Chapter 5: Time Value of Money
Answers and Solutions
99
5-38 0 1 2 3
12/31/13 12/31/14 12/31/15 12/31/16 12/31/17
| | | | |
34,000.00 35,020.00 36,070.60 37,152.72 38,267.30
Step 1: Calculate salary amounts (2013-2017):
2013: $34,000
5-39 1. Will save for 10 years, then receive payments for 25 years. How much must he deposit at the
end of each of the next 10 years?
7%
100
Answers and Solutions
Chapter 5: Time Value of Money
So, the time line looks like this:
Retires
50 51 52 59 60 61 83 84 85
| | | • • • | | | • • • | | |
5-40 Step 1: Determine the annual cost of college. The current cost is $15,000 per year, but that is
escalating at a 5% inflation rate:
College Current Years Inflation Cash
Year Cost from Now Adjustment Required
1 $15,000 5 (1.05)5 $19,144.22
Now put these costs on a time line:
13 14 15 16 17 18 19 20 21
| | | | | | | | |
-19,144 –20,101 –21,107 –22,162
How much must be accumulated by age 18 to provide these payments at ages 18 through
8%
Chapter 5: Time Value of Money
Comprehensive/Spreadsheet Problem
101
Comprehensive/Spreadsheet Problem
Note to Instructors:
The solution to this problem is not provided to students at the back of their text. Instructors
can access the
Excel
file on the textbook’s website.
5-41 a.
b.
c.
Inputs: PV = –$1,000
Inputs: PV = $1,000
Years (D11)
1,610.51$ 0% 5% 20%
0$1,000.00 $1,000.00 $1,000.00
Interest Rate (D10)
Inputs: FV = $1,000
102
Comprehensive/Spreadsheet Problem
Chapter 5: Time Value of Money
f.
g.
h.
Inputs: PMT (1,000)$
N 5
I15%
For the PV, each payment would be received one period sooner, hence would be discounted back one
less year. This would make the PV larger. We can find the PV of the annuity due by finding the PV of
an ordinary annuity and then multiplying it by (1 + I).
Exactly the same adjustment is made to find the FV of the annuity due.
Part a. FV with semiannual compounding: Orig. Inputs: New Inputs:
Chapter 5: Time Value of Money
Comprehensive/Spreadsheet Problem
103
k.
Beginning Ending
Year Balance Payment Interest Principal Balance
Year Payment x
(1 + I )^(N – t)
=FV
(1) A B C D E
Each of these nominal rates based on the frequency of compounding will provide an EAR of 6% .
104
Integrated Case
Chapter 5: Time Value of Money
Integrated Case
5-42
First National Bank
Time Value of Money Analysis
You have applied for a job with a local bank. As part of its evaluation process,
you must take an examination on time value of money analysis covering the
following questions.
A. Draw time lines for (1) a $100 lump sum cash flow at the end of
Year 2; (2) an ordinary annuity of $100 per year for 3 years; and (3)
an uneven cash flow stream of –$50, $100, $75, and $50 at the end
of Years 0 through 3.
ANSWER: [Show S5–1 through S5-4 here.] A time line is a graphical
representation that is used to show the timing of cash flows. The
Chapter 5: Time Value of Money
Integrated Case
105
B. (1) What’s the future value of $100 after 3 years if it earns 4%, annual
compounding?
ANSWER: [Show S5–5 through S5-7 here.] Show dollars corresponding to
question mark, calculated as follows:
106
Integrated Case
Chapter 5: Time Value of Money
B. (2) What’s the present value of $100 to be received in 3 years if the
interest rate is 4%, annual compounding?
Answer: [Show S5-8 through S5–10 here.] Finding present values, or
Chapter 5: Time Value of Money
Integrated Case
107
C. What annual interest rate would cause $100 to grow to $119.10 in 3
years?
ANSWER: [Show S5–11 here.]
0 1 2 3
| | | |
–100 119.10
108
Integrated Case
Chapter 5: Time Value of Money
D. If a company’s sales are growing at a rate of 10% annually, how
long will it take sales to double?
ANSWER: [Show S5–12 here.] We have this situation in time line format:
0 1 2 3 3.8 4
| | | | | |
-1 2
10%
Chapter 5: Time Value of Money
Integrated Case
109
Optional Question
A farmer can spend $60/acre to plant pine trees on some marginal land. The
expected real rate of return is 2%, and the expected inflation rate is 3%. What
is the expected value of the timber after 20 years?
E. What’s the difference between an ordinary annuity and an annuity
due? What type of annuity is shown here? How would you change it
to the other type of annuity?
0 1 2 3
| | | |
0 100 100 100
ANSWER: [Show S5-13 here.] This is an ordinary annuity—it has its payments