Problem 8-1 Calculating Payback [LO 1] Consider the following cash flows: Year Cash Flow 0 –$6,800 1 1,950 2 4,100 3 1,750 4 1,450

Problem 8-1 Calculating Payback [LO 1]

Consider the following cash flows:

Year	Cash Flow
0	–$6,800
1	1,950
2	4,100
3	1,750
4	1,450

Required:

What is the payback period for the above set of cash flows? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Payback period

years

Explanation:

To calculate the payback period, we need to find the time the project needs to recover its initial investment. After two years, the project has created:

$1,950 + 4,100 = $6,050

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

$6,800 – 6,050 = $750

in cash flows. During the third year, the cash flows from the project will be $1,750. So, the payback period will be 2 years, plus what we still need to make divided by what we will make during the third year. The payback period is:

Payback = 2 + ($750 / $1,750)

Payback = 2.43 years

Kaleb Konstruction, Inc., has the following mutually exclusive projects available. The company has historically used a three-year cutoff for projects. The required return is 11 percent.

Kaleb Konstruction, Inc., has the following mutually exclusive projects available. The company has historically used a three-year cutoff for projects. The required return is 11 percent.

Year	Project F		Project G
0	–$	139,000	–$	209,000
1		58,000		38,000
2		52,000		53,000
3		62,000		92,000
4		57,000		122,000
5		52,000		137,000

Required:

(a)	Calculate the payback period for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	Payback period
Project F	years
Project G	years

(b)	Calculate the NPV for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	Net present value
Project F	$
Project G	$

(c)	Which project should the company accept?
	Project G

Explanation:

(a)

The payback period for each project is:

F:     2 + ($29,000 / $62,000) = 2.47 years

G:    3 + ($26,000 / $122,000) = 3.21 years

The payback criterion implies accepting project F because it pays back sooner than project G. Project G does not meet the minimum payback of three years.

(b)

The NPV for each project is:

F:     NPV = – $139,000 + $58,000 / 1.11 + $52,000 / 1.112 + $62,000 / 1.113 + $57,000 / 1.114

+ $52,000 / 1.115

NPV = $69,197.62

G:    NPV = – $209,000 + $38,000 / 1.11 + $53,000 / 1.112 + $92,000 / 1.113

+ $122,000 / 1.114 + $137,000 / 1.115

NPV = $97,187.84

The NPV criterion implies we should accept project G because project G has a higher NPV than project F.

(c)

Even though Project G does not meet the payback period of three years, it does provide the largest increase in shareholder wealth, therefore, choose Project G. Payback period should generally be ignored in this situation.

    

Calculator Solution:

 

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

   

Project F		Project G
CFo	–$139,000	CFo	–$209,000
C01	$58,000	C01	$38,000
F01	1	F01	1
C02	$52,000	C02	$53,000
F02	1	F02	1
C03	$62,000	C03	$92,000
F03	1	F03	1
C04	$57,000	C04	$122,000
F04	1	F04	1
C05	$52,000	C05	$137,000
F05	1	F05	1
I = 11		I = 11
NPV CPT		NPV CPT
$69,197.62		$97,187.84

Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 19 percent. Year Project M Project N 0 –$140,000 –$355,000 1 63,500 152,500 2 81,500 180,000 3 72,500 137,500 4 58,500 110,000

Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 19 percent.

Year	Project M	Project N
0	–$140,000	–$355,000
1	63,500	152,500
2	81,500	180,000
3	72,500	137,500
4	58,500	110,000

Required:
(a)	What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	IRR
Project M	%
Project N	%

(b)	What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	NPV
Project M	$
Project N	$

(c)	Which, if either, of the projects should the company accept?
	Project M

Explanation: (a)

The IRR for each project is:

M:	$140,000 = $63,500 / (1 + IRR) + $81,500 / (1 + IRR)2 + $72,500 / (1 + IRR)3 + $58,500 / (1 + IRR)4

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

IRR = 34.47%

N:	$355,000 = $152,500 / (1 + IRR) + $180,000 / (1 + IRR)2 + $137,500 / (1 + IRR)3 + 110,000 / (1 + IRR)4

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

IRR = 24.61%

The IRR decision rule implies we accept project M because the IRR for M is greater than the IRR for N.

