Question

Exercise 6-11 Future and present value [LO6-3, 6-6, 6-7]

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) $66,000 cash immediately, (2) $22,000 cash immediately and a six-period annuity of $7,800 beginning one year from today, or (3) a six-period annuity of $13,000 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 5%, determine the present value for the above options. Which option should Alex choose?
2. The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2027. Weimer will make annual deposits of $120,000 into a special bank account at the end of each of 10 years beginning December 31, 2018. Assuming that the bank account pays 6% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2027?
  

Answer 1

Solution 1:

Option 1:$66,000 cash immediately

Present value = $66,000

Option 2: $22,000 cash immediately and a six-period annuity of $7,800 beginning one year from today

Present value = $22,000 + $7,800 * Cumulative PV factor at 5% for 6 periods

= $22,000 + $7,800 * 5.075692 = $61,590.40

Option 3: a six-period annuity of $13,000 beginning one year from today​

Present value = $13,000 * Cumulative PV factor at 5% for 6 periods

$13,000 * 5.075692 = $65,984

As present value of option 1 (immediate payment of $66,000) is higher, therefore Alex should choose first option.

Solution 2:

Annual payments = $120,000

Period = 10 years

Interest rate = 6%

Fund balance after last payment on Dec 31, 2017 = $120,000 * cumulative FV factor at 6% for 10 periods

= $120,000 * 13.18079 = $1,581,695.39