Chapter
5
•Introduction to Valuation:
The Time Value of Money
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 5 – Index of Sample
Problems
•
•
•
•
•
•
•
•
•
•
Slide # 02 - 03
Slide # 04 - 06
Slide # 07 - 09
Slide # 10 - 12
Slide # 13 - 15
Slide # 16 - 18
Slide # 19
Slide # 20
Slide # 21
Slide # 22
Simple interest versus compound interest
Future value
Present value
Interest rate for a single period
Interest rate for multiple periods
Number of time periods
Present value and rate changes
Future value and rate changes
Present value and time changes
Future value and time changes
Interest rate
•
•
•
•
Principle =1 (future rate)
Interest rate: r (per period), periods: n
Simple interest rate: 1+nr
Compound interest rate: (1+r)^n
• Interest rate: r (annually), time: t years
• Continuous compound interest rate: e^(rt)
Discount rate
• Future rate is the value of now one dollar at
end.
• Discount rate is the value of end one dollar at
now.
• Discount rate = 1/future rate
2: Simple versus compound interest
First United Bank pays 4% simple interest on their savings
accounts. Second Federal Bank pays 4% interest compounded
annually on their savings accounts.
If you invest $1,000 in each bank, how much will you have in your
accounts after twenty years?
Why are the balances different?
3: Simple versus compound interest
First United Bank
$1,000  .04  $40
$40  20  $800
$1,000  $800  $1,800
Second Federal Bank
FVt  PV  (1  r) t
 $1,000 1.04 20
 $2,191.12
Difference
$2,191.12  $1,800  $391.12
4: Future value
You invest $3,000 in the stock market today.
How much will your account be worth forty years from now if you
earn a 9% rate of return?
5: Future value
FVt  PV  1  r 
t
 $3,000  1  .09 
40
 $3,000  31.40942
 $94,228.26
6: Future value
Enter
Solve for
40
N
9
I/Y
3,000
PV
PMT
FV
94,228.26
7: Present value
You want to have $7,500 three years from now to buy a car. You
can earn 6% on your savings.
How much money must you deposit today to have the $7,500 in
three years?
8: Present value
FVt
PV 
t
1  r 
$7,500

3
1  .06
$7,500

1.191016
 $6,297.14
9: Present value
Enter
Solve for
3
N
6
I/Y
PV
-6,297.14
PMT
7,500
FV
10: Interest rate for a single period
Last year your investments were worth $369,289. Today they are
worth $401,382. No deposits or withdrawals were made during the
year.
What rate of return did you earn on your investments this year?
11: Interest rate for a single period
FVt  PV  1  r 
t
$401,382  $369,289  1  r 
1.086905  1  r
r  .086905
r  8.6905%
1
12: Interest rate for a single period
Enter
Solve for
1
N
I/Y
8.6905
369,289
PV
PMT
401,382
FV
13: Interest rate for multiple periods
The City Museum owns a rare painting currently valued at $1.2
million. The museum paid $240,000 to purchase the painting twelve
years ago.
What is the rate of appreciation on this painting?
14: Interest rate for multiple periods
FVt  PV  1  r 
t
$1,200,000  $240,000  1  r 
12
5  1  r 
12
1
12
5  1 r
5.0833333  1  r
1.1435298  1  r
r  .1435298
r  14.35298%
15: Interest rate for multiple periods
Enter
Solve for
12
N
240,000
I/Y
PV
14.35298
PMT
1,200,000
FV
16: Number of time periods
Tom originally started to work for Jackson Enterprises at an annual
salary of $36,500. Today, Tom earns $68,200. Tom calculated that
his average annual pay raise has been 3.4%.
How long has Tom worked for Jackson Enterprises?
17: Number of time periods
FVt  PV  1  r 
t
68,200  36,500  1.034
t
1.8684932  1.034t
ln 1.8684932  t  ln 1.034
ln 1.8684932
t
ln 1.034
.6251323
t
.0334348
t  18.697
18: Number of time periods
Enter
Solve for
N
18.697
3.4
I/Y
36,500
PV
PMT
68,200
FV
19: Present value and rate changes
Enter
1
N
6
I/Y
1
N
7
I/Y
Solve for
Enter
Solve for
PV
-94.34
PV
-93.46
PMT
100
FV
PMT
100
FV
20: Future value and rate changes
Enter
1
N
6
I/Y
100
PV
PMT
FV
106
I/Y
100
PV
PMT
FV
107
Solve for
Enter
Solve for
1
N
21: Present value and time changes
Enter
1
N
5
I/Y
2
N
5
I/Y
Solve for
Enter
Solve for
PV
-95.24
PV
-90.70
PMT
100
FV
PMT
100
FV
22: Future value and time changes
Enter
1
N
5
I/Y
100
PV
PMT
FV
105
2
N
5
I/Y
100
PV
PMT
FV
110.25
Solve for
Enter
Solve for
Chapter
5
•End of Chapter 5
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.