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Kenan-Flagler Business School
The University of North Carolina
MBA 772 / MAC718
Introductory Finance
Week 1 Homework: Problem Set 1
Weekly problem sets are to be submitted in a well-organized set of calculations with
clearly visible (suggest circled) answers PRIOR TO your synchronous session. You may
submit in Excel, Word, PDF, hand-written or typed. Homework may be done in groups
up to no more than 4 students, but assignments must be individually submitted and a
student’s own work (i.e. you cannot simply copy group work). If you work in a group, all
students names must be identified on your submission file.
1. You are considering various retirement plans. Your goal is to have a lump
sum of $3,000,000 available (‘in the bank’) when you retire at age 67. The
various plans, with their payment schedules, are listed below. In each case,
calculate the payment(s) that must be made into the plan to ensure that you
have the $3,000,000 available. For each plan, you may assume that your
opportunity cost of funds is 6% per year; for each plan, you may assume that
the phrase “at age XX” means the same thing as “on your XX’th birthday”.
Plan 1: Single lump sum at age 25
Plan 2: Single lump sum at age 50
Plan 3: Equal annual payments, commencing at age 31 and ending at age 67
Plan 4: Equal annual payments, commencing at age 51 and ending at age 67
Plan 5: Equal annual panicky payments, commencing at age 60 and ending at
age 67
2. You have just taken out a mortgage for $575,000, at a fixed rate of 4.75% per
year, compounded monthly, and a term of 30 years.
a) Calculate the monthly payments
) For the first six months’ payments, calculate the portion that is interest and
the portion that is principal
c) Immediately after the sixth payment, what is the balance remaining on the
mortgage?
d) If you design the mortgage so that the payments will grow at 0.20% per
month, what will be the first payment on the mortgage?
3. You are saving for your child’s college education. Your child will start
college in 16 years, and college tuition is due at the beginning of the year (i.e.,
the first tuition payment will occur at t=16). Average college tuition at a
private school this year is $38,500 per year. You may assume that your
opportunity cost of funds is 6.0% per year, compounded monthly.
a) Calculate the value, at t=16, of four years’ worth of college tuition if
tuition charges grow at the general inflation rate of 2.4% per year,
compounded monthly.
) Calculate the value, at t=16, of four years’ worth of college tuition if
tuition charges grow at the recent education inflation rate of 6.4% per
year, compounded monthly.
c) Calculate the single payment you must make into the child’s college
account to pay for the entire college experience, if you make the payment
now. Assume the education inflation rate of 6.4%, compounded monthly.
d) Calculate the monthly payment you must make into your child’s college
account to pay for four years of college under the assumption that tuition
will grow at the general inflation rate; you may assume that the first
payment into the college account comes in one month’s time and the last
payment will come one month prior to the first college tuition payment.
e) Calculate the monthly payment you must make into your child’s college
account to pay for four years of college under the assumption that tuition
will grow at the education inflation rate; you may assume that the first
payment into the college account comes in one month’s time and the last
payment will come one month prior to the first college tuition payment.
4. You have been offered the following opportunity: receive a tax ‘fo
earance’
credit of $10,000 today, and in return, you must make higher tax payments of
$1,000 per year for 15 years. The first of the annual payments will come in
one year’s time. What is the internal rate of return on this investment?
5. A recent graduate of the university has gotten into a little more credit card
debt than he had anticipated. He cu
ently owes $22,000; the credit card
company charges him 1.5% per month on this debt.
a) If he wishes to pay off his credit card bill in 5 years of equal monthly
installments, promises to make the first payment next month and not use
the credit card again, what monthly payments must he make? You may
assume that there are no additional fees or charges related to the card, and
that the credit card interest rate is not expected to change.
) After solving for the payment in a), the graduate realizes that he can’t
afford the first payments, given the salary of his new job. He wishes his
payment to start small, then increase; the first payment will still come in
one month’s time. If he wishes his payments to grow at, say, 0.50% per
month and still let him pay off the credit card debt in 5 years of monthly
payments, what must the first payment be?
c) The graduate’s parents hear of his plight. They offer to extend him a loan
to pay off the debt, with the interest rate charged equal to 8% per year,
compounded monthly. The student wishes to know the incremental value
of this new bo
owing opportunity (relative to the credit card debt) today
(so that he can go shopping.) That is, he wishes to know how much he can
spend today and still have the same monthly payments as in p art a). What
can he spend on today’s shopping trip?
6. Your opportunity cost of funds can be expressed as 6% per year, compounded
quarterly.
a) You have been offered a three-month internship. If the internship pays
$24,000 at the end of the three month period, what is the value today of
that salary?
) Assume now that the internship pays $8,000 per month (paid at the end of
the month.) What is the value today of the salary?
7. Spot rates over three different horizons are given below. Each of the rates is
expressed as a ‘per annum’ rate, which assumes monthly compounding.
One-month 0.18%
Two-month 0.24%
Three-month 0.375%
What is the value today of an investment that pays $100 at the end of each of
the next 3 months?
Week 1 Homework: Problem Set 1