Question

P26-40 Using payback, ARR, NPV, and IRR to make capital investment decisions

This problem continues the Piedmont Computer Company situation from Chapter 25. Piedmont Computer Company is considering purchasing two different types of servers. Server A will generate net cash inflows of \(25,000 per year and have a zero residual value. Server A’s estimated useful life is three years, and it costs \)45,000. Server B will generate net cash inflows of \(25,000 in year 1, \)15,000 in year 2, and \(5,000 in year 3. Server B has a \)5,000 residual value and an estimated useful life of three years. Server B also costs $45,000. Piedmont Computer Company’s required rate of return is 14%.

Requirements

1. Calculate payback, accounting rate of return, net present value, and internal rate of return for both server investments. Use Microsoft Excel to calculate NPV and IRR.

2. Assuming capital rationing applies, which server should Piedmont Computer Company invest in?

Short answer

1. Capital budgeting figures:

Methods	Server A	Server B
Payback period	1.8 years	3 years
ARR	44.45%	6.67%
IRR	31%	6%
NPV	$13,040.80	-$4778.45

2.Capital rationing:Based on capital rationing, the business entity must select server A.

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.

Capital budgeting on both investments

Calculation of payback period:

1) Server A:

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\mathbf{=}\frac{\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}{\mathbf{E}\mathbf{x}\mathbf{p}\mathbf{e}\mathbf{c}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{25}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

2) Server B:

The total cost of initial investment is recovered in year 3. Therefore, the payback period of server B is 3 years.

Working note:

Year	Cash inflow	Cumulative
1	$25,000	$25,000
2	$15,000	$40,000
3	$5,000	$45,000

Calculation of accounting rate of return:

1) Server A:

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}\mathbf{\times }\mathbf{100}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{000}}{\frac{\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{0}}{\mathbf{2}}}\mathbf{\times }\mathbf{100}\\ \mathbf{=}\mathbf{44}\mathbf{.}\mathbf{45}\mathbf{\%}\end{array}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	$75,000
Less: Total depreciation during the life of the assetrole="math" localid="1656916821918" $\left(\$45,000-\$0\right)$	$45,000
Total operating income during the operating life	$30,000
Asset operating life in years	3
Average annual operating incomerole="math" localid="1656916874860" $\left(\frac{\$30,000}{3}\right)$	$10,000

Server B:

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}\mathbf{\times }\mathbf{100}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{667}}{\frac{\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{000}}{\mathbf{2}}}\mathbf{\times }\mathbf{100}\\ \mathbf{=}\mathbf{6}\mathbf{.}\mathbf{67}\mathbf{\%}\end{array}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	$45,000
Less: Total depreciation during the life of the asset$\left(\$45,000-\$5,000\right)$	$40,000
Total operating income during the operating life	$5,000
Asset operating life in years	3
Average annual operating income$\left(\frac{\$5,000}{3}\right)$	$1,667

Calculation of NPV and IRR:

Project	Server A		Server B
Useful life	3		3
Discounting rate	0.14		0.14
Initial investment	-45,000		-45,000
Year
1	25,000		25,000
2	25,000		15,000
3	25,000		10,000	(5,000+5,000)
Total	75,000		50,000
Output
NPV	$13,040.80		($4,778.45)
IRR	31%		6%

Excel formula for NPV: =NPV(Discount rate, Cash flow from 1^st year to 10^th year)+Initial investment

Excel formula for IRR: =IRR(All cash flows from year 1^st year to 10^th year including initial investment)

Using capital rationing

Server	Total present value of cash flows	/	Initial investment	=	Profitability index
A	75,000	/	45,000	=	1.67
B	50,000	/	45,000	=	1.11