Question

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?

Answer 1

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