Chapter 16, Problem 20P

Problem 10-20A Using the payback period and unadjusted rate of return to evaluate alternative investment opportunities

Seth Fitch owns a small retail ice cream parlor. He is considering expanding the business and has identified two attractive alternatives. One involves purchasing a machine that would enable Mr. Fitch to offer frozen yogurt to customers. The machine would cost $16,200 and has an expected useful life of three years with no salvage value. Additional annual cash revenues and cash operating expenses associated with selling yogurt are expected to be $12,400 and $1,800, respectively.

Alternatively, Mr. Fitch could purchase for $20,160 the equipment necessary to serve cappuccino. That equipment has an expected useful life of four years and no salvage value. Additional annual cash revenues and cash operating expenses associated with selling cappuccino are expected to be $17,000 and $4,860, respectively.

Income before taxes earned by the ice cream parlor is taxed at an effective rate of 20 percent.

Required

Round your figures, including percentage rates, to two decimal points.

1. a. Determine the payback period and unadjusted rate of return (use average investment) for each alternative.
2. b. Indicate which investment alternative you would recommend. Explain your choice.

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.

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:

$\begin{array}{c}\begin{array}{l}\text{Payback period }\\ \text{for alternative 1}\end{array}\}=\frac{\text{Cost of investment}}{\text{Cash flows per year (1)}}\\ =\frac{\$16,200}{\$9,560}\\ =1.69\text{ years}\end{array}$

Alternative 2:

$\begin{array}{c}\begin{array}{l}\text{Payback period }\\ \text{for alternative 2}\end{array}\}=\frac{\text{Cost of investment}}{\text{Cash flows per year (1)}}\\ =\frac{\$20,160}{\$10,720}\\ =1.88\text{ years}\end{array}$

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

Alternative 1:

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\$4,160}{\left(\frac{\$16,200}{2}\right)}\times 100\\ =\frac{\$4,160}{\$8,100}\times 100\\ =51.36\%\end{array}$

Alternative 2:

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\$5,680}{\left(\frac{\$20,160}{2}\right)}\times 100\\ =\frac{\$5,680}{\$10,080}\times 100\\ =56.35\%\end{array}$

Working note:

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

Particulars	Alternative 1	Alternative 2
Cash revenue	$12,400	$17,000
Less: Operating expense	1,800	4,860
Depreciation expense	5,400(4)	5,040(5)
Income before tax	5,200	7,100
Income tax expense	1,040 (2)	1,420 (3)
Net Income	4,160	5,680
Add: Depreciation  expense	5,400	5,040
Cash flow per year	$9,560	$10,720

Table (1)

(1)

Calculate the amount of income tax expense for alternative 1:

$\begin{array}{c}\begin{array}{l}\text{Income tax expense}\\ \text{for alternative 1}\end{array}\}=\text{Rate of tax}\times \text{Income before tax}\\ =\frac{20}{100}\times \$5,200\\ =\$1,040\end{array}$

(2)

Calculate the amount of income tax expense for alternative 2:

$\begin{array}{c}\begin{array}{l}\text{Income tax expense}\\ \text{for alternative 2}\end{array}\}=\text{Rate of tax}\times \text{Income before tax}\\ =\frac{20}{100}\times \$7,100\\ =\$1,420\end{array}$

(3)

Calculate the amount of depreciation expense for alternative 1:

$\begin{array}{c}\begin{array}{l}\text{Depreciation expense}\\ \text{for alternative 1}\end{array}\}=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\\ =\frac{\$16,200-0}{3\text{ Years}}\\ =\$5,400\end{array}$

(4)

Calculate the amount of depreciation expense for alternative 2:

$\begin{array}{c}\begin{array}{l}\text{Depreciation expense}\\ \text{for alternative 2}\end{array}\}=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\\ =\frac{\$20,160-0}{\text{4 Years}}\\ =\$5,040\end{array}$

(5)

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.