Question

Answer each of the following independent questions. Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $74,000 cash immediately, (2) $26,000 cash immediately and a six-period annuity of $8,300 beginning one year from today, or (3) a six-period annuity of $15,000 beginning one year from today. (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.) 1. Assuming an interest rate of 6%, determine the present value for the above options. Which option should Alex choose

Answer 1

The best alternative is option 1.

Step-by-step explanation:

Giving the following information:

(1) $74,000 cash immediately

(2) $26,000 cash immediately and a six-period annuity of $8,300 beginning one year from today

(3) a six-period annuity of $15,000 beginning one year from today.

The option with the higher present value is the most profitable.

1) PV= $74,000

2) We need to calculate the present value of the $8,300 annuity. First, we need to calculate the future value:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

FV= {8,300*[(1.06^6) - 1]} / 0.06

FV= $57,895.14

Now, the present value:

PV= FV/(1+i)^n

PV= 57,895.14/1.06^6

PV= 40,813.79 + 26,000

Total PV= $66,813.79

3) FV= {15,000*[(1.06^6) - 1]} / 0.06

FV= $104,629.79

Now, the present value:

PV= 104,629.79 / 1.06^6

PV= $73,759.87

The best alternative is option 1.