Use straight-line depreciation based on the equipment's useful life. Compute the simple rate of return on the equipment. (Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Simple rate of return

7.1  %

2b.	Would the equipment be purchased if the company's required rate of return is 8%?
	No