Question

In: Finance

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

Solutions

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

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