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WG Investors is looking at three different investment opportunities. Investment one is a​ five-year investment with...

WG Investors is looking at three different investment opportunities. Investment one is a​ five-year investment with a cost of ​$400 and a promised payout of ​$800 at maturity. Investment two is a​ seven-year investment with a cost of ​$400 and a promised payout of ​$1,040. Investment three is a​ ten-year investment with a cost of ​$400 and a promised payout of ​$1,960. WG Investors can take on only one of the three investments. Assuming that all three investment opportunities have the same level of​ risk, calculate the effective annual return for each​ investment, and select the best investment choice.

What is the effective annual return for investment​ one, a​ five-year investment with a cost of ​$400 and a promised payout of $800 at​ maturity?

Solutions

Expert Solution

One
IRR is the rate at which NPV =0
IRR 14.87%
Year 0 1 2 3 4 5
Cash flow stream -400.000 0.000 0.000 0.000 0.000 800.000
Discounting factor 1.000 1.149 1.320 1.516 1.741 2.000
Discounted cash flows project -400.000 0.000 0.000 0.000 0.000 400.000
NPV = Sum of discounted cash flows
NPV One = 0.000
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor
IRR= 14.87%
Two
IRR is the rate at which NPV =0
IRR 14.63%
Year 0 1 2 3 4 5 6 7
Cash flow stream -400.000 0.000 0.000 0.000 0.000 0.000 0.000 1040.000
Discounting factor 1.000 1.146 1.314 1.506 1.726 1.979 2.268 2.600
Discounted cash flows project -400.000 0.000 0.000 0.000 0.000 0.000 0.000 400.000
NPV = Sum of discounted cash flows
NPV Two = 0.000
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor
IRR= 14.63%
Three
IRR is the rate at which NPV =0
IRR 17.22%
Year 0 1 2 3 4 5 6 7 8 9 10
Cash flow stream -400.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1960.000
Discounting factor 1.000 1.172 1.374 1.611 1.888 2.214 2.595 3.042 3.566 4.180 4.900
Discounted cash flows project -400.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 400.001
NPV = Sum of discounted cash flows
NPV Three = 0.001
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor
IRR= 17.22%

Choose three as it has highest return


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