Exam 4: Time Value of Money

A "growing annuity" is any cash flow stream that grows over time.

Cochrane Associate's net sales last year were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?

Your bank pays 4% interest annually. You have $2,500 invested in the bank. How long will it take for your funds to double?

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

Your uncle just won the weekly lottery, receiving $375,000, which he invested at a 7.5% annual rate. He now has decided to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Brockman's EPS to triple?

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

Which of the following statements regarding a 20-year (240-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Cyberhost Corporation's sales were $225 million last year. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment?

An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him with income of $50,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost him to buy such an annuity today?

Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25. Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Julian's 65th birthday. The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age. Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until Jonathan turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday?