CHAPTER 4
DISCOUNTED CASH FLOW VALUATION
Answers to Concepts Review and Critical Thinking Questions 1.
Assuming positive cash
flows and interest rates, the future value increases and the present value decreases.
2.
Assuming positive cash flows and interest rates, the present value will fall and the future value
will
rise.
3.
The better deal is the one with equal installments.
4.
Yes, they should. APRs generally don’t provide the relevant rate. The only advantage is that
they are easier to compute, but, with modern computing equipment, that advantage is not very im-
portant.
5.
A freshman does. The reason is that the freshman gets to use the money for much longer before
interest starts to accrue.
6.
It’s a reflection of the time value of money. GMAC gets to use the $500 immediately. If
GMAC uses it wisely, it will be worth more than $10,000 in thirty years.
7.
Oddly enough, it actually makes it more desirable since GMAC only has the right to pay the
full
$10,000 before it is due. This is an example of a “call” feature. Such features are discussed at
length in a later chapter.
8.
The key considerations would be: (1) Is the rate of return implicit in the offer attractive relative
to other, similar risk investments? and (2) How risky is the investment; i.e., how certain are we
that we will actually get the $10,000? Thus, our answer does depend on who is making the prom-
ise to repay.
9.
The Treasury security would have a somewhat higher price because the Treasury is the
strongest of all borrowers.
10.
The price would be higher because, as time passes, the price of the security will tend to rise
toward $10,000. This rise is just a reflection of the time value of money. As time passes, the time
until
receipt of the $10,000 grows shorter, and the present value rises. In 2010, the price will
probably be higher for the same reason. We cannot be sure, however, because interest rates could
be much higher, or GMAC’s financial position could deteriorate. Either event would tend to de-
press the security’s price.
B-48 SOLUTIONS
Solutions to Questions and Problems
NOTE: All-end-of chapter problems
were solved using a spreadsheet. Many problems require multiple steps. Due to space and read-
ability constraints, when these intermediate steps are included in this solutions manual, rounding
may appear to have occurred. However, the final answer for each problem is found without
rounding during any step in the problem.
Basic
1.
The simple interest per year is:
$5,000 × .07 = $350
So, after 10 years, you will have:
$350 × 10 = $3,500 in interest.
The total balance will be $5,000 + 3,500 = $8,500
With compound interest, we use the future value formula:
FV = PV(1 +
r
)
t
FV = $5,000(1.07)
10
= $9,835.76
The difference is:
$9,835.76 – 8,500 = $1,335.76
2.
To find the FV of a lump sum, we use:
FV = PV(1 +
r
)
t
a.
FV = $1,000(1.05)
10
= $1,628.89
b.
FV = $1,000(1.07)
10
= $1,967.15
c.
FV = $1,000(1.05)
20
= $2,653.30
d.
Because interest compounds on the interest already earned, the future value in part
c
is more
than twice the future value in part
a
. With compound interest, future values grow exponentially.

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