Chapter 3 Time Value of Money: An Introduction
1.. Plan: The benefit of the rebate is that Honda will sell more vehicles and earn a profit on
each additional vehicle sold:
Benefit  Profit of $6,180 per vehicle  14,400 additional vehicles sold  $88,992,000.
Execute: The cost of the rebate is that Honda will make less on the vehicles it would have
sold without the rebate:
Cost  Loss of $2000 per vehicle
 38,700 vehicles that would have sold without rebate
 $77,400,000.
Evaluate: Thus, Benefit  Cost  $88,992,000  $77,400,000  $11.592 million, and
offering the rebate looks attractive.
(Alternatively, we could view it in terms of total, rather than incremental, profits. The

benefit is $6180/vehicle  53,100 sold  $328,158,000, and the cost is $8180/vehicle
38,700 sold  $316,566,000.)
3. Plan: There are two related, but different, decisions to analyze. In both cases, you will take
the choice that will give you the highest value.
Execute:
a. Value of the stock bonus today  100  $62.66  $6,266
Value of the cash bonus today  $5,100
Because you can sell the stock for $6,266 in cash today, its value is $6,266, which is
better than the cash bonus of $5,100 today. Take the stock.
b. Because you could buy the stock today for $6,266 if you wanted to, the value of the
stock bonus cannot be more than $6,266. But if you are not allowed to sell the
company’s stock for the next year, its value to you could be less than $6,266. Its value
will depend on what you expect the stock to be worth in one year, as well as how you
feel about the risk involved. There is no clear-cut answer to which alternative is best
because taking the stock today and holding it for a year involves risk. You might decide
that it is better to take the $5,100 in cash than to wait for the uncertain value of the stock
in one year. This would be especially true if you believed you could invest the $5,100
today in another asset that would be worth more than $6,266 in one year.
Evaluate: Part (a) has a clear-cut answer. Take the stock today because it is worth more
than the cash bonus. Part (b) does not have a clear-cut answer because you cannot directly
compare $5,100 cash today against the uncertain value of 100 shares of stock in one year.
Different people could make different decisions based largely on their estimate of the future
value of the stock.
5. Apple cannot charge more than the cost of doing it yourself, so the maximum is $25, the
same as the cost of buying the CD and ripping the tracks to your iPod.
7. Plan: Determine the value to Bubba of 1 ton of shrimp, and determine the change in value
to Bubba of 1 ton of shrimp because of his allergy.
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Execute:
a. The value to Bubba of 1 ton of shrimp is $10,000 because that is the market price.
b. No. As long as he can buy or sell shrimp at $10,000 per ton, his personal preference or
use for shrimp is irrelevant to the value of the shrimp.
Evaluate: In well-functioning markets, the price, and therefore the value, is set by the
supply and demand of all suppliers and users.
9. Plan: You need to compute the future value (FV) based on a 4% interest rate and a
present value (PV) of $900. 4% interest rate means for every $1 today, you get
$1.04 in a year.
Execute:
 $1.04 in one year 
FV  $900 today  
  $936 in one year
$ today


Evaluate:
$900 today and $936 in one year have equivalent values to you because with $900 today,
you could deposit it and have $936 in one year.
11. Plan: You need to calculate the amount of interest you would have paid at 9.3% and then
the amount of interest you will pay at 7%, and then compute the difference. Alternatively,
you can calculate the amount of interest you would pay at 2.3%.
Execute: At 9.3%, you will pay $14,000 x 9.3% = $1,302. At 7%, you will pay $14,000 x 7%
= $980. The difference is then $1,302 – $980 = $322 = $14,000 x 2.3%
Evaluate: You will save $322 in interest this year through the reduction.
13. Plan: The discount factor is equal to the inverse of 1 + the interest rate.
Execute: Given a discount rate of 5%, the discount factor will be the following:
 1 
Discount Factor  
  0.9524
 1.05 
Evaluate: The discount factor equivalent to a 5% discount rate is 0.9524.
15. From your perspective:
Today
1 year
5000
5400
From the bank’s perspective:
Today
1 year
5000
5400
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17. Plan: You are considering three related questions. As usual, you will select the alternative
that makes you the financially best off (wealthiest).
Execute:
a. Having $500 today is equivalent to having $500 × 1.039 = $519.5 in one year.
b. Having $500 in one year is equivalent to having $500 / 1.039 = $481.23 today.
Evaluate: Because money today is worth more than money in the future, $500 today is
preferred to $500 in one year. This answer is correct even if you don’t need the money today,
because by investing the $500 you receive today at the current interest rate, you will have
more than $500 in one year.
19. FV = $100, n = 10, r = 0.02
$100
PV 
 $82.03
10
1.02 
21. a. Balance after 3 years = 800 × 1.023 = $848.87
Interest = 800 × 0.02 × 3 = $48
Interest on interest = 848.87 – 48 = $0.87
b. Balance after 25 years = 800 × 1.0225 = $1312.49
Interest = 800 × 0.02 × 25 = $400
Interest on interest = 1312.49 – 400 = $112.48
Rate
0
800
Year
Balance
Interest
Int. on
int.
2%
1
816
16
2
832.32
32
3
848.9664
48
25
1312.4848
400
0
0.32
0.97
112.48
23. Plan: Determine the present values of the different interest rates and the different periods.
Compare the differences in present values.
Execute:
a. Timeline:
0
1
2
3
PV = ?
PV 
13, 000
10
10
13,000
 8, 782.33
1.04
b. Timeline
0
1
2
3
PV = ?
PV 
13, 000
1.08
20
20
13,000
 2, 789.13
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c. Timeline:
0
1
2
3
4
5
PV =
?
PV =
13,000
13,000
= 11,774.50
1.025
25. FV = $1,300(1.028)2 + $750(1.028) = $2,144.82
27. Plan: Your mom is being offered a choice in how she will take her retirement benefit:
either $250,000 today or $350,000 in 5 years. If mom wants the alternative that is going to
give her the most wealth, then she should take the alternative with the highest net present
value. Your job is to determine the present values of the $350,000 in 5 years at different
interest rates.
Execute:
0
1
2
3
4
PV  ?
5
350,000
350, 000
1.05
= 350, 000
a. PV =
Given:
N
I/Y
5
0.00%
Solve for PV:
PV
PMT
FV
0
350,000
Excel Formula
PV(0,5,0,350000)
350,000.00
350, 000
1.085
= 238, 204
b. PV =
Given:
N
I/Y
5
8.00%
Solve for PV:
PV
PMT
FV
0
350,000
Excel Formula
PV(0.08,5,0,350000)
238,204.12
350, 000
1.25
= 140, 657
c. PV =
Given:
Solve for PV:
N
I/Y
5
20.00%
PV
140,657.15
PMT
FV
0
350,000
Excel Formula
PV(0.2,5,0,350000)
Evaluate:
a. If the interest rate is zero, an unlikely situation, then your mom should take the $350,000
in 5 years. If she takes the $250,000 today and invests it at 0% for 5 years, she will have
$250,000 in 5 years. $350,000 is better in 5 years than $250,000.
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b. If the interest rate is 8%, she should take the $250,000 today.
c. If the interest rate is 20%, she should take the $250,000 today.
29. a. 1000(1.07)34  9,978.11
b. 1000(1.07)24  5,072.37
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