Question

Mary Alice just won the lottery and is trying to decide between the options of receiving the annual cash flow payment option of $450,000 per year for 25 years beginning today, or receiving one lump-sum amount today. Mary Alice can earn 5% investing this money. At what lump-sum payment amount would she be indifferent between the two alternatives? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided and round final answer to nearest whole dollar amount.)

Answer 1

Lump sum payment today =$6,659,388.81

Step-by-step explanation:

The lump sum payment that would make her indifferent is the present value of the annuity discounted at the required rate of return of 5%.

PV = A × (1 - ((1+r)^(-n))/n)

A- $450,000, r- 5%, n = 25-1 = 24

Because , the first payment occurs today, we wil take the number of payment to be 24 (i.e 25 - 1) . And then add the first payment to the Present value the of the 24 year annuity.

This is so because the first payment need not be discounted because it is already in present value.

PV = $450,000 × 1- (1.05)^(-24)/0.05

= 6,209,388.81

Total Present value = $450,000 + 6,209,388.81

= $6,659,388.81