Introduction to Valuation:

1
Chapter 5

• Introduction to Valuation
• The Time Value of Money

2
JACKPOT!!!!

• You just won the POWERBALL jackpot for 364
  million!!!! You have two options
• Receive a lump sum of 172 million today
• Receive 12.13 million each year for the next 30
  years
• Which would you choose????

3
Business is expanding

• McGees Catering is considering a new project
  which will cost 5,000,000 today and will bring
  in 1,000,000 in profits each year for the next
  five years.
• Would you advise them to initiate this project?

4
Spring Break Cancun 2008

• You have placed a spring break trip to Cancun on
  your credit card today. The trip cost 1,000.
  You pay 50 on the card each month so you will
  have paid for trip by May 2009.
• True or false?

5
Key Concepts and Skills

• Be able to compute the future value of an
  investment made today
• Be able to compute the present value of cash to
  be received at some future date
• Be able to compute the return on an investment
• Be able to compute the number of periods that
  equates a present value and a future value given
  an interest rate
• Be able to use a financial calculator to solve
  time value of money problems

6
Outline

• Future Value and Compounding
• Present Value and Discounting
• More on Present and Future Values

7
Definitions

• Present Value earlier money on a time line
• Future Value later money on a time line
• Interest rate exchange rate between earlier
  and later money
• Discount rate
• Cost of capital
• Opportunity cost of capital
• Required return

8
Future Values

• Suppose you invest 1000 for one year at 5 per
  year. What is the future value in one year?
• Value in one year Principal Interest
• 1000 (1000.05) 1,050
• FV 1000(1.05)
• Suppose you leave the money in for another year.
  How much will you have two years from now?
• FV 1000(1.05)(1.05) 1000(1.05)2 1102.50

9
Future Values General Formula

• FV PV(1r)t
• FV Future Value
• PV Present Value
• r period interest rate (as a decimal)
• t number of periods
• Future value interest factor (1r)t

10
Compounding

• Simple interest
• Interest is paid only on principal
• Previous example
• 1000 invested for 2 years at 5
• FV10002(1000.05)
• FV 1100

• Compound interest
• Interest is paid on principal and interest earned
  in previous periods
• FV1000(1.05)2 or 10001000(.05) 1050(.05)
• FV 1,102.50

Therefore, all other things held constant,
interest payments are higher with compounding for
problems with greater than one period.
11
More Future Value Examples

• Invest 1000 for 5 years at 5 per year
• Compounding
• FV 1000(1.05)5 1276.28
• Simple interest
• Simple interest 1000 5 (1000.05) 1250

12
More Future Value Examples

• Suppose a relative deposited 10 at 5.5 interest
  200 years ago. How much would that be worth
  today?
• FV 10(1.055)200 447,189.84
• What is the difference between simple and
  compound interest in this case?
• Simple 10 10(200.055) 120

13
Future Value without

• Suppose your company expects to increase unit
  sales of CDs by 15 per year for the next 5
  years. If you currently sell 3 million CDs per
  year, how many CDs do you expect to sell in 5
  years?
• FV 3,000,000 (1.15)5 6,034,072

14
Quick Quiz 1

• What is the difference between simple and
  compound interest?
• Suppose you invest 500 and you can earn 8 each
  year for 15 years
• How much would you have at the end of 15 years
  with compound interest?
• How much would you have using simple interest?

15
Present Values

• How much do I have to invest today to have some
  amount in the future?
• FV PV(1r)t
• Rearrange PV FV/ (1r)t
• Discounting- finding the present value of some
  future amount
• Value- usually means present value unless future
  value is indicated

16
Present Value One Period

• Suppose you need 10,000 in one year for the down
  payment of a new car. If you can earn 7
  annually, how much should you invest today
• PV 10,000/ (1.07) 9,345.79

17
Present Value- Example 2

• You want to start saving for your daughters
  college education and you estimate that she will
  need 150,000 in 17 years. If you can earn 8
  per year, how much should you invest today?
• PV 150,000/ (1.08)17 40,540.34

18
More Present Value Examples

• Your parents set up a trust fund for you 10 years
  ago that is now worth 19,671.51. If the
  fund earned 7 per year, how much did your
  parents invest?
• PV 19,671.51/(1.07)10 10,000

19
Present Value- Important Relationship 1

• For a given interest rate the longer the time
  period, the lower the present value
• What is the present value of 500 to be received
  in 5 years? 10 years? Use 10 as the discount
  rate.
• 5 years PV 500/(1.1)5 310.46
• 10 years PV 500/(1.1)10 192.77

20
Present Value Important Relationship 2

• For a given time period - the higher the
  interest rate, the smaller the present value
• What is the present value of 500 received in 5
  years if the interest rate is 10? 15?
• 10 PV 500/(1.1)5 310.46
• 15 PV 500/(1.15)5 248.58

21
Quick Quiz Part 2

• What is the relationship between present value
  and future value?
• Suppose you need 15,000 in 3 years. If you can
  earn 6 annually, how much do you need to invest
  today?
• If you could invest the money at 8, would you
  have to invest more or less than at 6? How much?

22
The Basic PV Equation

• PV FV/(1r)t
• The equation has four parts
• PV, FV, r and t
• If we know any three, we can solve for the fourth
• Remember to enter PVs as negative!!!

23
Calculator Keys

• FV Future Value
• PV Present Value
• Must be entered as a negative number b/c it is an
  outflow
• I/Y period interest rate
• P/Y must equal 1? hit 2nd P/Y, push 1, enter,
  down, 2nd QUIT
• Enter interest rates as a percent (i.e. 5.00
  instead of .05)
• N number of periods
• Hit 2nd CLR TVM to clear the register after each
  problem

24
Discount Rates

• Often we will need to compute the implied
  interest rate for an investment
• Rearrange the PV equation and solve for r
• FV PV(1r)t
• r (FV/PV)1/t - 1

25
Discount Rate Example 1

• An investment will pay 1200 in 5 years if you
  invest 1000 today. What is the implied rate of
  interest?
• R(1200/1000)1/5 1 .03714
• Calculator
• -1000 PV 5 N
• 1200 FV CPT I/Y

26
Discount Rate Example 2

• Suppose you can invest 10,000 and double your
  investment in 6 years. What is the implied rate
  of interest?
• R (20000/10000)1/6 1 .1225
• Calculator
• 20,000 FV
• -10,000 PV
• 6 N
• CPT I/Y

27
Discount Rate Example 3

• Suppose you have a 1-year old son and you want to
  have 75,000 for his college education in 17
  years. You have 5000 today, what interest rate
  must you earn?
• 75,000 FV 5,000 PV
• 17 N CPT I/Y

28
Quick Quiz Part III

• When might you want to compute the interest rate?
• If you are offered the following investment
  choices
• Invest 500 today and receive 600 in 5 years.
  (this is a low risk investment)
• Invest 500 in a bank account paying 4
• Compute I/Y for the first option. Which option
  should you choose?

29
Finding the Number of Periods

• Start with the FV equation
• FV PV(1r)t
• t ln(FV/PV)/ln(1r)

30
Number of PeriodsExample 1

• You want to buy a new car for 20,000. If you can
  invest at 10 per year and you currently have
  15,000. How long will it be before you have
  enough money to pay cash for the car?
• 20,000 FV 10 I/Y
• 15,000 PV CPT n

31
Quick Quiz Part IV

• When might you want to compute the number of
  periods?
• You need to buy furniture that costs 600. You
  currently have 500 and can earn 6 per year.
  How long will you have to wait if you dont add
  any additional money?

32
TVM Formulas

• FV PV (1r)t
• PV FV/(1r)t, where
• PV Present value
• FV Future value
• t number of periods (n)
• rinterest rate (I/Y)

33
Chapter Review

• Assume you deposit 10,000 today in an account
  that pays 6 percent interest. How much will you
  have in 5 years?

34
Chapter Review

• Suppose you have just celebrated your 19th
  birthday and your rich uncle has set up a trust
  fund that will pay you 150,000 when you turn 30.
  If the relevant discount rate is 9 percent, how
  much is the fund worth today?

35
Chapter Review

• Youve been offered an investment that will
  double your money in 10 years. What rate of
  return are you being offered?
• Check your answer using the Rule of 72

36
Chapter Review

• Youve been offered an investment that will pay
  you 9 percent per year. If you invest 15,000,
  how long will take you to have 30,000? 45,000?