Chapter 10, Problem 20PSA

a.

To determine

Ascertain the payback period and unadjusted rate of return (use average investment) for each alternative.

Explanation of Solution

The annual rate of return method:

The annual rate of return is the amount of income which is earned over the life of the investment. It is used to measure the annual income as a percent of the annual investment of the business, and it is also known as the accounting rate of return.

The annual rate of return is computed as follows:

$\text{Average rate of return}=\frac{\text{Estimated average net income}}{\text{average investment}}$

Payback period:

Payback period is the expected time period which is required to recover the cost of investment. It is one of the capital investment method used by the management to evaluate the proposal of long-term investment (fixed assets) of the business.

Ascertain the payback period for each alternative as follows:

Alternative 1:

$\begin{array}{c}\begin{array}{l}\text{Payback period }\\ \text{for alternative 1}\end{array}\}=\frac{\text{Cost of investment}}{\text{Cash flows per year (1)}}\\ =\frac{\$8,100}{\$4,780}\\ =1.69\text{ years}\end{array}$

Alternative 2:

$\begin{array}{c}\begin{array}{l}\text{Payback period }\\ \text{for alternative 2}\end{array}\}=\frac{\text{Cost of investment}}{\text{Cash flows per year (1)}}\\ =\frac{\$10,080}{\$5,360}\\ =1.88\text{ years}\end{array}$

Ascertain the unadjusted rate of return for each alternative as follows:

Alternative 1:

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\$2,080}{\left(\frac{\$8,100}{2}\right)}\times 100\\ =\frac{\$2,080}{\$4,050}\times 100\\ =51.36\%\end{array}$

Alternative 2:

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\$2,840}{\left(\frac{\$10,080}{2}\right)}\times 100\\ =\frac{\$2,840}{\$5,040}\times 100\\ =56.35\%\end{array}$

Working note:

Calculate the amount of cash flow per year for both alternatives:

Particulars	Alternative 1	Alternative 2
Cash revenue	$6,200	$8,500
Less: Operating expense	900	2,430
Depreciation expense	2,700	2,520
Income before tax	2,600	3,550
Income tax expense	520 (2)	710 (3)
Net Income	2,080	2,840
Add: Depreciation  expense	2,700	2,520
Cash flow per year	$4,780	$5,360

Table (1)

…… (1)

Calculate the amount of income tax expense for alternative 1:

$\begin{array}{c}\begin{array}{l}\text{Income tax expense}\\ \text{for alternative 1}\end{array}\}=\text{Rate of tax}\times \text{Income before tax}\\ =\frac{20}{100}\times \$2,600\\ =\$520\end{array}$

…… (2)

Calculate the amount of income tax expense for alternative 2:

$\begin{array}{c}\begin{array}{l}\text{Income tax expense}\\ \text{for alternative 2}\end{array}\}=\text{Rate of tax}\times \text{Income before tax}\\ =\frac{20}{100}\times \$3,550\\ =\$710\end{array}$

…… (3)

Calculate the amount of depreciation expense for alternative 1:

$\begin{array}{c}\begin{array}{l}\text{Depreciation expense}\\ \text{for alternative 1}\end{array}\}=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\\ =\frac{\$8,100-0}{3\text{ Years}}\\ =\$2,700\end{array}$

…… (4)

Calculate the amount of depreciation expense for alternative 2:

$\begin{array}{c}\begin{array}{l}\text{Depreciation expense}\\ \text{for alternative 2}\end{array}\}=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\\ =\frac{\$10,080-0}{\text{4 Years}}\\ =\$2,520\end{array}$

…… (5)

b.

To determine

Indicate the investment alternative that is recommendable and explain the reason behind it.

Explanation of Solution

Indicate the investment alternative that is recommendable and explain the reason behind it as follows:

From the above calculation it is clear that alternative 2 appears better than alternative 1. This is because alternative 2 has a longer useful life and higher unadjusted rate of return, while alternative 1 has a shorter useful life and shorter unadjusted rate of return.

If the investor prefers shorter payback period then the investor can go for alternative 1 since it provide a quicker payback than alternative 2.