(b)

The NPV for each project is:

M:	NPV = – $140,000 + $63,500 / 1.19 + $81,500 / 1.192 + $72,500 / 1.193 + $58,500 / 1.194
	NPV = $43,108.55

N:	NPV = – $355,000 + $152,500 / 1.19 + $180,000 / 1.192 + $137,500 / 1.193 + $110,000 / 1.194
	NPV = $36,709.17

The NPV criterion implies we accept project M because project M has a higher NPV than project N.

(c)

Accept project M since the NPV is higher. IRR cannot be used to rank mutually exclusive projects.

   

Calculator Solution:

 

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

    

Project M
CFo	–$140,000	CFo	–$140,000
C01	$63,500	C01	$63,500
F01	1	F01	1
C02	$81,500	C02	$81,500
F02	1	F02	1
C03	$72,500	C03	$72,500
F03	1	F03	1
C04	$58,500	C04	$58,500
F04	1	F04	1
CPT IRR		I = 19
34.47%		NPV CPT
		$43,108.55

   

Project N
CFo	–$355,000	CFo	–$355,000
C01	$152,500	C01	$152,500
F01	1	F01	1
C02	$180,000	C02	$180,000
F02	1	F02	1
C03	$137,500	C03	$137,500
F03	1	F03	1
C04	$110,000	C04	$110,000
F04	1	F04	1
CPT IRR		I = 19
24.61%		NPV CPT
		$36,709.17

Problem 8-9 Calculating NPV [LO 4] Consider the following cash flows: Year Cash Flow 0 –$ 32,000 1 14,200 2 17,500 3 11,600

Problem 8-9 Calculating NPV [LO 4]

Consider the following cash flows:

Year	Cash Flow
0		–$	32,000
1			14,200
2			17,500
3			11,600

Requirement 1:

What is the NPV at a discount rate of zero percent? (Do not round intermediate calculations.) Net present value $   Requirement 2: What is the NPV at a discount rate of 10 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Requirement 3: What is the NPV at a discount rate of 20 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign.Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Requirement 4: What is the NPV at a discount rate of 30 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Explanation: 1: The NPV of a project is the PV of the outflows plus the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is:   NPV = – $32,000 + 14,200 + 17,500 + 11,600 NPV = $11,300   2: The NPV at a 10 percent required return is:   NPV = – $32,000 + $14,200 / 1.10 + $17,500 / 1.102 + $11,600 / 1.103 NPV = $4,087.15   3: The NPV at a 20 percent required return is:   NPV = – $32,000 + $14,200 / 1.20 + $17,500 / 1.202 + $11,600 / 1.203 NPV = –$1,300.93   4: And the NPV at a 30 percent required return is:   NPV = – $32,000 + $14,200 / 1.30 + $17,500 / 1.302 + $11,600 / 1.303 NPV = – $5,441.97   Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project.     Calculator solution:   Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.    CFo  –$32,000 CFo  –$32,000 C01  $14,200 C01  $14,200 F01  1 F01  1 C02  $17,500 C02  $17,500 F02  1 F02  1 C03  $11,600 C03  $11,600 F03  1 F03  1   I = 0%   I = 10%   NPV CPT   NPV CPT   $11,300.00   $4,087.15     CFo  –$32,000 CFo  –$32,000 C01  $14,200 C01  $14,200 F01  1 F01  1 C02  $17,500 C02  $17,500 F02  1 F02  1 C03  $11,600 C03  $11,600 F03  1 F03  1   I = 20%   I = 30%   NPV CPT   NPV CPT   –$1,300.93   –$5,441.97

Problem 8-8 Calculating IRR [LO 3] Consider the following cash flows: Year Cash Flow 0 –$ 32,000 1 14,200 2 17,500 3 11,600

Problem 8-8 Calculating IRR [LO 3]

Consider the following cash flows:

Year	Cash Flow
0		–$	32,000
1			14,200
2			17,500
3			11,600

Required:

What is the IRR of the above set of cash flows? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Internal rate of return

