Tables for your use:
Your client is interested in buying a business. You help structure the transaction and draw up the appropriate dcouments. The client has been offered to ways to pay the $400,000 purchase price. One is for cash, which your client could finance by borrowing from the bank with a 9% loan payable over 10 years -- annuial payments due on December 31 of each year. THe other is a strcutrued purchase as follows: $40,000.00/yr. for 10 years, payable by December 31 of each year, beginning next year plus each year accrued interest on the outstanding balance at an interest rate of 6%/year for the first five years, then 10% for years 6 through 10.
Which is the better deal for your client?
1 - Time
value of money (delayed judgment)
Your client ran over Missy's poodle. You believe that
your client will be held liable in the amount of $20,000,
but you guess that it will take three years before your
client will have to pay. How much should your client
set aside right now and invest at 6.2% annual interest
to cover this likely judgment?
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2 - Power of compounding
You are 25 years old and start investing $2,000 every
year (on January 1) in a tax-deferred IRA. The IRA has
annual returns of 12%. After ten years you stop investing
and let the IRA continue to grow at 12%. Your twin sister
waits for ten years and then starts investing $2,000
every year in an IRA that also has 12% annual returns.
She continues until the end of her 65th year. At this
point, whose IRA is larger?
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3 - Different compounding
methods
You are in a car accident on April 15. Three years
later you win a $100,000 judgment that calls for "interest
as provided by statute." The statute allows successful
plaintiffs to collect interest on any judgment at a
"rate of 12% per annum" from the time they
were injured. The statute does not mention whether and
how interest is compounded. How much interest are you
entitled to, if:
a. interest is not compounded?
b. interest is compounded annually?
c. interest is compounded continuously?
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4 - Time to double/tenfold
At a growth rate of 8.4 percent, how long does it take
a sum to double? for it to increase ten times?
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5 - Annuities
Which 10-year annuity will be worth more --
a. Payments of $2,500 per year, earning 8% per year.
b. Payments of $2,200 per year, earning 11% per year.
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6 - Annuities discount
rate
Your brother-in-law asks for advice. He has won the
$1,000,000 West Virginia lottery. He will receive $100,000
at the end of each year for 10 years. He has gotten
offers to sell his winning ticket and has been surprised
that they are all for less than $1 million.
a. He asks you how much he should sell it for. Without
considering the tax implications, what is the ticket
worth assuming 6.7% percent return on current 10-year
annuities sold by insurance companies?
b. Your brother-in-law gets a serious offer of $500,000.
What rate of return, or yield, does this offer entail?
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7 - Annuity valuation
Your client wants to make sure she will have a comfortable
retirement. She has been offered an annuity that will
pay $24,000 per year for the next 25 years. (If your
client dies before the term ends, her estate will receive
the annuity's value at death.) The annuity company would
have her purchase the annuity for a lump-sum amount.
Ignoring taxes, what is the most she should pay if she
could invest her money in investments with a similar
risk as the annuity company that pay 7.5%?
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8 - Mixed returns (bond
valuation)
RealmBank is considering purchasing debt. Three companies,
with identical risk profiles, offer three series of
newly issued bonds, each with the same level of priority
and a par (face amount) of $1,000. One, with a five-year
maturity that pays $120 interest annually, sells in
the market at par (face value). RealmBank consider the
other two bonds:
a. A six-year bond that pays only $60 interest annually.
What should RealmBank pay for this bond?
b. A zero-coupon bond (that pays no interest) with
a maturity of three years. What should RealmBank pay
for this bond?
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9 - Investment choices
You are considering two investment opportunities A
and B. A is expected to pay $400 a year for the first
10 years, $600 a year for the 15 years thereafter, and
then nothing. B is expected to pay $1,000 a year for
10 years and nothing thereafter. You find that other
investments of similar risk to A yield 8% and to B yield
14%.
a. Find the present value of each investment.
b. Which is the more risky investment? Why?
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10 - Internal rates
of return
A bakery is considering buying a dough-making machine.
There are two options, each promising a five-year useful
life. Machine A will produce steady cash flow; Machine
B will be expensive to install and learn, but will eventually
produce greater cash flows. Each machine's purchase
price is $25,000.
|
Year |
Machine A |
Machine B |
1 |
$10,000 |
$3,000 |
2 |
10,000 |
5,000 |
3 |
10,000 |
16,000 |
4 |
10,000 |
16,000 |
5 |
10,000 |
16,000 |
a. Why is the payback method (which measures how long
its takes for the original cost to be recouped) a poor
measure of the machine's value?
b. What is the present value of each machine, assuming
the bakery's cost of capital (discount rate) is 12%?
Which machine seems the better buy?
c. What is the internal rate of return (the discount
rate) that would produce the anticipated cash flows?
Now which machine seems the better buy?
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11 - Loan amortization
You are thinking of refinancing your house. You will
take out a loan for $120,000.
a. What would be your monthly payments with a 30-year
loan that carries an annual interest rate of 6.5%?
b. How much interest would you pay, and thus be able
to deduct, during the first year of the loan?
c. Assuming you are in a 28% tax bracket, what is
the after-tax rate you are paying in the first year
for this 6.5% loan?
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Chapter 1 - Time Value of Money
