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