Question

Henderson Manufacturing, Inc. has a manufacturing machine that needs attention. The company is considering two options. Option 1 is to refurbish the current machineat a cost of \(1,200,000. If refurbished, Henderson expects the machine to last anothereight years and then have no residual value. Option 2 is to replace the machine at acost of \)4,600,000. A new machine would last 10 years and have no residual value.Henderson expects the following net cash inflows from the two options:

YearRefurbish CurrentPurchase New

MachineMachine

1 \( 350,000 \) 3,780,000

2 340,000 510,000

3 270,000 440,000

4 200,000 370,000

5 130,000 300,000

6 130,000 300,000

7 130,000 300,000

8 130,000 300,000

9 300,000

10 300,000

Total \( 1,680,000 \) 6,900,000

Henderson 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 twooptions.

2. Which option should Henderson choose? Why?

Short answer

NPV for refurbishing:$19,810

NPV for new machine:$732,930

Step-by-step solution

Computation of capital budgeting ratios

For refurbishing the current Machine

$\begin{array}{c}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{1}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{2}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{3}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{4}\mathbf{+}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{5}\\ \mathbf{=}\mathbf{\$}\mathbf{350}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{340}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{200}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{40}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\mathbf{=}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\frac{\mathbf{\$}\mathbf{40}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{130}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{31}\\ \mathbf{=}\mathbf{4}\mathbf{.}\mathbf{31}\mathbf{Y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}{\mathbf{N}\mathbf{o}\mathbf{.}\mathbf{o}\mathbf{f}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{680}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}{\mathbf{8}}\\ \mathbf{=}\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}{\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}{\mathbf{2}}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{600}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{o}\mathbf{r}\mathbf{10}\mathbf{\%}\end{array}$

Year	Cash Inflow	PV factor	Present Value
1	$350,000	0.909	$318,150
2	340,000	0.826	280,840
3	270,000	0.751	202,770
4	200,000	0.683	136,600
5	130,000	0.621	80,730
6	130,000	0.564	73,320
7	130,000	0.513	66,690
8	130,000	0.467	60,710
Total			$1,219,810

$\begin{array}{c}\mathbf{N}\mathbf{P}\mathbf{V}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{219}\mathbf{,}\mathbf{810}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{810}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{t}\mathbf{a}\mathbf{b}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}\mathbf{=}\frac{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}}{\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{219}\mathbf{,}\mathbf{810}}{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{017}\end{array}$

For purchasing new Machine

$\begin{array}{c}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{1}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{2}\mathbf{+}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{3}\\ \mathbf{=}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{780}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{510}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{310}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\mathbf{=}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\frac{\mathbf{\$}\mathbf{310}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{440}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{705}\\ \mathbf{=}\mathbf{2}\mathbf{.}\mathbf{7}\mathbf{Y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}{\mathbf{N}\mathbf{o}\mathbf{.}\mathbf{o}\mathbf{f}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{900}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}}{\mathbf{10}}\\ \mathbf{=}\mathbf{\$}\mathbf{230}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{230}\mathbf{,}\mathbf{000}}{\frac{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}}{\mathbf{2}}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{230}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{300}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{o}\mathbf{r}\mathbf{10}\mathbf{\%}\end{array}$

Year	Cash Inflow	PV factor	Present Value
1	$ 3,780,000	0.909	$ 3,436,020
2	510,000	0.826	421,260
3	440,000	0.751	330,440
4	370,000	0.683	252,710
5	300,000	0.621	186,300
6	300,000	0.564	169,200
7	300,000	0.513	153,900
8	300,000	0.467	140,100
9	300,000	0.424	127,200
10	300,000	0.386	115,800
Total			$ 5,332,930

$\begin{array}{c}\mathbf{N}\mathbf{P}\mathbf{V}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{332}\mathbf{,}\mathbf{930}\mathbf{-}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{732}\mathbf{,}\mathbf{930}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{t}\mathbf{a}\mathbf{b}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}\mathbf{=}\frac{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}}{\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{332}\mathbf{,}\mathbf{930}}{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{16}\end{array}$

Recommended Option

Based on the above analysis, the payback period for refurbishing the current machine is higher than for purchasing a new machine. Furthermore, the NPV is also lower for refurbishing g current machine than for purchasing a new machine.

So the recommended option would be to purchase the new machine.