Chapter
6
•Discounted Cash Flow
Valuation
McGraw-Hill/Irwin
Copyright © 2006 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 DuePV  C  
  1  r 
r




1  1 / 1  .036 
 $5,000  
  (1  .03)
.03



.162515743
1.03
 $5,000 
.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
20.0304
C  $188.71
C
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
7.170136
C  $1,673.61
C
25: Annuity – quarterly payments
Enter
Solve for
8
N
10%/4
I/Y
12,000
PV
PMT
-1,673.61
FV
26: Annuity time periods
You own a landscaping business. Your goal is to purchase a
professional lawnmower costing $7,500. To do this, you are saving
$2,000 a year. Your savings account pays 3% interest.
How long will you have to wait to buy the lawnmower if you want to
pay cash for the purchase?
27: Annuity time periods
 1  r t  1
AFV  C  

r


 1  .03t  1
$7,500  $2,000  

.
03


$7,500
t
 .03  1.03  1
$2,000
.1125  1.03  1
t
1.1125  1.03
t
ln 1.1125  t  ln 1.03
.10661  t  .02956
.10661
.02956
t  3.61
t
28: Annuity time periods
Enter
Solve for
N
3.61
3
I/Y
PV
2,000
PMT
7,500
FV
29: Annuity interest rate
You owe $1,000 on your credit card. At the end of each month you
pay $20 towards the balance. You’ve been told that it will take you
99.11 months to pay off this account.
What annual interest rate are you paying?
30: Annuity interest rate
Enter
Solve for
99.11
N
I/Y
18.9%/12
1,000
PV
20
PMT
FV
31: Present value – uneven cash
flows
You are going to receive $500 one year from now, $700 two years
from now and $1,200 three years from now.
What are these payments worth to you today at a 9% discount
rate?
32: Present value – uneven cash
flows

1  
1  
1 
NPV  C1 
 C 2 
 C 3 
1
2
3






1

r
1

r
1

r

 
 



 
 
1
1
1
 $500 
 $700 
 $1,200 
3
1
2
(
1

.
09
)
(
1

.
09
)
1  .09 

 
 
 $458.716  $589.176  $926.620
 $1,974.51
33: Present value – uneven cash
flows
Enter
1
N
9
I/Y
2
N
9
I/Y
3
N
9
I/Y
Solve for
Enter
Solve for
Enter
Solve for
PV
- 458.716
PV
-589.176
PV
-926.620
PMT
500
FV
PMT
700
FV
PMT
1,200
FV
Total PV = $458.716 + $589.176 + $926.620 = $1,974.512  $1,974.51
34: Future value – uneven cash
flows
You have $500 in your investment account today. You are going to
add the following amounts to this account:
End of year 1
End of year 2
End of year 3
$600
$700
$800
Assume you earn an 8% rate of return.
How much money will you have in your account three years from
now?
35: Future value – uneven cash
flows
FV  $500(1.08) 3  $600(1.08) 2  $700(1.08)1  $800
 $629.86  $699.84  $756.00  $800.00
 $2,885.70
36: Future value – uneven cash
flows
Enter
3
N
8
I/Y
500
PV
PMT
FV
629.86
2
N
8
I/Y
600
PV
PMT
FV
699.84
1
N
8
I/Y
700
PV
PMT
FV
756.00
Solve for
Enter
Solve
Enter
Solve for
Total FV = $629.86 + $699.84 + $756.00 + $800.00 = $2,885.70
37: Perpetuity present value
You are establishing a trust fund to provide $100,000 in
scholarships to college students each year in perpetuity.
How much money are you contributing to this trust if the discount
rate is 8%?
38: Perpetuity present value
C
PV 
r
$100,000

.08
 $1,250,000
39: Effective annual rate
You have a credit card with a quoted annual percentage rate of
17.9%. Interest is applied to your account monthly.
What is the effective annual rate?
40: Effective annual rate
m
  quoted rate 
EAR  1  
  1
m

 
12
  .179 
EAR  1  
  1
  12 
 1.014917  1
12
 .19444
 19.44%
41: Effective annual rate
Enter
Solve for
17.9
NOM
EFF
19.44
12
C/Y
42: Continuous compounding
What is the effective annual rate of 14.9% compounded
continuously?
43: Continuous compounding
EAR  e.149  1
 2.71828
.149
 .16067
 16.07%
1
44: Continuous compounding
.149
2nd
ex
-1
=
.16067
Which is rounded to 16.07%
45: Pure discount loan
You are borrowing money today at a 9% interest rate. You will
repay the loan in one lump sum payment of $5,000 two years from
today.
How much are you borrowing today?
46: Pure discount loan
1
PV  C t 
t
1  r 
1
 $5,000 
2
1  .09
$5,000

1.1881
 $4,208.40
47: Pure discount loan
Enter
Solve for
2
N
9
I/Y
PV
4,208.40
5,000
PMT
FV
48: Interest only loan
You are borrowing $2,500 today for five years at a 7% rate of
interest. This is an interest only loan with payments paid annually.
How much must you pay each year until this loan is repaid in full?
49: Interest only loan
Year 1 payment  $2,500  .07  $175
Year 2 payment  $2,500  .07  $175
Year 3 payment  $2,500  .07  $175
Year 4 payment  $2,500  .07  $175
Year 5 payment  $2,500  .07   $2,500  $2,675
50: Amortized loan
You borrow $1,000 at 8% interest. This loan is being amortized over
five years with payments being made annually.
What is the amount of each annual payment?
51: Amortized loan

1 
1  (1  r ) t 

PV  C  
r
1 

1  1.085 
$1,000  C 
.08
.3194168
$1,000  C 
.08
$1,000  C  3.99271
C  $250.46
52: Amortized loan
Enter
Solve for
5
N
8
I/Y
1,000
PV
PMT
-$250.46
FV
Chapter
6
•End of Chapter 6
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.