Question

will receive $200 payment at the end of 11 year to 20th year

salveage value is $1000

12% interest rate.

What's the present value? Please explain why "end of year" matters

Answer 1

present value = sum of present values of cash flows

present value of each cash flow = cash flow / (1 + interest rate)ⁿ, where n = number of years after which the cash flow occurs

Cash flow at end of years 11 to 19 = $200

Cash flow at end of year 20 = $200 + $1000 = $1200

present value = $467.51

A B C 1 Year CF PV of CF 2 11 $ 200 $ 57 3 12 $ 200 $ 51 4 13 $ 200 $ 46 5 14 $ 200 $ 41 6 15 $ 200 $ 37 16 $ 200 $ 33 8 17 $ 200 $ 29 9 18 $ 200 $ 26 19 $ 200 $ 23 20 $ 1,200 $ 124 12 Total $ 467.51 |

A 1 Year CF 4 13200 5 14 200 6 15 200 7 16 200 8 17 200 9 18 200 10 19 200 11 20 1200 Total PV of CF =B2/(1+12%)^A2 =B3/(1+12%)^A3 =B4/(1+12%)^A4 =B5/(1+12%)^A5 =B6/(1+12%) A6 =B7/(1+12%)^A7 =B8/(1+12%)^A8 =B9/(1+12%)^A9 =B10/(1+12%)^A10 =B11/(1+12%)^A11 =SUM(C2:011)

End of year matters because if the payment is received at the end of the year, the payment is discounted for that year as well. However, if the payment is received at the beginning of the year, it is not discounted for that year because it is equivalent to receiving the payment at the end of the previous year. Thus, the present value is higher if the payment is received at the beginning of the year, and lower if the payment is received at the end of the year.