Question

Consider the following two mutually exclusive projects:

  

Year	Cash Flow (A)	Cash Flow (B)
0	–$260,730	–$15,011
1	27,800	4,942
2	56,000	8,023
3	55,000	13,040
4	426,000	9,138

  

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

Qa)  Payback period for project A

Years	Cashflow	Cumulative cashflow
0	-260,730	-260,730
1	27,800	-232,930
2	56,000	-176,930
3	55,000	-121,930
4	426,000	304,070

Payback period= year before full recovery + Cumulative cash flow of the year before recovery / cash flow of year after recovery

= 3 + 121,930 / 426,000

= 3 + 0.29

= 3.29 years

Qb) Payback period of Project B

Years	Cash flow	Cumulative Cash flow
0	-15,011	-15,011
1	4,942	-10,069
2	8,023	-2,046
3	13,040	10,994
4	9,138	20,132

Payback period= year before full recovery + cumulative cash flow of the year before full recovery / cash flow of the year after recovery

= 2 + 2,046 / 13,040

= 2 + 0.16

= 2.16 years

Qc) Discounted payback period of project A

Years	Cashflow(a)	Discounting factor (b)	Discounted cash flow(a × b)	Cumulative discounted Cashflow
0	-260,730	-	-260,730	-260,730
1	27,800	0.943	26,215.4	-234,514.6
2	56,000	0.890	49,840	-184,674.6
3	55,000	0.840	46,200	-138,474.6
4	426,000	0.792	337,392	198,917.4

Discounted payback period = year before full recovery + Cumulative discounted cashflow in the year before full recovery / discounted cash flow of the year after full recovery

= 3 + 138,474.6 / 198,917.4

= 3 + 0.70

= 3.70 years

Qd) Discounted payback period of project B

Years	Cashflow ( a)	Discounting factor (b)	Discounted Cashflow (a × b)	Cumulative discounted Cash flow
0	-15,011	0	-15,011	-15,011
1	4,942	0.943	4,660.31	-10,350.69
2	8,023	0.890	7,140.47	-3,210.22
3	13,040	0.840	10,953.6	7,743.38
4	9,138	0.792	7,237.3	14,980.68

Discounted payback period = Year before full recovery + Cumulative discounted cash flow in the year before full recovery / discounted cash flow of the year after full recovery

= 2 + 3,210.22 / 10,953.60

= 2 + 0.29

= 2.29 year

Note :- Using PVF table for discounting factors

Answer may differ , due to discounting factor for project A (answer when using financial calculator for project A discounted payback  = 3.41 years)