Question

Consider the following two mutually exclusive projects:

  

Year	Cash Flow (A)	Cash Flow (B)
0	–$190,440	–$14,895
1	26,800	4,528
2	56,000	8,200
3	53,000	13,097
4	393,000	9,394

  

Whichever project you choose, if any, you require a 6 percent return on your investment.

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

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

= 3 + ( 54,640 / 393000)

= 3.14 Years

Hence the correct answer is 3.14 Years

Note:

Year	Investment	Cash Inflow	Net Cash Flow
0	-1,90,440	-	-1,90,440	(Investment + Cash Inflow)
1	-	26,800	-1,63,640	(Net Cash Flow + Cash Inflow)
2	-	56,000	-1,07,640	(Net Cash Flow + Cash Inflow)
3	-	53,000	-54,640	(Net Cash Flow + Cash Inflow)
4	-	3,93,000	3,38,360	(Net Cash Flow + Cash Inflow)

b.

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

= 2 +( 2167 / 13097)

= 2.17 Years

Hence the correct answer is 2.17 Years

Note:

Year	Investment	Cash Inflow	Net Cash Flow
0	-14,895	-	-14,895	(Investment + Cash Inflow)
1	-	4,528	-10,367	(Net Cash Flow + Cash Inflow)
2	-	8,200	-2,167	(Net Cash Flow + Cash Inflow)
3	-	13,097	10,930	(Net Cash Flow + Cash Inflow)
4	-	9,394	20,324	(Net Cash Flow + Cash Inflow)

c.

Discounted Payback Period for Project A = ( 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 + ( 70817.3584905661 / 3,11,292.809652542)

= 3.23 Years

Hence the correct answer is 3.23 Years

Note:

	Cash Flow	Discounting Factor ( 6%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-1,90,440	1	-1,90,440.00	-1,90,440.00
1	26,800	0.943396226415	25,283.018867925	-1,65,156.981132
2	56,000	0.889996440014	49,839.800640797	-1,15,317.180491
3	53,000	0.839619283032	44,499.822000712	-70,817.358491
4	3,93,000	0.792093663238	3,11,292.809652542	2,40,475.451162

d.

Discounted Payback Period for Project A =( 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 + ( 3325.33107867569 / 10996.4937498741)

= 2.30 Years

Hence the correct answer is 2.30 Years

Note:

	Cash Flow	Discounting Factor ( 6%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-14,895	1	-14,895.00	-14,895.00
1	4,528	0.943396226415	4,271.698113208	-10,623.301887
2	8,200	0.889996440014	7,297.970808117	-3,325.331079
3	13,097	0.839619283032	10,996.493749874	7,671.162671
4	9,394	0.792093663238	7,440.927872458	15,112.090544