Chapter 6 - Discounted Cash Flow Valuation - QZ 01

The actual interest rate on a loan that is compounded monthly but expressed as an annual rate is referred to as the _____ rate.

effective annual

You would like to provide $125,000 a year forever for your heirs. How much money must you deposit today to fund this goal if you can earn a guaranteed 4.5 percent rate of return?

$2,777,778 Explanation PV = $125,000/.045PV = $2,777,778

Grace is retiring today and has $300,000 in her retirement savings. She expects to earn 8.5 percent per year compounded monthly. How much can she withdraw from her retirement savings each month if she plans to spend her last penny 17 years from now?

$2,784.88 Explanation PVA = $300,000 = C[(1 − {1/[1 + (.085/12)](17)(12)})/(.085/12)]C = $2,784.88

Jones Stoneware has a liability of $75,000 due four years from today. The company is planning to make an initial deposit today into a savings account and then deposit an additional $10,000 at the end of each of the next four years. The account pays interest of 4.5 percent. How much does the firm need to deposit today for its savings to be sufficient to pay this debt?

$27,016.84 Explanation FVA = $10,000[(1.0454 − 1)/.045]FVA = $42,781.91Additional FV needed = $75,000 − 42,781.91Additional FV needed = $32,218.09Initial deposit = $32,218.09/1.0454Initial deposit = $27,016.84

Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $2,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

$37,537.88 Explanation GAPV = $2,500{[1 −(1.05/1.075)20]/(.075 − .05)}GAPV = $37,537.88

You just won the magazine sweepstakes and opted to take unending payments. The first payment will be $50,000 and will be paid one year from today. Every year thereafter, the payments will increase by 2.5 percent annually. What is the present value of your prize at a discount rate of 7.9 percent?

$925,925.93 Explanation GPPV = $50,000/(.079 − .025)GPPV = $925,925.93

Your insurance agent is trying to sell you an annuity that costs $50,000 today. By buying this annuity, your agent promises that you will receive payments of $250 a month for the next 20 years. What is the rate of return on this investment?

1.88% Explanation PVA = $50,000 = $250[(1 − {1/[1 + (r/12)](20)(12)})/(r/12)]r = .0188, or 1.88%

Your father helped you start saving $25 a month beginning on your fifth birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 15th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings?

4.67% Explanation FVADue = $6,528.91 = $25({[1 + (r/12)](15)(12) − 1}/(r/12))(1 + r/12)r = .0467, or 4.67%

A new sports coupe costs $41,750 and the finance office has quoted you an APR of 7.7 compounded monthly for 36 months. What is the EAR?

7.98% Explanation EAR = (1 + .077/12)12 − 1EAR = .0798, or 7.98%

Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at Year 5 and an annual percentage rate of 10 percent?

Annual