Chapter 26: Q37PGB (page 1474)

Using payback, ARR, and NPV with unequal cash flows
Hughes Manufacturing, Inc. has a manufacturing machine that needs attention. The company is considering two options. Option 1 is to refurbish the current machine at a cost of $2,600,000. If refurbished, Hughes expects the machine to last another eight years and then have no residual value. Option 2 is to replace the machine at a cost of $3,800,000. A new machine would last 10 years and have no residual value. Hughes expects the following net cash inflows from the two options:
Year
Refurbish current machine
Purchase new machine
1
$1,760,000
$2,970,000
2
440,000
490,000
3
360,000
410,000
4
280,000
330,000
5
200,000
250,000
6
200,000
250,000
7
200,000
250,000
8
200,000
250,000
9
250,000
10
250,000
Total
$3,640,000
$5,700,000
Hughes uses straight-line depreciation and requires an annual return of 10%.
Requirements
1. Compute the payback, the ARR, the NPV, and the profitability index of these two options.
2. Which option should Hughes choose? Why?

Short Answer

Expert verified

Capital budgeting calculations:

Method	Refurbish current machine	Purchase new machine
Payback	3.86 years	3 years
ARR	10%	10%
NPV	$257,880	$581,520
Profitability index	1.10	1.15

2. The business entity must select the option of purchasing a new machine.

Step by step solution

Definition of Payback Period

A capital budgeting metric that determines the time period in which the investment will give back the cash invested or the investment/cash recovery period is known as the payback period.

Calculation of payback period, ARR, NPV, and profitability index

Calculation of payback period:

1. Refurbishment of current machine:

$\begin{matrix} Payback period = Year prior to full recovery + (\frac{Recovery amount in last year}{Cash flow in last year}) \\ = 3 + (\frac{$ 2, 840, 000 - $ 2, 600, 000}{$ 280, 000}) \\ = 3 + 0.86 \\ = 3.86 \end{matrix}$

2. Purchase of new machine:

$\begin{matrix} Payback period = Year prior to full recovery + (\frac{Recovery amount in last year}{Cash flow in last year}) \\ = 2 + (\frac{$ 3, 870, 000 - $ 3, 460, 000}{$ 410, 000}) \\ = 2 + 1 \\ = 3 \end{matrix}$

Working note:

Year	Refurbish current machine	Cumulative	Purchase new machine	Cumulative
1	$1,760,000	$1,760,000	$2,970,000	$2,970,000
2	440,000	$2,200,000	490,000	$3,460,000
3	360,000	$2,560,000	410,000	$3,870,000
4	280,000	$2,840,000	330,000
5	200,000		250,000
6	200,000		250,000
7	200,000		250,000
8	200,000		250,000
9			250,000
10			250,000
Total	$3,640,000		$5,700,000

Calculation of ARR:

Refurbishment of machine:

$\begin{matrix} ARR = \frac{Average annual operating income}{Average investment} \times 100 \\ = \frac{$ 130, 000}{\frac{$ 2, 600, 000 + 0}{2}} \times 100 \\ = 10 % \end{matrix}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	$3,640,000
Less: Total depreciation during the life of the asset $($ 2, 600, 000 - $ 0)$	2,600,000
Total operating income during the operating life	$1,040,000
Asset operating life in years	8
Average annual operating income $(\frac{$ 1, 040, 000}{8})$	$130,000

2. Purchase a new machine:

$\begin{matrix} ARR = \frac{Net cash in flows}{Initial investment} \times 100 \\ = \frac{$ 190, 000}{\frac{$ 3, 800, 000 + $ 0}{2}} \times 100 \\ = 10 % \end{matrix}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	$5,700,000
Less: Total depreciation during the life of the asset $($ 3, 800, 000 - $ 0)$	3,800,000
Total operating income during the operating life	$1,900,000
Asset operating life in years	10
Average annual operating income $(\frac{$ 1, 900, 000}{8})$	$190,000

Calculation of NPV:

Refurbish of current machine:

Year	Refurbish current machine	X	Present value factor $(\frac{1}{{(1 + r)}^{n}})$	=	Present value
1	$1,760,000	X	0.909	=	$1,599,840
2	440,000	X	0.826	=	$363,440
3	360,000	X	0.751	=	$270,360
4	280,000	X	0.683	=	$191,240
5	200,000	X	0.621	=	$124,200
6	200,000	X	0.564	=	$112,800
7	200,000	X	0.513	=	$102,600
8	200,000	X	0.467	=	$93,400
Total present value of net cash inflow					$2,857,880
Less: initial investment					(2,600,000)
Net present value					$257,880

2. Purchase of new machine:

Year	Purchase new machine	X	Present value factor $(\frac{1}{{(1 + r)}^{n}})$	=	Present value
1	$2,970,000	X	0.909	=	$2,699,730
2	490,000	X	0.826	=	$404,740
3	410,000	X	0.751	=	$307,910
4	330,000	X	0.683	=	$225,390
5	250,000	X	0.621	=	$155,250
6	250,000	X	0.564	=	$141,000
7	250,000	X	0.513	=	$128,250
8	250,000	X	0.467	=	$116,750
9	250,000	X	0.424	=	$106,000
10	250,000	X	0.386	=	$96,500
Total present value net cash inflow					$4,381,520
Less: initial investment					(3,800,000)
Net present value					$581,520

Calculation of profitability index:

1. Refurbish current machine:

$\begin{matrix} Profitability index = \frac{Total present value of net cashflows}{Initial investment} \\ = \frac{$ 2, 857, 880}{$ 2, 600, 000} \\ = 1.10 \end{matrix}$

2. Purchase of new machine:

$\begin{matrix} Profitability index = \frac{Total present value of net cashflows}{Initial investment} \\ = \frac{$ 4, 381, 520}{$ 3, 800, 000} \\ = 1.15 \end{matrix}$

Appropriate option

The business entity must purchase a new machine because its payback period is lower, and NPV and profitability index are higher than the current machine’s refurbishing.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Business Studies Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Net Cash Inflows
	Project L		Project M		Project N
Year	Annual	Accumulated	Annual	Accumulated	Annual	Accumulated
1	\) 100,000	\( 100,000	\) 200,000	\( 200,000	\) 400,000	$ 400,000
2	100,000	200,000	250,000	450,000	400,000	800,000
3	100,000	300,000	350,000	800,000
4	100,000	400,000	400,000	1,200,000
5	100,000	500,000	500,000	1,700,000
6	100,000	600,000
7	100,000	700,000
8	100,000	800,000

Short Answer

Step by step solution

Definition of Payback Period

Calculation of payback period, ARR, NPV, and profitability index

Appropriate option

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Business Studies Textbooks

Organizational Communication

Corporate Finance

Business Development

Business Case Studies

Intermediate Accounting

Organizational Behavior

Study anywhere. Anytime. Across all devices.