Question

You have just won the lottery and will receive $620,000 in one year. You will receive payments for 15 years, which will increase 3 percent per year. The appropriate discount rate is 12 percent.

Required:

What is the present value of your winnings?

Answer 1

Sol:

Annuity payment (P) = $620,000 per year

Period (n) = 15 years

Discount rate (r) = 12%

Growth rate (g) = 3%

To determine present value (PV) of winnings:

PV of growth annuity = P x (1 - (1 + g)^n x (1 + r)^-n / (r - g)

PV of growth annuity = 620,000 x (1 - (1 + 3%)^15 x (1 + 12%)^-15 / (12% - 3%)

PV of growth annuity = 620,000 x (1 - (1 + 0.03)^15 x (1 + 0.12)^-15 / (0.12 - 0.03)

PV of growth annuity = 620,000 x (1 - (1.03)^15 x (1.12)^-15 / 0.09

PV of growth annuity = 620,000 x 7.948502 = 4,928,071.22

Therefore PV of the winning will be 4,928,071.22