Question

Using a discount rate of five percent compounded semiannually, what is the value today of the following cash flow stream?

($200), year 1             $200, year 2                $400, year 3                $800, year 5                $1,600, year 6

What is the value of each of these cash flows at the end of the six years? Also, what is the relevant time for each?

Answer 1

Year 1 Cash Flow: -200 Value at the end of Year 6 = 200(1+0.05/2)^2*6 = 200*(1.025)^12 = $268.97

Year 2 Cash Flow: 200   Value at the end of Year 6 = 200(1+0.05/2)^2*5 = 200*(1.025)^10 = $256

Year 3 Cash Flow: 400   Value at the end of Year 6 = 400(1+0.05/2)^2*4 = 400*(1.025)^8 = $487.36

Year 5 Cash Flow: 800   Value at the end of Year 6 = 800(1+0.05/2)^2*1 = 800*(1.025)^2 = $840.5

Year 6 Cash Flow:1600    Value at the end of Year 6 = 1600(1+0.05/2)^2*0 = $1600