Question

You have just won the lottery and will receive $460,000 in one year. You will receive payments for 27 years, and the payments will increase 3 percent per year. If the appropriate discount rate is 12 percent, what is the present value of your winnings?

Answer 1

Answer:

The present Value of my winnings = $4,578,716.35

Explanation:

An annuity is a series od annual cash outflows or inflows which payable or receivable for a certain number of periods. If the annual cash flow is expected  to increase by a certain percentage yearly, it is called a growing annuity.

To work out the the present value of a growing annuity,

we the formula:

PV = A/(r-g) ×  (1-  (1+g/1+r)^n)

I will break out the formula into two parts to make the workings very clear to follow. So applying this formula, we can work out the present value of the growing annuity (winnings) as follows.

A/(r-g)

= 460,000/(12%-3%)

= $5,111,111.11

(1-  (1+g/1+r)^n

1 - (1+3%)/(1+12%)^(27)

=0.8958

PV = A/(r-g) ×  (1-  (1+g/1+r)^n)

$5,111,111.11 × $0.8958

= $4,578,716.35

The present Value of my winnings = $4,578,716.35