Chapter 6, Problem 32PS

Replacement decisions Hayden Inc. has a number of copiers that were bought four years ago for $20,000. Currently maintenance costs $2,000 a year, but the maintenance agreement expires at the end of two years, and thereafter, the annual maintenance charge will rise to $8,000. The machines have a current resale value of $8,000, but at the end of year 2, their value will have fallen to $3,500. By the end of year 6, the machines will be valueless and would be scrapped. Hayden is considering replacing the copiers with new machines that would do essentially the same job. These machines cost $25,000, and the company can take out an eight-year maintenance contract for $1,000 a year. The machines would have no value by the end of the eight years and would be scrapped. Both machines are depreciated using seven-year straight-line depreciation, and the tax rate is 39%. Assume for simplicity that the inflation rate is zero. The real cost of capital is 7%. When should Hayden replace its copiers?

Summary Introduction

To determine: The time at which company H need to replace its copiers.

Explanation of Solution

The net cash flows of current copiers are as follows:

Year	Calculation	Post-tax cash flow ($)
1	$\left(-2,000\times 0.61\right)+\left(0.39\times \frac{1}{7}\times 20,000\right)$	-105.71
2	$\left(-2,000\times 0.61\right)+\left(0.39\times \frac{1}{7}\times 20,000\right)$	-105.71
3	$\left(-8,000\times 0.61\right)+\left(0.39\times \frac{1}{7}\times 20,000\right)$	-3,765.71
4	$\left(-8,000\times 0.61\right)+\left(0.39\times \frac{1}{7}\times 20,000\right)$	-3,765.71
5	$\left(-8,000\times 0.61\right)$	-4,880
6	$\left(-8,000\times 0.61\right)$	-4,880

Table (1)

Therefore, the present value at 7% is as follows:

$\begin{array}{c}\text{EAC}=-1\times \left[\frac{-\$12,869.05}{\left(\left(\frac{1}{0.07}\right)-\left\{\frac{1}{\left[0.07{\left(1+0.07\right)}^6\right]}\right\}\right)}\right]\\ =-\$2,699.87\end{array}$

Therefore, the copier should be replaced only when the EAC of the replacements is less than $2,699.87.

Following computation showing the net cash flows of new copier when purchased:

The decision to replace must also take into account the post-tax resale value of the old machine as well as any cash flows for the old machine prior to its replacement.

Consider the following three situations:

1. I.            If the replacement is done now, then the present value of the cash flows is:

$\begin{array}{c}\text{PV}=-\$19,735.25+\$8,000-0.39\times \left\{\$8,000-\left[\$20,000\times \left(\frac{4}{7}\right)\right]\right\}\\ =-\$10,398.11\end{array}$

$\begin{array}{c}\text{EAC}=-1\times \left[\frac{-\$10,398.11}{\left(\left(\frac{1}{0.07}\right)-\left\{\frac{1}{\left[0.07{\left(1+0.07\right)}^8\right]}\right\}\right)}\right]\\ =\$1,741.35\end{array}$

1. II.            If the existing copiers are replaced two years from now, then the present value of the cash flows is:

$\begin{array}{c}\text{PV}=\frac{\left(-\$105.71\right)}{\left(1+0.07\right)}+\frac{\left(-\$105.71\right)}{{\left(1+0.07\right)}^2}+\frac{-\$19,753.25}{{\left(1+0.07\right)}^2}+\$3,500-\frac{0.39\times \left\{\$3,500-\left[\$20,000\times \left(\frac{2}{7}\right)\right]\right\}}{{\left(1+0.07\right)}^2}\\ =-\$14,840.81\end{array}$

$\begin{array}{c}\text{EAC}=-1\times \left[\frac{-\$14,840}{\left(\left(\frac{1}{0.07}\right)-\left\{\frac{1}{\left[0.07{\left(1+0.07\right)}^{10}\right]}\right\}\right)}\right]\\ =\$2,113\end{array}$

1. III.            Six years from now, both the book value and the resale value of the existing copiers will be zero. If the existing copiers are replaced six years from now, then the present value of the cash flows is:

   $\begin{array}{c}\text{PV}=-\$12,868.05+\frac{-\$21,135.98}{{\left(1+0.07\right)}^6}\\ =-\$26,952.84\end{array}$

$\begin{array}{c}\text{EAC}\text{}=-1\times \left[\frac{-\$26,952.84}{\left(\left(\frac{1}{0.07}\right)-\left\{\frac{1}{\left[0.07{\left(1+0.07\right)}^{14}\right]}\right\}\right)}\right]\\ =\$3,081.92\end{array}$

Therefore, the copier should be replaced immediately since that option has the lowest EAC.