Chapter 5: The Time Value of Money
5.1
a.
$1,000
×
1.05
10
= $1,628.89
b.
$1,000
×
1.07
10
= $1,967.15
c.
$1,000
×
1.05
20
= $2,653.30
d.
Interest compounds on the interest already earned.
Therefore, the interest earned
in part c, $2653.30, is more than double the amount earned in part a, $628.89.
5.2
a.
$1,000 / 1.1
7
= $513.16
b.
$2,000 / 1.1 = $1,818.18
c.
$500 / 1.1
8
= $233.25
5.3
You can make your decision by computing either the present value of the $2,000 that you
can receive in ten years, or the future value of the $1,000 that you can receive now.
Present value:
$2,000 / 1.08
10
= $926.39 is less than $1000 today;
Future value:
$1,000
×
1.08
10
= $2,158.92 is greater than $2000 in 10 years.
Either calculation indicates you should take the $1,000 now.
5.4
Since this bond has no interim coupon payments, its present value is simply the present
value of the $1,000 that will be received in 25 years.
Note: As will be discussed in the next
chapter, the present value of the payments associated with a bond is the price of that bond.
PV = $1,000 /1.1
25
= $ 92.30
5.5
PV = $1,500,000 / 1.04
27
= $520,224.86
5.6
a.
At a discount rate of zero, the future value and present value are always the same.
Remember, FV = PV (1 + r)
t
.
If r = 0, then the formula reduces to FV = PV.
Therefore, the values of the alternatives are $10,000,000 and $20,000, 000,
respectively.
You should choose the second option.
b.
Option one:
$10,000,000 / 1.1 = $9,090,909
Option two:
$20,000,000 / 1.1
5
= $12,418,426
Choose the second option.
c.
Option one:
$10,000,000 / 1.2 = $8,333,333
Option two:
$20,000,000 / 1.2
5
= $ 8,037,551
Choose the first option.
d.
You are indifferent at the rate that equates the PVs of the two alternatives.
You
know that rate must fall between 10% and 20% because the option you would
choose differs at these rates.
Let r be the discount rate that makes you indifferent
between the options.
$10,000,000 / (1 + r) = $20,000,000 / (1 + r)
5
(1 + r)
4
= $20,000,000 / $10,000,000 = 2
1 + r = 1.189207115
r = 0.189207115 = 18.92%
5.7
PV of Joneses’ offer = $150,000 / (1.1)
3
= $ 112,697.22
Answers to End-of-Chapter Problems
B-21