Question

Suppose a project requires an initial investment of ＄2000 and it is expected to generate a

cash flow of ＄100 for 3 years plus ＄12500 in the third year. The target rate of return of

the project is 10% per annum. Calculate the net present value of the project.

Answer 1

We shall find the net present value for the project after 3 years

we know the formula for net present value is

(ALL CALCULATIONS IN $)

$\sum_{t=0}^{n}\frac{cash flow}{(1+i)^{t}}-initial$ $investment$

we let $R_{t}=cash\hspace{0.1cm}flow$ at point $t$

$\sum_{t=0}^{n}\frac{cash flow}{(1+i)^{t}}$

$\sum_{t=0}^{n}\frac{R_{t}}{(1+i)^{t}}$

where $n=3$

$=\frac{100}{(1+0.10)^{0}}+\frac{100}{(1+0.10)^{1}}+\frac{100}{(1+0.10)^{2}}+\frac{12500}{(1+0.10)^{3}}$

$=\frac{100}{(1.10)^{0}}+\frac{100}{(1.10)^{1}}+\frac{100}{(1.10)^{2}}+\frac{12500}{(1.10)^{3}}$

$=90.91+82.64+9391.44$

$=9564.99$

NOW,

The Net Present Value is thereby given by

$NPV=9564.99-initial\hspace{0.1cm}investment$

$=9564.99-2000\\=7564.99$

Therefore, the Net Present Value at the end of the third year is $$7564.99$