Question

You have just won the lottery and will receive $600,000 in one year. You will receive payments for 16 years, and the payments will increase 5 percent per year. If the appropriate discount rate is 12 percent, what is the present value of your winnings?

Answer 1

We need to find out the PVa i.e(Present value) of growing annuity or Present value of winning which will be received in installment for a fixed period at a certain growing rate at a discounted value.

Formula For present value of growing annuity i.e PV_a={P/(r-g)} [1-{(1+g)/(1+r)}ⁿ]

Where

P=$600,000 ,i.e First Payment received

t=16 years ,I.e Number Of period

g=5% or 0.05, i.ePayment will increase @ 5% per year

r=12% or 0.12 ,i.e Discount Rate

Putting values in formula we have:

PV_a={$600,000/(0.12-.05)} [1-{(1+.05)/(1+0.12)}¹⁶}]

={$600,000/0.07} [1-{1.05/1.12}¹⁶]

=$ 8,571,429*[1-0.35607]

= $ 8,571,428.57 * 0.64393

=$ 5,519,400

Thus $ 5,519,400 is the  present value of winning