Question

You have just won the lottery and will receive $650,000 in one year. You will receive payments for 15 years, and the payments will increase 4 percent per year. If the appropriate discount rate is 11 percent, what is the present value of your winnings?

Answer 1

Ans:

The present value of your winnings = $5790525

Here, We can use the present value of a growing annuity equation to find the value of winnings today

Present Value = P / r - g [1 - (1 + g / 1 + r)ⁿ ]

P = first payment received= $650000

r = discount rate = 11% or 0.11

g = growth rate = 4% or 0.04

n = number of period = 15 years

Putting value into above formula we get,

PV = $650000 / 0.11 - 0.04 [1- (1+ 0.04 / 1+ 0.11)¹⁵ ]

= $650000 / 0.11 - 0.04 [1 - 0.376405]

= $650000 / 0.11 - 0.04 [0.623595]

= $650000 / 0.07 [0.623595]

= $9285714.286 x 0.623595

= $5790525