%

Explanation:

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:

0 = – $32,000 + $14,200 / (1 + IRR) + $17,500 / (1 + IRR)2 + $11,600 / (1 + IRR)3

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

IRR = 17.32%

   

Calculator solution:

 

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

  

CFo	–$32,000
C01	$14,200
F01	1
C02	$17,500
F02	1
C03	$11,600
F03	1
IRR CPT
17.32%

Problem 8-7 Calculating NPV and IRR [LO 3, 4] A project that provides annual cash flows of $2,800 for nine years costs $9,200 today. Requirement 1: At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Problem 8-7 Calculating NPV and IRR [LO 3, 4]

A project that provides annual cash flows of $2,800 for nine years costs $9,200 today.

Requirement 1:

At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Requirement 2:

At a required return of 27 percent, what is the NPV of the project? (Do not round intermediate calculations. A negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Requirement 3:

At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Discount rate

%

Explanation:

1:

The NPV of a project is the PV of the outflows plus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 11 percent required return is:

NPV = – $9,200 + $2,800(PVIFA11%, 9)

NPV = $6,303.73

At an 11 percent required return, the NPV is positive, so we would accept the project.

2:

The equation for the NPV of the project at a 27 percent required return is:

NPV = – $9,200 + $2,800(PVIFA27%, 9)

NPV = –$36.22

At a 27 percent required return, the NPV is negative, so we would reject the project.

3:

We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is:

0 = – $9,200 + $2,800(PVIFAIRR, 9)

IRR = .2686, or 26.86%

   

Calculator Solution:

 

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

  

CFo	–$9,200	CFo	–$9,200	CFo	–$9,200
C01	$2,800	C01	$2,800	C01	$2,800
F01	9	F01	9	F01	9
I = 11%		I = 27%		IRR CPT
NPV CPT		NPV CPT		26.86%
$6,303.73		–$36.22

A firm evaluates all of its projects by applying the IRR rule. Year Cash Flow 0 –$ 158,000 1 58,000 2 81,000 3 65,000

A firm evaluates all of its projects by applying the IRR rule.

Year	Cash Flow
0	–$	158,000
1		58,000
2		81,000
3		65,000

Requirement 1:

What is the project's IRR? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Internal rate of return

%

Requirement 2:

If the required return is 15 percent, should the firm accept the project?

No

Explanation:

1:

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:

0 = – $158,000 + $58,000 / (1 + IRR) + $81,000 / (1 + IRR)2 + $65,000 / (1 + IRR)3

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

IRR = 13.66%

2:

Since the cash flows are conventional and the IRR is lower than the required return, we would not accept the project.

   

Calculator Solution:

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

  

CFo	–$158,000
C01	$58,000
F01	1
C02	$81,000
F02	1
C03	$65,000
F03	1
IRR CPT
13.66%

Global Toys, Inc., imposes a payback cutoff of three years for its international investment projects. Assume the company has the following two projects available.

Global Toys, Inc., imposes a payback cutoff of three years for its international investment projects. Assume the company has the following two projects available.

Year	Cash Flow A		Cash Flow B
0	–$	62,000	–$	107,000
1		25,500		27,500
2		33,200		32,500
3		27,500		26,500
4		13,500		233,000

Requirement 1:

What is the payback period for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	Payback period
Project A	years
Project B	years

Requirement 2:

Should it accept either of them?

Accept project A and reject project B

Explanation: 1: 

Project A has cash flows of:

Cash flows = $25,500 + 33,200

Cash flows = $58,700

during the first two years. The cash flows are still short by $3,300 of recapturing the initial investment, so the payback for Project A is:

Payback = 2 + ($3,300 / $27,500)

Payback = 2.12 years

Project B has cash flows of:

Cash flows = $27,500 + 32,500 + 26,500

Cash flows = $86,500

during the first three years. The cash flows are still short by $20,500 of recapturing the initial investment, so the payback for Project B is:

Payback = 3 + ($20,500 / $233,000)

Payback = 3.09 years

2:

Using the payback criterion and a cutoff of 3 years, accept project A and reject project B.