Question

A project provides annual cash flows of £800 per year for 8 years and costs £3000 today. Is this a good project if the required return is 8%?

Answer 1

We have to calculate the present value of all future cash inflows and then deduct the initial investment in order to get the net present value. If the net present value is positive, the project is viable as it is generating the required rate of return else it is not viable

When cash inflows are fixed each period, we use annuity factor in order to calculate the present value of cash inflows

Annuity Factor

= [ 1 – ( 1 + r ) ^ - n ] / r

Where,

r = Rate of interest = 8% or 0.08

n = Number of years = 8

So, Annuity factor

= [ 1 – (1.08) ^ - 8] / 0.08

= [ 1 - 0.540269 ] / 0.08

= 0.459731 / 0.08

= 5.746639

So, Present value of cash inflows

= Annuity factor x Cash inflow each year

= 5.746639 x £ 800

= £ 4,597.31

So, Net Present Value

= Present values of inflows – Initial Investment

= £ 4,597.31 - £ 3,000

= £ 1,597.31

So, since the net present value is positive, it is a good project for investment as it is generating the required rate of return of 8% ( in fact, the return is more than 8% )