Question

Consider a capital expenditure project to purchase and install new equipment with an initial cash outlay of $25,000. The project is expected to generate net after-tax cash flows each year of $6800 for ten years, and at the end of the project, a one-time after-tax cash flow of $11,000 is expected. The firm has a weighted average cost of capital of 12 percent and requires a 3-year payback on projects of this type. Determine whether this project should be accepted or rejected using NPV, IRR, PI, and PB. (Please show work without excel)

Answer 1

		PVF/PVAF AT 12%
Year	cash flow		disccf
1--10	6,800.00	5.65	38,420.00
10th year	11,000.00	0.322	3,542.00
			41,962.00
Net present value(NPV)=present value of cash inflows-present value of cash outflows

=$ 41962-$ 25000

=$ 16962.00

As per NPV,Project should be accepted as it has positive NPV

IRR is the rate at which present value of cash inflow equals present value of cash outflow.

IRR=small rate+(cash flow at small rate-target cash flow)/(cash flow at small rate-cash flow at big rate)*(big rate-small rate)

		PVF/PVAF AT 12%		PVF/PVAF AT 26%
year	cash flow		disccf		disccf
1--10	6,800.00	5.65	38,420.00	3.4648	23,560.64
10th year	11,000.00	0.322	3,542.00	0.099	1,089.00
			41,962.00		24,649.64

Target cash flow=initial investment=25000

IRR=12%+(41962-25000)/(41962-24649.64)*(26-12)

=12%+13.72%

=25.72%

As per IRR,Project should be accepted as the IRR is morethan the weighted average cost of capital.

Profitability Index(PI)=Present value of cash inflows/Present value of cash outflows

=41962/25000

=1.68

Pay back Period(PB) is the time required to earn the initial investment.

Pay back period=initial investment/pay back per year

=25000/6800

=3.68 years

As industry Pay back period is 3 years which is less than project pay back.project should not be accepted.

Note:The formula for calculating Present value factor is [1/(1+r)ⁿ] where “r” is the discount rate of interest and “n” is the number of years.

The formula for calculating Present value Annuity factor is 1*((1 - (1 / (1 + r) ^ n)) / r)