Question

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$198,205 –$15,654 1 26,400 5,862 2 58,000 8,338 3 56,000 13,300 4 381,000 8,095 Whichever project you choose, if any, you require a 6 percent return on your investment. Required: (a) What is the payback period for Project A? (b) What is the payback period for Project B? (c) What is the discounted payback period for Project A? (d) What is the discounted payback period for Project B? (e) What is the NPV for Project A? (f) What is the NPV for Project B ? (g) What is the IRR for Project A? (h) What is the IRR for Project B? (i) What is the profitability index for Project A? (j) What is the profitability index for Project B?

Answer 1

Year	A	B	DCF A	DCF B
0	-$     198,205	-$     15,654	-$198,205.00	-$15,654.00
1	$        26,400	$        5,862	$   24,905.66	$   5,530.19
2	$        58,000	$        8,338	$   51,619.79	$   7,420.79
3	$        56,000	$      13,300	$   47,018.68	$ 11,166.94
4	$      381,000	$        8,095	$ 301,787.69	$   6,412.00
Payback	3.15	2.11
Discounted	3.25	2.24
NPV	$ 227,126.82	$ 14,875.91
IRR	33.00%	39.00%
PI	2.15	1.95

Payback Period is the no. of years it take to recover the initial investment. We can observe that in the case of A, the investment is recovered in year 4.

Payback (A) = 3 + (198,205 - 26,400 - 58,000 - 56,000) / 381,000 = 3.15 years

and similarly for B, Payback (B) = 2 + (15,654 - 5,862 - 8,338) / 13,300 = 2.11 years

In order to calculate the discounted payback, we need to calculate the discounted cash flows.

DCF = CFn / (1 + r)^n, where, CFn - Cash Flow in year n, r - discount rate = 6%, n - period

Using DCF for the both project, discounted payback period is calculated in the same fashion as normal payback.

NPV = Sum of DCF

IRR can be calculated using IRR function in excel or calculator

Profitability Index (PI) = 1 + NPV / Investment