Question

Joe and Rich are both considering investing in a project that costs $25,500 and is expected to produce cash inflows of $15,800 in Year 1 and $15,300 in Year 2. Joe has a required return of 8.5 percent but Rich demands a return of 12.5 percent. Who, if either, should accept this project?

Answer 1

Calculate the Net Present Value for Individual \(\mathrm{J}\) at required return of \(8.5 \%\) as follows:

Net Present Value \(=\) Present value of cash inflows - Initial investment

$$ \begin{array}{l} =\frac{\text { Cash flow for year } 1}{(1+\text { Interest rate })^{1}}+\frac{\text { Cash flow for year } 2}{(1+\text { Interest rate })^{2}}-\$ 25,500 \\ =\frac{\$ 15,800}{(1+0.085)^{1}}+\frac{\$ 15,300}{(1+0.085)^{2}}-\$ 25,500 \\ =\$ 14,562.211981567+\$ 12,996.665887999-\$ 25,500 \\ =\$ 2,058.877869566 \\ =\$ 2,058.88 \end{array} $$

Calculate the Net Present Value for Individual \(\mathrm{R}\) at required return of \(12.5 \%\) as follows:

Net Present Value \(=\) Present value of cash inflows - Initial investment

$$ \begin{array}{l} =\frac{\text { Cash flow for year } 1}{(1+\text { Interest rate })^{1}}+\frac{\text { Cash flow for year } 2}{(1+\text { Interest rate })^{2}}-\$ 25,500 \\ =\frac{\$ 15,800}{(1+0.125)^{1}}+\frac{\$ 15,300}{(1+0.125)^{2}}-\$ 25,500 \\ =\$ 14,044.444444444+\$ 12,088.888888889-\$ 25,500 \\ =\$ 633.333333333 \\ =\$ 633.33 \end{array} $$

Here, the Net Present Value for both \(\mathbf{J}\) and \(\mathbf{R}\) is positive and above zero. So, both \(\mathbf{J}\) and R should accept this project.