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