Question

1. Assume that the risk adjusted cost of capital is 16% for project A, 18% for project B, and 20% for project C.
   

Project A:              Estimated cash flow is $25,800 per year for 10 years.
                              Cost $100,000

Project B:              Estimated cash flow is $33,500 per year for 8 years.
                              Cost $125,000

Project C:              Estimated cash flow is $44,000 per year for 7 years.
                              Cost $155,000

A. Compute the Payback, NPV, IRR and Profitability Index for each.
B. Rank order the Projects according to the value to the firm

Answer 1

A

Project A
Year	Cash flow stream	Cumulative cash flow
0	-100000	-100000
1	25800	-74200
2	25800	-48400
3	25800	-22600
4	25800	3200
5	25800	29000
6	25800	54800
7	25800	80600
8	25800	106400
9	25800	132200
10	25800	158000
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-(-22600))/(3200-(-22600))
3.88 Years
Project A
Discount rate	0.16
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-100000	25800	25800	25800	25800	25800	25800	25800	25800	25800	25800
Discounting factor	1	1.16	1.3456	1.560896	1.8106394	2.100342	2.436396	2.82622	3.278415	3.802961	4.411435
Discounted cash flows project	-100000	22241.38	19173.6	16528.97	14249.11	12283.72	10589.41	9128.802	7869.657	6784.187	5848.437
NPV = Sum of discounted cash flows
NPV Project A =	24697.27
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project A
IRR is the rate at which NPV =0
IRR	22%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-100000	25800	25800	25800	25800	25800	25800	25800	25800	25800	25800
Discounting factor	1	1.223746	1.497555	1.832628	2.2426724	2.744462	3.358526	4.109985	5.029579	6.15493	7.532074
Discounted cash flows project	-100000	21082.8	17228.08	14078.14	11504.132	9400.748	7681.941	6277.396	5129.654	4191.762	3425.351
NPV = Sum of discounted cash flows
NPV Project A =	7.92529E-05
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	22.37%
Project A
PI= (NPV+initial inv.)/initial inv.
=(24697.27+100000)/100000
1.25

B

Based on NPV

Rank 1 Project A

Rank 2 Project B

Rank 3 Project C