FINC 3400
Time Value of Money
Question One:
(a)
If the discount (or interest) rate is positive, the present value of an expected series of payments will always
exceed the future value of the same series.
(True/false/uncertain)
Explain your answer.
(b)
Assume that you will receive $2,000 a year in years 1 through 5, $3,000 a year in years 6 through 8, and
$4,000 in year 9, with all cash flows to be received at the end of the year. If you require a 14% rate of
return, what is the present value of these cash flows?
(c)
If you presently have $6,000 invested at a rate of 15%, how many years will it take for your investment to
triple? (Round up to obtain a whole number of years if necessary).
Question Two:
Your subscription to Jogger's World Monthly is about to run out and you have the choice of renewing it by
sending in the $10 a year regular rate or getting a lifetime subscription to the magazine by paying $100.
Your cost of capital is 7%. How many years would you have to live to make the lifetime subscription the
better buy? Payments for the regular subscription are made at the beginning of each year.
Question Three:
A father, concerned about the rapidly rising cost of a college education, is planning a savings program to
put his daughter through college. She is now 13 years old, plans to enroll in the university in 5-years time,
and it should take her 4-years to complete her education. Currently, the cost per year (for everything –
food, clothing, tuition, books etc.) is $10,500, but a 5.5% annual inflation rate in these costs is forecasted.
The daughter recently received $8,000 from her grandfather’s estate; this money is invested in a bank
account that pays 9% interest compounded annually and will be used to help meet the costs of the
daughter’s education. The rest of the costs will be met by money the father will deposit in a savings
account. He will make equal deposits to the account in each year from now until, and including, the year
his daughter starts college. These deposits will also earn 9% interest.
If the first deposit is made today, how large must each deposit be in order to put his daughter through
college?
Question Four:
(a)
As the winner of a breakfast cereal competition, you can choose one of the following prizes:
(1) $100,000 now,
(2) $180,000 at the end of five years,
(3) $16,000 per year for each of ten years, cash paid at the end of the year
(4) $11,400 per year forever, cash paid at the end of t he year
Assume the interest rate is 12 %. Which is the most valuable prize?
(b)
You have just graduated from the MBA program here at Seattle University, you plan to work for 10 years
then head off to the wilderness of Alaska. You figure you can save $2,000 a year for the first 3 years, since
you have to pay off some student loans. You think you will be able to save $8,000 for the next 3 years and
$15,000 for the last 4 years. These savings cash flows will start one year from now. In addition, you have
just won $4,500 from a graduation trip to Las Vegas. If you put your winnings now, and your future
savings when they start, into an account which pays you 6.5% compounded annually, what will your
financial "stake" be when you leave for Alaska in ten years time?
Question Five:
(a)
You want to buy an Accura Integra on your 27th birthday. You have priced these cars and found that they
currently sell for $25,000. You believe that the price will increase by 10% per year until you are ready to
buy. You can presently invest to earn 14%. If you just turned 20 years old, how much must you invest at
the end of each of the next 7 years to be able to purchase the Accura in 7 years?
(b)
On January 1, 1993, a graduate student developed a 5-year financial plan that would provide enough money
at the end of her graduate work (January 1, 1998) to open a business of her own. Her plan was to deposit
$8,000 per year for 5-years, starting immediately, into an account paying 10% compounded annually. Her
activities proceeded according to plan with the following exceptions; at the end of her third year she
withdrew $5,000 to take a European holiday, at the end of her fourth year she withdrew $5,000 to buy a
used Saab, and at the end of the fifth year she had to withdraw $5,000 to pay to have her dissertation typed
and bound. Her account, at the end of the fifth year, was less than the amount she had originally planned
on by how much?
Question Six:
Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live
for 25 years after he retires, that is, until he is 85 years old. He wants a fixed retirement income that has the
same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his
retirement income will decline year by year after he retires). His retirement income will begin the day he
retires, 10 years from now, and he will then get 24 additional annual payments. Inflation is expected to be
5% per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his
savings of 8% per year, annual compounding. To the nearest dollar, how much must he save during each
of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal?