Fundamentals of coroprate finance 7th ross westerfield CH06
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Chapter
6
•Discounted Cash Flow
Valuation
McGraw-Hill/Irwin
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 6 – Index of Sample
Problems
•
•
•
•
•
•
•
•
•
•
Slide # 03 - 04
Slide # 05 - 07
Slide # 08 - 10
Slide # 11 - 13
Slide # 14 - 16
Slide # 17 - 19
Slide # 20 - 22
Slide # 23 - 25
Slide # 26 - 28
Slide # 29 - 30
Financial calculator review
Ordinary annuity present value
Annuity due present value
Ordinary annuity future value
Annuity due future value
Annuity – annual payments
Annuity – monthly payments
Annuity – quarterly payments
Annuity time periods
Annuity interest rate
(Index continued on next slide)
Chapter 6 – Index of Sample
Problems
•
•
•
•
•
•
•
•
Slide # 31 - 33
Slide # 34 - 36
Slide # 37 - 38
Slide # 39 - 41
Slide # 42 - 44
Slide # 45 - 47
Slide # 48 - 49
Slide # 50 - 52
Present value – uneven cash flows
Future value – uneven cash flows
Perpetuity present value
Effective annual rate
Continuous compounding
Pure discount loan
Interest only loan
Amortized loans
3: Financial calculator review
If you invest $100 today for one year at a 10% rate of return, how
much money will you have one year from now?
Enter
1
N
10
I/Y
Solve for
(continued on next slide)
±100
PV
PMT
FV
110
4: Financial calculator review
Enter
Solve for
1
N
10
I/Y
±100
PV
PMT
FV
110
You are spending $100 by investing it. You input that as a negative
value using the “±” key. You are receiving $110 back at the end of
one year. That is the positive value.
Positives and negatives are used to denote the direction of the
cash flow. Generally you use a positive value to indicate a cash
inflow and a negative value to indicate a cash outflow. All dollar
amounts in this type of problem are, in actuality, positive values.
5: Ordinary annuity present value
You will receive $12,000 a year for the next ten years from a trust
fund your grandmother is establishing.
What is this gift worth today at a 9% discount rate?
6: Ordinary annuity present value
[
]
1 − 1 / (1 + r ) t
APV = C ×
r
1 − 1 /(1 + .09)10
= $12,000 ×
.
09
.5775892
= $12,000 ×
.09
= $12,000 × 6.4176578
= $77,011.89
[
]
7: Ordinary annuity present value
Enter
Solve for
10
N
9
I/Y
PV
-77,011.89
12,000
PMT
FV
8: Annuity due present value
You are buying some land from your parents today. You agree to
pay them $5,000 a year for six years. The first payment is due
today.
What is the actual selling price of the land if your parents are only
charging you 3% interest?
9: Annuity due present value
[
]
1 − 1 / (1 + r ) t
A Due PV = C ×
× (1 + r )
r
[
]
1 − 1 / (1 + .03) 6
= $5,000 ×
× (1 + .03)
.03
(
.162515743)
= $5,000 ×
× 1.03
.03
= $5,000 × 5.4171914 × 1.03
= $27,898.54
10: Annuity due present value
Enter
Solve for
6
N
3
I/Y
PV
27,898.54
±5,000BGN
PMT
FV
11: Ordinary annuity future value
You are planning on investing $3,500 in the stock market every
year for your retirement. You will make your first investment at the
end of this year. The average rate of return you expect to earn is
7%.
How much money do you expect to have when you retire forty
years from now?
12: Ordinary annuity future value
(1 + r ) t − 1
AFV = C ×
r
(1.07) 40 − 1
= $3,500 ×
.07
= $3,500 ×199.63511
= $698,722.89
13: Ordinary annuity future value
Enter
Solve for
40
N
7
I/Y
PV
±3,500
PMT
FV
698,722.89
14: Annuity due future value
Your parents are giving you $3,000 at the beginning of each year
for four years. You are saving this money and earning a 2.5% rate
of return on your savings.
How much money will you have at the end of the four years?
15: Annuity due future value
( 1 + r)t − 1
AFV = C ×
× (1 + r )
r
(1.025) 4 − 1
= $3,000 ×
× (1 + .025)
.025
= $3,000 × 4.1525156 × 1.025
= $12,768.99
16: Annuity due future value
Enter
Solve for
4
N
2.5
I/Y
PV
±3,000BGN
PMT
FV
12,768.99
17: Annuity – annual payments
You plan on retiring at age 60 and then living another 25
years. Your goal is to have $500,000 in your retirement
savings on the day you retire and spend it all by the time you
die. During your retirement, you expect to earn 5% on your
savings.
How much money can you withdraw from your savings each
year during your retirement if you withdraw the funds on the
last day of each year?
What if you withdraw the money on the first day of each year?
18: Annuity – annual payments
[
]
1 − 1 / (1 + r ) t
APV = C ×
r
1 − 1 / (1 + .05) 25
$500,000 = C ×
.
05
$500,000 = C ×14.0939446
[
]
$500,000
C=
14.0939446
C = $35,476.2286
C = $35,476.23 (rounded)
C
(1 + r )
$35,476.2286
=
1 + .05
= $33,786.88
C AD =
19: Annuity – annual payments
Enter
25
N
5
I/Y
Solve for
Enter
Solve for
25
N
5
I/Y
±500,000
PV
PMT
35,476.23
FV
±500,000
PV
PMT
FV
33,786.88BGN
20: Annuity – monthly payments
You currently owe $3,780 on your credit card. You are not
charging any more on the account. The interest rate is 1.5% per
month.
How much do you have to pay each month if you want to have this
bill paid off within two years?
21: Annuity – monthly payments
[
]
1 − 1 / (1 + r ) t
APV = C ×
r
1 − 1 / (1 + .015) ( 2×12 )
$3,780 = C ×
.
015
.300456
$3,780 = C ×
.015
$3,780 = C × 20.0304
$3,780
C=
20.0304
C = $188.71
[
]
22: Annuity – monthly payments
Enter
Solve for
2x12=24
N
1.5
I/Y
3,780
PV
PMT
-188.71
FV
23: Annuity – quarterly payments
Your company recently borrowed $12,000 to buy some office
equipment. The financing terms call for eight equal quarterly
payments. The interest rate is 10%.
What is the amount of each quarterly payment?
24: Annuity – quarterly payments
[
]
1 − 1 / (1 + r ) t
APV = C ×
r
.10 8
1 − 1 / 1 +
4
$12,000 = C ×
.
10
/
4
.1792534
$12,000 = C ×
.025
$12,000 = C × 7.170136
$12,000
C=
7.170136
C = $1,673.61
