Question

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$308,674 –$16,230 1 27,700 5,833 2 58,000 8,577 3 51,000 13,587 4 412,000 8,448 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

Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

a) The  payback period for Project A = 3 + ( $ 171,974 / $ 412,000)

= 3.417412621 Years

= 3.42 Years

Hence the correct answer is 3.42 Years

Year	Investment	Cash Inflow	Net Cash Flow
0	-3,08,674.00	-	-3,08,674.00	(Investment + Cash Inflow)
1	-	27,700	-2,80,974.00	(Net Cash Flow + Cash Inflow)
2	-	58,000	-2,22,974.00	(Net Cash Flow + Cash Inflow)
3	-	51,000	-1,71,974.00	(Net Cash Flow + Cash Inflow)
4	-	4,12,000	2,40,026.00	(Net Cash Flow + Cash Inflow)

b)

The  payback period for Project B = 2 + ( $ 1,820/ $ 13,587)

= 2.133951571 Years

= 2.13 Years

Hence the correct answer is 2.13 Years

Year	Investment	Cash Inflow	Net Cash Flow
0	-16,230.00	-	-16,230.00	(Investment + Cash Inflow)
1	-	5,833	-10,397.00	(Net Cash Flow + Cash Inflow)
2	-	8,577	-1,820.00	(Net Cash Flow + Cash Inflow)
3	-	13,587	11,767.00	(Net Cash Flow + Cash Inflow)
4	-	8,448	20,215.00	(Net Cash Flow + Cash Inflow)

c) The  discounted payback period for Project A:

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 3 + ( 188,101.55/ 326,343)

= 3.57639217 Years

= 3.58 Years

Hence the correct answer is 3.58 Years

	Cash Flow	Discounting Factor ( 6%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow
0	-3,08,674	1	-3,08,674	-3,08,674
1	27,700	0.943396226	26,132	-2,82,541.92
2	58,000	0.88999644	51,620	-2,30,922.13
3	51,000	0.839619283	42,821	-1,88,101.55
4	4,12,000	0.792093663	3,26,343	1,38,241.04

d)

The  discounted payback period for Project B:

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 2+ ( $ 3,093.67/ 11,408)

= 2.271184257 Years

= 2.27 Years

Hence the correct answer is 2.27 Years

	Cash Flow	Discounting Factor ( 6%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow
0	-16,230	1	-16,230	-16,230
1	5,833	0.943396226	5,503	-10,727.17
2	8,577	0.88999644	7,633	-3,093.67
3	13,587	0.839619283	11,408	8,314.24
4	8,448	0.792093663	6,692	15,005.84