Question

Consider the following two mutually exclusive projects:

  

Year	Cash Flow (A)	Cash Flow (B)
0	–$216,888	–$15,026
1	26,900	4,016
2	51,000	8,270
3	54,000	13,423
4	420,000	9,668

  

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 Period A:

Payback period = full years until recovery + unrecovered cost at the beginning of last year/cash flow during the last year

Year	Cash flow	Cumulative Cash flow
1	26,900	26,900
2	51,000	26,900+51,000= 77,900
3	54,000	77,900+54,000= 1,31,900
4	420,000

Payback period = 3 years+ 216,888-131,900/420,000

= 3 years + 0.2 years

= 3.2 years

b) Payback period of Project B:

Year	Cash flows	Cumulative cash flows
1	4,016	4,016
2	8,270	4,016+8,270=122,86
3	13,423
4	9,668

Payback period = 2 years+ 15,026-122,86/13,423

= 2 years+0.2 years

= 2.2 years

c) Calculation of discounted payback period of project A:

Year	Cash flow (1)	Discount rate@6% (2)	Discounted Cash flow (3) (1*2)	Cumulative cash flow
1	26,900	1/1.06=0.943	25,367	25,367
2	51,000	1/(1.06)^2=0.890	45,390	25,367+45,390=70,757
3	54,000	1/(1.06)^3=0.840	45,360	70,757+45,360=116,117
4	420,000	1/(1.06)^4=0.792	332,640

Discounted pay back period = 3 years + 216,888-116,117/332,640

= 3 years+0.30 years

= 3.3 years

d) Discounted payback period of project B:

Year	Cash flow (1)	Discount rate @6% (2)	Discounted cash flow (3) (1*2)	Cumulative Cash flows
1	4,016	1/1.06=0.943	3,787	3,787
2	8,270	1/(1.06)^2=0.890	7,360	3,787+7,360=111,47
3	13,423	1/(1.06)^3=0.840	11,275
4	9,668	1/(1.06)^4=0.792

Discounted payback period = 2 years + (15,026-111,47)/11,275

= 2 years + 0.34 years

= 2.34 years

e) Calculation of NPV of project A:

Year	Cash flows (1)	Discount rate @6% (2)	Discounted cash flows (3) (1*2)
1	26,900	1/1.06=0.943	25,367
2	51,000	1/(1.06)^2=0.890	45,390
3	54,000	1/(1.06)^3=0.840	45,360
4	420,000	1/(1.06)^4=0.792	332,640
		Cash inflows	448,757

NPV = Cash inflows - Cash outflows

= 448,757-216,888

= 231,869

f) Calculation of NPV of Project B:

Year	Cash flow (1)	Discount rate @6% (2)	Discounted cash flow (3) (1*2)
1	4,016	1/1.06=0.943	3,787
2	8,270	1/(1.06)^2=0.890	7,360
3	13,423	1/(1.06)^3=0.840	11,275
4	9668	1/(1.06)^4=0.792	7,657
		Cash inflows	30,079

NPV = Cash inflows - Cash Outflows

= 30,079-15,026

= 150,53

g) Calculation of IRR of project A:

Cash flows @ 7%

Year	Cash flows (1)	Discount rate @7% (2)	Discounted cash flows (3) (1*2)
1	26,900	1/1.07=0.934	25,124
2	51,000	1/(1.07)^2=0.873	44,523
3	54,000	1/(1.07)^3=0.816	44,064
4	420,000	1/(1.07)^4=0.763	320,460
		Cash inflows	434,171

NPV = 434,171- 216,888

= 217,283

IRR = 6%+(448,757-216,888)/(448,757-434,171)*(7%-6%)

= 6%+231,869/14,586*1%

= 6%+15.89%

= 21.89% (approxiamately)

h) Calculation of IRR of project B:

Cash flows @7%

Year	Cash flows (1)	Discount rate @7% (2)	Discounted cash flows (3) (1*2)
1	4,016	0.934	3,751
2	8,270	0.873	7,219
3	13,423	0.816	10,953
4	9,668	0.763	7,377
		Cash inflows	29,300

IRR = 6%+(30,079-15,026)/(30,079-29,300)*(7%-6%)

= 6%+15,053/779*1%

= 6%+19.32%

= 25.32% (approx)

i) Profitability index of project A:

Profitability index = present value of future cash flows/initial investment

Present value of future cash flows = 448,757

Initial investment = 216,888

Profitability index = 448,757/216,888

= 2.07

j) profitability index of project B:

Present value of future cash flows = 30,079

Initial investment = 15,026

Profitability index = 30,079/15,026

= 2