Fundamentals of coroprate finance 7th ross westerfield CH05

Chapter

5

•Introduction to Valuation:
The Time Value of Money

McGraw-Hill/Irwin

Copyright © by The McGraw-Hill Companies, Inc. All rights


Chapter 5 – Index of Sample
Problems
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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


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 )

= $3,000 × 31.40942
= $94,228.26
40


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 )
5 = (1 + r )

12

1
12

5 = 1+ r
5.0833333 = 1 + r
1.1435298 = 1 + r
r = .1435298
r = 14.35298%

12


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

Solve for

Enter
Solve for

2
N

PV

-95.24

PMT

100
FV

5
I/Y

PV
-90.70

100
PMT

FV


22: Future value and time changes

Enter

1
N

5
I/Y

±100

PV

PMT

Solve for

Enter
Solve for

2
N

5
I/Y

PV

±100
PMT

FV
105

FV
110.25


Chapter

5

•End of Chapter 5

McGraw-Hill/Irwin

Copyright © by The McGraw-Hill Companies, Inc. All rights