Chapter 12, Problem 8E

Payback Period and Simple Rate of Return
Nicks Novelties, Inc., is considering the purchase of Dew electronic games to place in its amusement houses. The games would cost a total of $300,000, have an eight-year useful life, and have a total salvage value of $20,000. The company estimates that annual revenues and expenses associated with the games would be as follows:

Required:
1. What is the payback period for the new electronic games? Assume that Nicks Novelties, Inc., il1 not purchase new games unless they provide a payback period of fire years or less. Would the company purchase the new games?
2. What is the simple rate of return promised by the games? If the company requires a simple rate of return of at least 12%, will the games be purchased?

To determine

Concept Introduction: When the Payback Period is computed after discounting the cash flows by a pre-determined rate (cut-off rate), it is called as the discounted payback period.

  $\begin{array}{l}Payback\text{ period}=\frac{Initial\text{ Investment}}{CFAT}\\ Therefore\text{CFAT}=Cashflow\text{After Tax}\end{array}$

Concept of simple Rate of return:

Simple Rate of Return is also known as Accounting (or) Average rate of return (ARR) Means the average annual yield on the project. In this method, Profit After Tax (PAT) instead of (FAT) is used for evaluation.

1. Payback period for the new electronic games. 2. Simple rate of interest.

Explanation of Solution

Calculation of cash flows after Tax

  $\begin{array}{l}\mathrm{Revenues}-200,000\\ (-)\text{ operating expenditure }-\underset{\_}{\text{ 100,000}}\\ \text{ 100,000}\\ \text{(}-\text{)Variable expenditure (Insurance) }-\underset{\_}{\text{ 7000}}\\ \text{ 93,000}\\ \text{(}-\text{) Fixed expenditure (Maintenance)}-\underset{\_}{\text{ 18,000}}\\ EBDIT-\text{ 75,000}\\ \text{(}-\text{) Depreciation }-\underset{\_}{\text{ 35,000}}\\ EBDIT-\text{ 40,000}\\ \text{(}-\text{) Tax }-\underset{\_}{\text{ 0}}\\ EAT-\underset{\_}{\text{ 40,000}}\\ \text{(+) Depreciation }-\underset{\_}{\text{35,000}}\\ \text{CFAT }-\text{ 75,000}\\ \end{array}$

  $\begin{array}{l}Therefore\text{ Payback period }=\frac{\text{Initial Investment}}{CFAT}\\ =\frac{300,000-20,000}{75,000}\\ =\frac{280,000}{75,000}\\ =\text{3}\text{.7 }\end{array}$

Here, the payback period is 3 years 7 months. So, Neck’s Novelties, Inc., would purchase the new games.

2. Simple rate of return

  $\begin{array}{l}ARR/SRR=\frac{\text{Average Profit After Tax}}{\text{Net Initial Investment}}\\ =\frac{\frac{40,000}{8}}{\frac{280,000}{2}}\times \text{100}\\ =\frac{5000}{140,000}\times \text{100}\\ =\text{3}\text{.57 \% }\end{array}$