Consider the following two projects: Cash flows Project A Project B C0 −$ 280 −$ 280...

Consider the following two projects:

Cash flows	Project A		Project B
C₀	−$	280	−$	280
C₁		120		148
C₂		120		148
C₃		120		148
C₄		120

a.What are the internal rates of return on the two projects?
b. If the opportunity cost of capital is 11%, what is the profitability index for each project?

Expert Solution

Project A
IRR is the rate at which NPV =0
IRR	0.256780467
Year	0	1	2	3	4
Cash flow stream	-280	120	120	120	120
Discounting factor	1	1.25678	1.579497	1.985081	2.4948112
Discounted cash flows project	-280	95.48207	75.97355	60.45093	48.099832
NPV = Sum of discounted cash flows
NPV Project A =	0.006376837
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

IRR=	25.68%



Project B
IRR is the rate at which NPV =0
IRR	0.271340432
Year	0	1	2	3
Cash flow stream	-280	148	148	148
Discounting factor	1	1.27134	1.616306	2.054876
Discounted cash flows project	-280	116.4126	91.56679	72.02382
NPV = Sum of discounted cash flows
NPV Project B =	0.003174004
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

IRR=	27.13%



b
Project A
Discount rate	0.11
Year	0	1	2	3	4
Cash flow stream	-280	120	120	120	120
Discounting factor	1	1.11	1.2321	1.367631	1.5180704
Discounted cash flows project	-280	108.1081	97.39469	87.74297	79.047717
NPV = Sum of discounted cash flows
NPV Project A =	92.29
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

PI= (NPV+initial inv.)/initial inv.
=(92.29+280)/280
1.33



Project B
Discount rate	0.11
Year	0	1	2	3
Cash flow stream	-280	148	148	148
Discounting factor	1	1.11	1.2321	1.367631
Discounted cash flows project	-280	133.3333	120.1201	108.2163
NPV = Sum of discounted cash flows
NPV Project B =	81.67
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

PI= (NPV+initial inv.)/initial inv.
=(81.67+280)/280
1.29

jeff jeffy answered 1 year ago

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