Question

Give an example of a retirement planning problem whose solution involves calculating the present value of multiple cash flows. Give another example whose solution involves calculating the future value of multiple cash flows.

Answer 1

Example : Suppose Mr. X is planning for his retirement after 5 years end & for this he is depositing yearly $1,000 @ 10% interest rate for 5 years in an retirement account. Calculate value of cash flows at the end of year 5 & value of cash flows at beginning of year 1.

Solutions :

i) Value of cash flows at the end of year 5 :

Future value (F. V.) of cash flows = Cash flow * (((1 + i)^n) - 1) / i)

i (interest rate) = 10% or 0.10

n (years) = 5

Cash flow = $1,000

Now,

F. V. Of cash flow = $1,000 * (((1 + 0.10)^5) - 1) / 0.10)

F. V. Of cash flow = $1,000 * ((1.6105 - 1) / 0.10)

F. V. Of cash flow = $1,000 * 6.105

F. V. (Future value) of cash flow = $6,105

ii) Value of cash flows at the beginning of year 1 :

Present value (P. V.)of cash flows = Cash flow * ((1 - (1/(1+i)^n)) / i)

i = 10% or 0.10

n = 5 years

Cash flow = $1,000

Now,

P. V. Of cash flow = $1,000 * ((1 - (1/(1+0.10)^5)) / 0.10)

P. V. Of cash flow = $1,000 * ((1 - 0.6209) / 0.10)

P. V. Of cash flow = $1,000 * 3.791

P. V. (Present value) of cash flow = $3,791