Question

A project with an initial investment of $451,700 will generate equal annual cash flows over its 8-year life. The project has a required return of 8.9 percent. What is the minimum annual cash flow required to accept the project

Answer 1

Answer:

$81,307.55

Explanation:

The minimum annual cash flow required to accept the project is the equal annual cash flow that makes net present value of the project to be at least equal to zero. In other words, it is the equal annual cash flow that equates the initial investment and the summation of the present values (PV) of all the 8-year equal annual cash flow.

This can be estimated as using the formula for calculating the ordinary annuity as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)

Where;

PV = Present values of equal annual cash flow that is equal to Initial investment = $451,700

P = annual cash flow = ?

r = required return = 8.9% = 0.089

n = number of years = 8

Substitute the values into equation (1) to have:

$451,700 = P × [{1 - [1 ÷ (1 + 0.089)]^8} ÷ 0.089]

$451,700 = P × 5.55544994023063

P = $451,700 / 5.55544994023063

P = $81,307.5457181148

P = $81,307.55 when approximated to two decimal places.

Therefore, the minimum annual cash flow required to accept the project is $81,307.55.