Question

Refer to the information in Exercise 24-11 and instead assume the company requires a 12% return on its investments. Compute each project’s

(a) net present value and

(b) profitability index. (Round present value calculations to the nearest dollar.) Express the profitability index as a percentage (rounded to two decimal places). If the company can choose only one project, which should it choose? Explain.

Short answer

The present value of project A is $13,686, project B is $1,906 and the profitability index of project A is 117.11%, and project B is 101.58%.

Step-by-step solution

Step-by-Step SolutionStep 1: Computation of net present value

Net present value of project X1

Initial Investment = $80,000, I = 12%
Year	Cash Inflow	x	PV Factor	=	Present Value
1	$25,000	X	0.8929	=	$22,322
2	35,500	X	0.7972	=	28,300
3	$60,500	X	0.7118	=	43,064
					93,686
Present value of cash inflows					93,686
Present Value of cash outflows					-80,000
Net Present Value					$13,686

Net present value of project X2

Initial Investment = $120,000, I = 12%
Year	Cash Inflow	x	PV Factor	=	Present Value
1	60,000	X	0.8929	=	$53,574
2	50,000	X	0.7972	=	39,860
3	40,000	X	0.7118	=	28,472
					121,906
Present value of cash inflows					121,906
Present Value of cash outflows					-120,000
Net Present Value					$1,906

Computation of profitability index

Project X1

$$\begin{gathered} \mathbf{Profitability}\mathbf{}\mathbf{Index}\mathbf{=}\frac{\mathrm{Present}\mathrm{Value}\mathrm{of}\mathrm{net}\mathrm{cash}\mathrm{flows}}{\mathrm{Initial}\mathrm{Investment}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$93,686}{\$80,000}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{117}\mathbf{.}\mathbf{11}\mathbf{\%} \end{gathered}$$

Project X2

$$\begin{gathered} \mathbf{Profitability}\mathbf{}\mathbf{Index}\mathbf{=}\frac{\mathrm{Present}\mathrm{Value}\mathrm{of}\mathrm{net}\mathrm{cashflows}}{\mathrm{Initial}\mathrm{Investment}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$121,906}{\$120,000}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{101}\mathbf{.}\mathbf{58}\mathbf{\%} \end{gathered}$$

The company should go for project X1 as the net present value of X1 is higher than project X2. Other than that project X1 has a better profitability index than the project X2.