Chapter 4
Time Value of Money
ANSWERS TO END-OF-CHAPTER QUESTIONS
4-1 a. PV (present value) is the value today of a future payment, or stream of payments,
discounted at the appropriate rate of interest. PV is also the beginning amount that
will grow to some future value. The parameter i is the periodic interest rate that an
c. An annuity is a series of payments of a fixed amount for a specified number of
periods. A single sum, or lump sum payment, as opposed to an annuity, consists of
one payment occurring now or at some future time. A cash flow can be an inflow (a
d. An ordinary annuity has payments occurring at the end of each period. A deferred
annuity is just another name for an ordinary annuity. An annuity due has payments
e. A perpetuity is a series of payments of a fixed amount that last indefinitely. In other
f. An outflow is a deposit, a cost, or an amount paid, while an inflow is a receipt. A
g. Compounding is the process of finding the future value of a single payment or series
h. Annual compounding means that interest is paid once a year. In semiannual,
i. The effective annual rate is the rate that, under annual compounding, would have
produced the same future value at the end of 1 year as was produced by more frequent
compounding, say quarterly. The nominal (quoted) interest rate, iNom, is the rate of
j. An amortization schedule is a table that breaks down the periodic fixed payment of an
installment loan into its principal and interest components. The principal component
4-2 The opportunity cost rate is the rate of interest one could earn on an alternative
investment with a risk equal to the risk of the investment in question. This is the value of
4-3 True. The second series is an uneven payment stream, but it contains an annuity of $400
4-4 True, because of compounding effects–growth on growth. The following example
demonstrates the point. The annual growth rate is I in the following equation:
The term (1 + I)10 is the FVIF for I percent, 10 years. We can find I in one of two ways:
2. Using a financial calculator, input N = 10, I/YR = 10, PV = -1, PMT = 0, and FV = ?.
4-5 For the same stated rate, daily compounding is best. You would earn more “interest on
interest.”
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
4-1 012345
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Alternatively, with a financial calculator enter the following: N = 5, I/YR = 10, PV =
4-2 0 5 10 15 20
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PV = ? FV20 = 5,000
4-3 0 18
| |
4-4 0 N = ?
| |
PV = 1 FVN = 2
4-5 0 1 2 N – 2 N – 1 N
7%
6.5%
12%
I/YR = ?
10%
| | | | | |
4-6 Ordinary annuity:
012345
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Annuity due:
012345
||||||
FVA5 = ?
4-7 0123456
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PV = ? FV = ?
Using a financial calculator, enter the following: CF0 = 0; CF1 = 100; Nj = 3; CF4 = 200
To solve for the FV of the cash flow stream with a calculator that doesn’t have the
M
N OM
M
I
1
= (1.01)12 – 1.0
7%
8%
7%
Alternatively, using a financial calculator, enter the following: NOM% = 12 and P/YR =
4-9 a. 0 1
-500 FV = ?
b. 0 1 2
-500 FV = ?
c. 0 1
PV = ? 500
d. 0 1 2
PV = ? 500
| | | | | | | | | | |
-500 FV = ?
| | | | | | | | | | |
-500 FV = ?
c. 0 1 2 3 4 5 6 7 8 9 10
PV = ? 500
d. 0 1 2 3 4 5 6 7 8 9 10
PV = ? 500
6%
6%
6%
6%
6%
12%
6%
12%
4-11 a. ?
| |
-200 400
c. ?
| |
-200 400 .
d. 100% ?
| |
-200 400 .
4-12
a. 0 1 2 3 4 5 6 7 8 9 10
| | | | | | | | | | |
400 400 400 400 400 400 400 400 400 400
FVA10 = ?
b. 5%
0 1 2 3 4 5
| | | | | |
200 200 200 200 200
FVA5 = ?
7%
18%
10%
c. 0 1 2 3 4 5
| | | | | |
400 400 400 400 400
FVA5 = ?
d. To solve Part d using a financial calculator, repeat the procedures discussed in Parts a,
(1) 0 1 2 3 4 5 6 7 8 9 10
| | | | | | | | | | |
400 400 400 400 400 400 400 400 400 400 FVA10 = ?
(2) 0 1 2 3 4 5
| | | | | |
200 200 200 200 200 FVA5 = ?
(3) 0 0% 1 2 3 4 5
| | | | | |
400 400 400 400 400 FVA5 = ?
4-13
a. 0 1 2 3 4 5 6 7 8 9 10
| | | | | | | | | | |
PV = ? 400 400 400 400 400 400 400 400 400 400
b. 0 1 2 3 4 5
| | | | | |
PV = ? 200 200 200 200 200
0%
10%
5%
10%
5%
c. 0 1 2 3 4 5
| | | | | | $400(5) = $2,000.00.
PV = ? 400 400 400 400 400
d. (1) 0 1 2 3 4 5 6 7 8 9 10
| | | | | | | | | | |
400 400 400 400 400 400 400 400 400 400
PV = ?
(2) 0 5% 1 2 3 4 5
| | | | | |
200 200 200 200 200
PV = ?
(3) 0 1 2 3 4 5
| | | | | |
400 400 400 400 400
PV = ?
0%