Question

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$356,000 –$40,000 1 31,000 23,000 2 42,000 15,200 3 50,000 14,100 4 445,000 11,200 The required return on these investments is 13 percent. Required: (a) What is the payback period for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Payback period Project A years Project B years (b) What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g.,32.16).) Net present value Project A $ Project B $ (c) What is the IRR for each project? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Internal rate of return Project A % Project B % (d) What is the profitability index for each project? (Do not round intermediate calculations. Round your answers to 3 decimal places (e.g., 32.161).) Profitability index Project A Project B (e) Based on your answers in (a) through (d), which project will you finally choose?

Answer 1

a

Project A
Year	Cash flow stream	Cumulative cash flow
0	-356000	-356000
1	31000	-325000
2	42000	-283000
3	50000	-233000
4	445000	212000

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-(-233000))/(212000-(-233000))

3.52 Years

Project B
Year	Cash flow stream	Cumulative cash flow
0	-40000	-40000
1	23000	-17000
2	15200	-1800
3	14100	12300
4	11200	23500

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-(-1800))/(12300-(-1800))

2.13 Years

b

Project A
Discount rate	13.000%
Year	0	1	2	3	4
Cash flow stream	-356000	31000	42000	50000	445000
Discounting factor	1.000	1.130	1.277	1.443	1.630
Discounted cash flows project	-356000.000	27433.628	32892.161	34652.508	272926.834
NPV = Sum of discounted cash flows
NPV Project A =	11905.13
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project B
Discount rate	13.000%
Year	0	1	2	3	4
Cash flow stream	-40000	23000	15200	14100	11200
Discounting factor	1.000	1.130	1.277	1.443	1.630
Discounted cash flows project	-40000.000	20353.982	11903.830	9772.007	6869.170
NPV = Sum of discounted cash flows
NPV Project B =	8898.99
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

c

Project A
IRR is the rate at which NPV =0
IRR	14.07%
Year	0	1	2	3	4
Cash flow stream	-356000.000	31000.000	42000.000	50000.000	445000.000
Discounting factor	1.000	1.141	1.301	1.484	1.693
Discounted cash flows project	-356000.000	27176.943	32279.523	33688.892	262854.641
NPV = Sum of discounted cash flows
NPV Project A =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project B
IRR is the rate at which NPV =0
IRR	24.90%
Year	0	1	2	3	4
Cash flow stream	-40000.000	23000.000	15200.000	14100.000	11200.000
Discounting factor	1.000	1.249	1.560	1.948	2.433
Discounted cash flows project	-40000.000	18415.417	9744.308	7237.361	4602.914
NPV = Sum of discounted cash flows
NPV Project B =	0.001
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

d

Project A

PI= (NPV+initial inv.)/initial inv.

=(11905.13+356000)/356000

1.03

Project B

PI= (NPV+initial inv.)/initial inv.

=(8898.99+40000)/40000

1.22

e

Accept project B as it has higher IRR and profitability index