Chapter 6, Problem 29PS

Mutually exclusive investments and project lives* As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $50,000. Its operating costs are $20,000 a year, but at the end of five years, the machine will require a $20,000 overhaul (which is tax deductible). Thereafter, operating costs will be $30,000 until the machine is finally sold in year 10 for $5,000. The older machine could be sold today for $25,000. If it is kept, it will need an immediate $20,000 (tax-deductible) overhaul. Thereafter, operating costs will be $30,000 a year until the machine is finally sold in year 5 for $5,000. Both machines are fully depreciated for tax purposes. The company pays tax at 21%. Cash flows have been forecasted in real terms. The real cost of capital is 12%. Which machine should United Automation sell? Explain the assumptions underlying your answer.

Summary Introduction

To determine: The machine which is going to sell by company U and explain the assumptions.

Equivalent annual cost (EAC) is the annual cost for owning, maintain, and operating an assert for its entire life. It can be used for making capital budgeting decision and it helps to compare the cost-effectiveness of various assets that have unequal lifespans.

Explanation of Solution

The computation of NPV and EAC of option 1 is as follows:

Option 1: The selling of new machine will provide or the company will receive the post-tax cash flow from the sale of the new machine and pay the costs associated with keeping the old machine, and at the end of the 5th year company will receive the post-tax proceeds from the sale of the old machine.

$\begin{array}{c}{\text{NPV}}_1\text{ = }\left[\begin{array}{l}\left(\text{Sale proceeds}-\text{operation costs}\right)\times \\ \left(\left(\frac{1}{\text{Discount rate}}\right)-\left\{\frac{1}{\left[\text{Discount rate}\times {\left(1+\text{Discount rate}\right)}^5\right]}\right\}\right)\end{array}\right]+\frac{\text{Scrap value(1}-\text{tax rate)}}{{\left(1+\text{discount rate}\right)}^5}\\ =\left(\$50,000-\$20,000-\$30,000\right)\times \left(\left(\frac{1}{0.12}\right)-\left\{\frac{1}{\left[0.12\times {\left(1+0.12\right)}^5\right]}\right\}\right)+\frac{\$5,000\left(1-0.21\right)}{{\left(1+0.12\right)}^5}\\ =-\$59,491.86\end{array}$

$\begin{array}{c}{\text{EAC}}_1\text{=}-1\times \frac{\text{NPV}\times \text{discount rate}}{1-{\left(1+\text{discount rate}\right)}^{-5}}\\ =-1\times \frac{-\$59,491.86\times 0.12}{1-{\left(1+0.12\right)}^{-5}}\\ =\$16,503.62\end{array}$

Therefore, the NPV and equivalent annual cost (EAC) of option 1 is -$59,491.86 and $16,503.62 respectively.

The computation of NPV and EAC of option 2 is as follows:

Option 2: The selling of old machine will provide or the company will receive the post-tax cash flow from the sale of the old machine and pay the costs associated with keeping the new machine, and at the end of the 10th year company will receive the post-tax proceeds from the sale of the new machine.

$\begin{array}{c}{\text{NPV}}_2\text{ = }\left\{\begin{array}{l}\left[\begin{array}{l}\left(\text{Sale proceeds}-\text{overhaul}\right)\times \\ \left(\left(\frac{1}{\text{Discount rate}}\right)-\left\{\frac{1}{\left[\text{Discount rate}\times {\left(1+\text{Discount rate}\right)}^5\right]}\right\}\right)\end{array}\right]\\ -\left[\frac{\text{overhaul}}{{\left(1+\text{discount rate}\right)}^5}\right]\\ -\left[\frac{\begin{array}{l}\text{operating cost}\times \\ \left(\left(\frac{1}{\text{Discount rate}}\right)-\left\{\frac{1}{\left[\text{Discount rate}\times {\left(1+\text{Discount rate}\right)}^5\right]}\right\}\right)\end{array}}{\left({\left(1+\text{discount rate}\right)}^5\right)}\right]\\ +\left[\frac{\text{Scrap value(1}-\text{tax rate)}}{{\left(1+\text{discount rate}\right)}^{10}}\right]\end{array}\right\}\\ =\left\{\begin{array}{l}\left[\begin{array}{l}\left(\$25,000-\$20,000\right)\times \\ \left(\left(\frac{1}{0.12}\right)-\left\{\frac{1}{\left[0.12\times {\left(1+0.12\right)}^5\right]}\right\}\right)\end{array}\right]\\ -\left[\frac{\$20,000}{{\left(1+0.12\right)}^5}\right]-\left[\frac{\begin{array}{l}\$30,000\times \\ \left(\left(\frac{1}{0.12}\right)-\left\{\frac{1}{\left[0.12\times {\left(1+0.12\right)}^5\right]}\right\}\right)\end{array}}{\left({\left(1+0.12\right)}^5\right)}\right]+\left[\frac{\text{\$5,000(1}-0.21\text{)}}{{\left(1+0.12\right)}^{10}}\right]\end{array}\right\}\\ =-\$93,376.10\end{array}$

$\begin{array}{c}{\text{EAC}}_2\text{=}-1\times \frac{\text{NPV}\times \text{discount rate}}{1-{\left(1+\text{discount rate}\right)}^{-10}}\\ =-1\times \frac{-\$93,376.10\times 0.12}{1-{\left(1+0.12\right)}^{-10}}\\ =\$16,526.09\end{array}$

Therefore, the NPV and equivalent annual cost (EAC) of option 2 is -$93,376.10 and $16,526.09 respectively.

Therefore, the above computation is showing that the new machine should be sold and keep the old machine since it is the least expensive option and it has the lowest EAC compared to the other one.

Assumption: The important and vital assumption is that if the machine has to be replaced, the replacement will be a machine that is compatible and efficient to operate in the manner in which the replaced machine has operated.