B1
SOLUTIONS
CHAPTER 6
DISCOUNTED CASH FLOW VALUATION
Answers to Concepts Review and Critical Thinking Questions
1.
The four pieces are the present value (PV), the periodic cash flow (
C
), the discount rate (
r
), and the
number of payments, or the life of the annuity,
t
.
2.
Assuming positive cash flows, both the present and the future values will rise.
3.
Assuming positive cash flows, the present value will fall and the future value will rise.
4.
It’s deceptive, but very common. The basic concept of time value of money is that a dollar today is
not worth the same as a dollar tomorrow. The deception is particularly irritating given that such
lotteries are usually government sponsored!
5.
If the total money is fixed, you want as much as possible as soon as possible. The team (or, more
accurately, the team owner) wants just the opposite.
6.
The better deal is the one with equal installments.
7.
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 important.
8.
A freshman does. The reason is that the freshman gets to use the money for much longer before
interest starts to accrue.
9.
The subsidy is the present value (on the day the loan is made) of the interest that would have accrued
up until the time it actually begins to accrue.
10.
The problem is that the subsidy makes it easier to repay the loan, not obtain it. However, ability to
repay the loan depends on future employment, not current need. For example, consider a student
who is currently needy, but is preparing for a career in a highpaying area (such as corporate
finance!). Should this student receive the subsidy? How about a student who is currently not needy,
but is preparing for a relatively lowpaying job (such as becoming a college professor)?
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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 readability 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.
To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a
lump sum, we use:
PV = FV / (1 +
r)
t
[email protected]% = $1,200 / 1.10 + $600 / 1.10
2
+ $855 / 1.10
3
+ $1,480 / 1.10
4
= $3,240.01
[email protected]% = $1,200 / 1.18 + $600 / 1.18
2
+ $855 / 1.18
3
+ $1,480 / 1.18
4
= $2,731.61
[email protected]% = $1,200 / 1.24 + $600 / 1.24
2
+ $855 / 1.24
3
+ $1,480 / 1.24
4
= $2,432.40
2.
To find the PVA, we use the equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
At a 5 percent interest rate:
[email protected]%:
PVA = $4,000{[1 – (1/1.05)
9
] / .05 } = $28,431.29
[email protected]%:
PVA = $6,000{[1 – (1/1.05)
5
] / .05 } = $25,976.86
And at a 22 percent interest rate:
[email protected]%: PVA = $4,000{[1 – (1/1.22)
9
] / .22 } = $15,145.14
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 Spring '07
 Selvili
 Finance, Time Value Of Money, Net Present Value, Valuation

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