Chapter 9, Problem 13PROB

Summary Introduction

Payback period:

Number of periods required for collecting initial investment is called payback period. It is traditional technique. Payback period uses normal cash flows. Therefore, the time value of money concept is ignored.

Calculate the payback period by using the following formula:

$\text{Payback period}=\left(\begin{array}{l}\text{The year prior }\\ \text{to full recovery }\\ \text{of initial investment}\end{array}\right)+\left(\frac{\begin{array}{l}\text{Amount of initial investment }\\ \text{that is unrecovered at the }\\ \text{start of the recovery year}\end{array}}{\begin{array}{l}\text{Total cash flow recovered }\\ \text{in the recovery year}\end{array}}\right)$

Decision for payback period:

$\begin{array}{c}\text{Payback period}<\text{Life of the project, Accept the project}\\ \text{Payback period}>\text{Life of the project, Reject the project}\end{array}$

Discounted payback period:

Number of periods required for collecting initial investment is called discounted payback period. It is a modern technique. Discounted Payback period uses discounted cash flows. Therefore, the time value of money concept is considered.

Calculate the discounted payback period by using the following formula:

$\text{Discounted Payback period}=\left(\begin{array}{l}\text{The year prior }\\ \text{to full recovery }\\ \text{of initial investment}\end{array}\right)+\left(\frac{\begin{array}{l}\text{Amount of initial investment }\\ \text{that is unrecovered at the }\\ \text{start of the recovery year}\end{array}}{\begin{array}{l}\text{Total discounted cash flow }\\ \text{recovered in the recovery year}\end{array}}\right)$

Decision for payback period:

$\begin{array}{c}\text{Discounted payback period}<\text{Life of the project, Accept the project}\\ \text{Discounted payback period}>\text{Life of the project, Reject the project}\end{array}$

Cost of the project is $270,000 and cash inflows are $75,000 for five years. Cost of capital is 11%.