Question

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$261,103 –$15,350 1 26,600 5,181 2 51,000 8,059 3 51,000 13,055 4 392,000 8,690 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
Project A
Year	Cash flow stream	Cumulative cash flow
0	-261103	-261103
1	26600	-234503
2	51000	-183503
3	51000	-132503
4	392000	259497
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 3 and 4
therefore by interpolation payback period = 3 + (0-(-132503))/(259497-(-132503))
3.34 Years
b
Project B
Year	Cash flow stream	Cumulative cash flow
0	-15350	-15350
1	5181	-10169
2	8059	-2110
3	13055	10945
4	8690	19635
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 2 and 3
therefore by interpolation payback period = 2 + (0-(-2110))/(10945-(-2110))
2.16 Years
c
Project A			Discount rate=	0.06
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow
0	-261103	-261103	1	-261103	-261103
1	26600	-234503	1.06	25094.34	-234503
2	51000	-183503	1.1236	45389.82	-183503
3	51000	-132503	1.191016	42820.58	-132503
4	39200000.00%	259497	1.262477	310500.7	259497
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 3 and 4
therefore by interpolation payback period = 3 + (0-(-147798.26))/(162702.46-(-147798.26))
3.48 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor
d
Project B			Discount rate=	0.06
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow
0	-15350	-15350	1	-15350	-15350
1	5181	-10169	1.06	4887.736	-10169
2	8059	-2110	1.1236	7172.481	-2110
3	13055	10945	1.191016	10961.23	10945
4	8690	19635	1.262477	6883.294	19635
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 2 and 3
therefore by interpolation payback period = 2 + (0-(-3289.78))/(7671.45-(-3289.78))
2.3 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor
e
Project A
Discount rate	0.06
Year	0	1	2	3	4
Cash flow stream	-261103	26600	51000	51000	392000
Discounting factor	1	1.06	1.1236	1.191016	1.262477
Discounted cash flows project	-261103	25094.34	45389.82	42820.58	310500.72
NPV = Sum of discounted cash flows
NPV Project A =	16270246.00%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
f
Project B
Discount rate	0.06
Year	0	1	2	3	4
Cash flow stream	-15350	5181	8059	13055	8690
Discounting factor	1	1.06	1.1236	1.191016	1.262477
Discounted cash flows project	-15350	4887.736	7172.481	10961.23	6883.2939
NPV = Sum of discounted cash flows
NPV Project B =	14554.74
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor