Discounted Cash Flow Valuation

1
Chapter 6

• Discounted Cash Flow Valuation

2
Key Concepts and Skills

• Be able to compute the future value of multiple
  cash flows
• Be able to compute the present value of multiple
  cash flows
• Be able to compute loan payments
• Be able to find the interest rate on a loan
• Understand how loans are amortized or paid off
• Understand how loan interest rates are quoted

3
Outline

• Future and Present Values of Multiple Cash Flows
• Valuing Level Cash Flows Annuities and
  Perpetuities
• Comparing Rates The Effect of Compounding
  Periods
• Loan Types and Loan Amortization

4
Multiple Cash Flows- FV Example

• You have 7000 today and you want to deposit
  4,000 at the end of each year for the next 3
  years in a banking account that pays 8 per year.
  How much will you have in 3 years? 4 years?

5
FV Example 6.1 Contd

• Timeline
• 7,000 4,000
  4,000 4,000
• i8 ----------------------------------
  ---------
• 0 1 2
  3 4
• Compute the FV for each cash flow

6
Example 6.1 Contd

• Year 0 (now) FV 7000(1.08)3 8,817.98
• Year 1 FV 4000(1.08)2 4,665.60
• Year 2 FV 4,000(1.08) 4,320
• Year 3 4000
• Total FV 8,817.984,665.64,3204,000
• 21803.58
• Year 4 FV 21,804(1.08) 23,547.87

7
Multiple Cash Flows FV Example 2

• Suppose you invest 500 in a mutual fund today
  and 600 in one year. If the fund pays 9
  annually, how much will you have in two years?
• Timeline
• 500 600
• i9 --------------------------
• 0 1 2
• FV 500(1.09)2 600(1.09) 1,248.05

8
Example 2 Contd

• How much will you have in 5 years if you make no
  further deposits
• Timeline
• 500 600 0 0 0 0
• i9 -----------------------------------------
  -------------
• 0 1 2 3
  4 5
• FV 500(1.09)5 600(1.09)4 1,616.26 OR
• FV 1,248(1.09)3 1,616.26

9
Multiple Cash Flows FV Example 3

• You plan to deposit 100 into an account in one
  year and 300 in three years. How much will you
  have in 5 years if the interest rate is 8?
• 100 300
  ?
• i8-----------------------------------------
  -----
• 0 1 2 3 4
  5
• FV 100(1.08)4 300(1.08)2 485.97

10
Multiple Cash Flows-PV Example 1

• An investment will pay you 200 in one year, 400
  the next year, 600 the third year and 800 the
  fourth year. The rate of return is 12 and your
  broker is offering the investment to you for
  1,500 today. Should you buy it?

11
Timeline
200 400 600
800
0 1 2
3 4
12
PV Example Contd

• Find the PV of each cash flow and add them
• Year 1 PV 200/(1.12) 178.57
• Year 2 PV 400/(1.12)2 318.88
• Year 3 PV 600/(1.12)3 427.07
• Year 4 PV 800/(1.12)4 508.41
• Total PV 1,432.93
• You should pay no more than this amount for the
  investment!

13
Multiple Cash Flows- PV Example

• An investment will pay you 1000 in one year,
  2000 in two years and 3,000 in three years. If
  you want to earn 10 per year, how much would you
  be willing to pay?
• Create the timeline
• Compute the total PV

14
Multiple Cash Flow PV Solution

• PV 1000/(1.1)1 909.09
• PV 2000/(1.1)2 1652.89
• PV 3000/(1.1)3 2253.94
• PV total 4815.93

15
Multiple Cash Flows with the TIBAII

• Press CF then enter the cash flow for year 0
  (today) if there is one, Press ENTER and the down
  arrow after each cash flow
• CF0 1000?ENTER? Down arrow
• At the CO1 prompt, enter cash flow for year 1
• CO11000?ENTER? Down arrow
• At the FO1 prompt, enter the number of times this
  cash flow will occur (i.e. 2 for 2 years)
• FO1 2 ? ENTER ? Down arrow
• Press NPV to compute the present value
• At the I prompt enter the rate 10?ENTER?Down
  arrow
• At the NPV prompt press CPT
• To clear press CF? 2nd? CLR Work

16
TIBAII CF Example 1

• Your broker tells you that if you invest 100
  today, you will receive 40 in one year and 75
  in two years. If you require a 15 return on
  investments of this risk, should you take the
  investment?

17
TIBAII Example contd

• CF
• CF0 0 ?ENTER?Down arrow
• CO1 40? ENTER? Down arrow
• FO1 1?ENTER?Down arrow
• CO2 75?ENTER? Down arrow
• FO2 1?ENTER? Down arrow
• Press NPV
• I 15? CPT ? NPV
• NPV 91.49, tell your broker NO!!!!!!!!!!!

18
Saving for Retirement

• You are offered the opportunity to put some money
  away for retirement. You will receive five
  annual payments of 25,000 each year beginning in
  40 years. How much would you be willing to
  invest today if you desire an interest rate of
  12?
• CF CF00 C010 F0139 C0225,000 F025
• NPV I 12 CPT NPV

19
Quick Quiz Part I

• Suppose you are looking at the following possible
  cash flows Year 1 CF 100 Years 2 and 3 CF
  200 Years 4 and 5 CF 300. The discount rate
  is 7
• What is the value of the cash flows at year 5?
• What is the value of the cash flows today?
• What is the value of the cash flows at year 3?

20
Intro to Annuities and Perpetuities

• Annuity finite series of equal payments that
  occur at regular intervals
• Ordinary annuity the first payment occurs at
  the end of the period
• Annuity due the first payment occurs at the
  beginning of the period
• Perpetuity - infinite series of equal payments

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Annuities and PerpetuitiesBasic Formulas

• Perpetuity PV C/r
• Annuities
• PV C 1- (1/(1r)t)
• r
• FV C(1r)t 1
• r

22
Annuities TI BA II

• PMT equal payments
• Ordinary annuity vs. Annuity due
• Ordinary due no changes
• Annuity due Switch payments to the beginning of
  the period
• 2nd BGN 2nd Set

23
Annuities Example 6.5

• You can pay 632 per month for a new sports car.
  The bank will loan you the money at a rate of 1
  per month for 48 months. How much money do you
  need to borrow?
• PV 6321- (1/(1.0148)) 23,999.54
• .01
• Calculator
• 48 N 632 PMT 1 I/Y CPT PV 23,999.54 24,000

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Youve won 10,000,000!!!!!!!!

• You just won the Publishers Clearinghouse 10
  million sweepstakes. The money is paid in equal
  installments of 333,333.33 over 30 years. If
  the discount rate is 5, how much is the
  sweepstakes worth today?
• PMT
• N
• I/Y
• CPT PV

25
Quick Quiz Part II

• If you know the payment amount for a loan and you
  want to know how much was borrowed, do you
  compute the present value or the future value?

26
Finding the Payment

• Suppose you want to borrow 20,000 for a new car.
  You can borrow at 8 per year, compounded
  monthly (8/12 .6667 per month). If you take a
  4 year loan, what is your monthly payment?
• - 20,000 PV .6667 I/Y 48 N CPT PMT
• Remember to adjust the number of periods and the
  interest rate when interest is compounded more
  than once a year (48 months 4 years 12
  months/year, .6667 8/12 months)

27
Finding the number of payments Ex. 6.6

• You charged a spring break trip on your credit
  card for 1,000. You can only afford to make the
  minimum payment of 20 per month. The interest
  rate is 1.5 per month
• PV
• PMT
• I/Y
• CPT N

28
Finding the Rate

• Suppose you borrow 10,000 from your parents to
  buy a car. You agree to pay 207.58 per month
  for 60 months. What is the monthly interest
  rate?
• N
• PV
• PMT
• CPT I/Y

29
Quick Quiz Part III

• You want to receive 5000 per month for the next
  5 years. How much would you need to deposit
  today if you can earn .75 per month?
• What monthly rate would you need to earn if you
  only have 200,000 to deposit?
• Suppose you have 200,000 to deposit and can earn
  .75 per month
• How many months could you receive the 5000
  payment?
• How much could you receive every month for 5
  years?

30
Future Values for Annuities

• You begin saving for your retirement by
  depositing 2000 per year in an IRA. If the
  interest rate is 7.5, how much will you have in
  40 years?
• PMT
• I/Y
• N
• CPT FV

31
Annuity Due

• You are saving for a new house and you put
  10,000 per year in an account paying 8. The
  first payment is made today. How much will you
  have at the end of 3 years?

32
Annuity Due Timeline

• 10,000 PMT 3 N 8 I/Y CPT PV 35,061.12

0 1 2 3 i8 ------------------
--------- 10K 10K 10K 2nd BGN,
2nd SET
33
Perpetuity Example 6.7

• Fellini Co. wants to sell preferred stock for
  100/share. One similar issue costs 40/share and
  pays a dividend of 1 every quarter. What
  dividend must Fellini pay in order for its
  preferred stock to sell?
• PV C/r
• Current required return
• Dividend for new preferred

34
Quick Quiz Part IV

• You want to have 1 million to use for retirement
  in 35 years. If you can earn 1 month, how much
  do you need to deposit on a monthly basis if the
  first payment is made in one month?
• What if the first payment is made today?
• You are considering preferred stock that pays a
  quarterly dividend of 1.50. If your desired
  return is 3 per quarter, how much would you be
  willing to pay?