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6. Discounted Cash Flow Valuation . Chapter 6 – Index of Sample Problems. Slide # 03 - 04Financial calculator review Slide # 05 - 07Ordinary annuity present value Slide # 08 - 10Annuity due present value Slide # 11 - 13Ordinary annuity future value - PowerPoint PPT Presentation
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Chapter
McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
6•Discounted Cash Flow
Valuation
Chapter 6 – Index of Sample Problems
• Slide # 03 - 04 Financial calculator review• Slide # 05 - 07 Ordinary annuity present value• Slide # 08 - 10 Annuity due present value• Slide # 11 - 13 Ordinary annuity future value• Slide # 14 - 16 Annuity due future value• Slide # 17 - 19 Annuity – annual payments• Slide # 20 - 22 Annuity – monthly payments• Slide # 23 - 25 Annuity – quarterly payments• Slide # 26 - 28 Annuity time periods• Slide # 29 - 30 Annuity interest rate
(Index continued on next slide)
Chapter 6 – Index of Sample Problems
• Slide # 31 - 33 Present value – uneven cash flows• Slide # 34 - 36 Future value – uneven cash flows• Slide # 37 - 38 Perpetuity present value• Slide # 39 - 41 Effective annual rate • Slide # 42 - 44 Continuous compounding• Slide # 45 - 47 Pure discount loan• Slide # 48 - 49 Interest only loan• Slide # 50 - 52 Amortized loans
formula
• 1+x+x^2+…+x^(n-1) = [(1-x^n)/(1-x)]• 1+x+x^2+…. =1/(1-x), if x<1
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 10 100 N I/Y PV PMT FV
Solve for 110
(continued on next slide)
4: Financial calculator review
Enter 1 10 100 N I/Y PV PMT FV
Solve for 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
89.011,77$4176578.6000,12$
09.5775892.000,12$
09.)09.1/(11000,12$
1/11 C APV
10
r
r t
7: Ordinary annuity present value
Enter 10 9 12,000 N I/Y PV PMT FV
Solve for -77,011.89
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
54.898,27$03.14171914.5000,5$
03.103.
.162515743 000,5$
)03.1(03.
03.1/11000,5$
11/11 C PVA
6
Due
rr
r t
10: Annuity due present value
Enter 6 3 5,000BGN N I/Y PV PMT FV
Solve for 27,898.54
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
89.722,698$63511.199500,3$
07.1)07.1(500,3$
1)1( AFV
40
rr C
t
13: Ordinary annuity future value
Enter 40 7 3,500 N I/Y PV PMT FV
Solve for 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
99.768,12$025.11525156.4000,3$
)025.1(025.
1)025.1(000,3$
)1(11 AFV
4
rr r) ( C
t
16: Annuity due future value
Enter 4 2.5 3,000BGN N I/Y PV PMT FV
Solve for 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
(rounded) $35,476.23C86$35,476.22C
14.0939446$500,000C
14.0939446C000,500$
05.05.1/11C000,500$
1/11 C APV
25
r
r t
88.786,33$05.1
2286.476,35$r1
CCAD
19: Annuity – annual payments
Enter 25 5 500,000 N I/Y PV PMT FV
Solve for 35,476.23
Enter 25 5 500,000 N I/Y PV PMT FV
Solve for 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
$188.71 C20.0304$3,780C
20.0304C780,3$.015
.300456C780,3$
015.015.1/11C780,3$
1/11 C APV
)122(
rr t
22: Annuity – monthly payments
Enter 2x12=24 1.5 3,780 N I/Y PV PMT FV
Solve for -188.71
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
$1,673.61 C7.170136$12,000 C
7.170136C000,12$025.
1792534. C $12,000
4/10.
410.1/11
C $12,000
1/11 C APV
8
r
r t
25: Annuity – quarterly payments
Enter 8 10%/4 12,000 N I/Y PV PMT FV
Solve for -1,673.61
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
61.302956.10661.
02956.10661.03.1ln1125.1ln
03.11125.1
103.11125.
103.103.000,2$500,7$
03.103.1000,2$500,7$
11 C AFV
t
t
tt
rr
t
t
t
t
t
28: Annuity time periods
Enter 3 2,000 7,500 N I/Y PV PMT FV
Solve for 3.61
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 99.11 1,000 20 N I/Y PV PMT FV
Solve for 18.9%/12
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
51.974,1$620.926$176.589$716.458$
09.11200,1$
)09.1(1700$
)09.1(1500$
11C
11C
11C NPV
321
332211
rrr
33: Present value – uneven cash flows
Enter 1 9 500 N I/Y PV PMT FV
Solve for - 458.716
Enter 2 9 700 N I/Y PV PMT FV
Solve for -589.176
Enter 3 9 1,200 N I/Y PV PMT FV
Solve for -926.620
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 $600End of year 2 $700End of year 3 $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
70.885,2$00.800$00.756$84.699$86.629$
800$)08.1(700$)08.1(600$$500(1.08) FV 123
36: Future value – uneven cash flows
Enter 3 8 500 N I/Y PV PMT FV
Solve for 629.86
Enter 2 8 600 N I/Y PV PMT FV
Solve 699.84
Enter 1 8 700 N I/Y PV PMT FV
Solve for 756.00
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
000,250,1$08.
000,100$
PV
rC
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
%44.1919444.
1014917.1
112179.1EAR
1rate quoted1EAR
12
12
m
m
41: Effective annual rate
Enter 17.9 12NOM EFF C/Y
Solve for 19.44
42: Continuous compounding
What is the effective annual rate of 14.9% compounded continuously?
43: Continuous compounding
%07.1616067.
171828.21 EAR
149.
149.
e
44: Continuous compounding
.1492nd
ex
-1=.16067Which 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
40.208,4$1881.1000,5$
09.11000,5$
11CPV
2
t
tr
47: Pure discount loan
Enter 2 9 5,000N I/Y PV PMT FV
Solve for 4,208.40
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
675,2$500,2$07.500,2$payment 5Year $175 .07 $2,500 payment 4Year $175 .07 $2,500 payment 3Year $175 .07 $2,500 payment 2Year $175 .07 $2,500 payment 1Year
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
46.250$99271.3000,1$
08.3194168.000,1$
08.08.111
000,1$
)1(11
PV
5
CC
C
C
rr
Ct
52: Amortized loan
Enter 5 8 1,000 N I/Y PV PMT FV
Solve for -$250.46
Chapter
McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
6•End of Chapter 6