# DISCOUNTED CASH FLOW VALUATION by xiuliliaofz

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```									DISCOUNTED CASH FLOW
VALUATION
CHAPTER 6

DR.LAKSHMI KALYANARAMAN   1
Future value with multiple cash flows
Example 6.1
• You think you will be able to deposit \$4,000 at
the end of each of the next 3 years in a bank
account paying 8% interest. You currently
have \$7,000 in the account how much will you
have in 3 years? In 4 years?

DR.LAKSHMI KALYANARAMAN       2
Multiple Cash Flows –Future Value
Example 6.1
• Find the value at year 3 of each cash flow and add
them together.
• \$7,000 in the account today will earn interest for 3
years
–   Today (year 0): FV = 7000(1.08)3 = 8,817.98
–   \$4,000 you invest at the end of year 1 will earn interest for 2 years
–   Year 1: FV = 4,000(1.08)2 = 4,665.60
–   \$4,000 that you invest at the end of year 2 will earn interest for 1
year
–   Year 2: FV = 4,000(1.08) = 4,320
–   \$4,000 you invest at the end of year 3 cannot earn any interest
–   Year 3: value = 4,000
–   Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 =
21,803.58
• Value at year 4 = 21,803.58(1.08) = 23,547.87
3
Example 6.2
• If you deposit \$100 in one year, \$200 in 2
years, and \$300 in 3 years, how much will you
have in 3 years? How much of this is interest?
How much will you have in 5 years if you don’t
interest rate throughout.

DR.LAKSHMI KALYANARAMAN      4
• \$100 deposited at the end of year 1 earns interest for 2 years
• Year 1: FV = 100(1.07)2 = 114.49
• \$200 deposited at the end of year 2 earns interest for 1 year
• Year 2: FV = 200(1.07) = 214.00
• \$300 deposited at the end of year 3 does not earn any interest
• Year 3: value = 300
• Total value in 3 years = 114.49+ 214 + 300 = 628.49
• Interest earned = Future value of your deposit – your deposit
• \$628.49 – (100+200+300) = \$28.49
• How much will you have in 5 years
• You do not deposit any additional amount. Leave \$628.49 for 2
more years
• \$628.49 ×(1.07)2=\$719.56

DR.LAKSHMI KALYANARAMAN                  5
Present value with multiple cash flows
Example 6.3
• You are offered an investment that will pay
you \$200 in one year, \$400 in the next year,
\$600 the next year and \$800 at the end of the
fourth year. You can earn 12% on very similar
investments. What is the most you should pay
for this one?

DR.LAKSHMI KALYANARAMAN     6
Multiple Cash Flows – Present Value
Example 6.3
• Find the PV of each cash flows and add them
– Year 1 CF: 200 / (1.12)1 = 178.57
– Year 2 CF: 400 / (1.12)2 = 318.88
– Year 3 CF: 600 / (1.12)3 = 427.07
– Year 4 CF: 800 / (1.12)4 = 508.41
– Total PV = 178.57 + 318.88 + 427.07 + 508.41 =
1,432.93

7
Example 6.3 Timeline
0       1      2    3      4

200   400   600   800
178.57

318.88

427.07

508.41
1,432.93

8
A note about cash flow timing
• It is always assumed that cash flows occur at
the end of each period.
• If it occurs at the beginning of the period you
will be told explicitly.

DR.LAKSHMI KALYANARAMAN          9
Annuities and Perpetuities Defined
• Annuity – finite series of equal payments that occur
at regular intervals
– If the first payment occurs at the end of the period, it is
called an ordinary annuity
– If the first payment occurs at the beginning of the period,
it is called an annuity due
• Perpetuity – infinite series of equal payments

10
Annuities and Perpetuities – Basic
Formulas
• Perpetuity: PV = C / r
• Annuities:
         1      
1
(1  r ) t 
PV  C                 
       r        

                

 (1  r ) t  1
FV  C                
      r        
C= dollars per period t = periods r = interest or rate of return

11
Example 6.5
• After carefully going through your budget, you
have determined you can afford to pay \$632
per month toward a new sports car. You call
up your local bank and find out that the going
rate is 1% per month for 48 months. How
much can you borrow?

DR.LAKSHMI KALYANARAMAN      12
Annuity – Example 6.5
• You borrow money TODAY so you need to compute
the present value.
• C = \$632 t = 48 r = 1%

      1      
1
 (1.01) 48   
PV  632                23,999 .54
   .01       

             


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Finding the payment
• Suppose you wish to start up a new business
that specializes in the latest of health food
trends, frozen yak milk. To produce and
market your product, you need to borrow
\$100,000. Because it strikes you unlikely that
this particular fad will be long-lived, you
propose to pay off the loan quickly in 5 equal
annual payments. If the interest rate is 18%,
what will the payment be?
DR.LAKSHMI KALYANARAMAN          14
Finding the payment
1  (1 / 1  r)^ t 
Annuity present value  C                     
         r         
\$100,000 = C×{(1-(1/1.185)/.18}

C = \$31,978

DR.LAKSHMI KALYANARAMAN      15
Future value of annuity
• Future value of C per period for t periods at r
per percent per period

 (1  r )^ t  1 
FVA  C                   
        r        

DR.LAKSHMI KALYANARAMAN          16
Annuity due
• An annuity for which the cash flows occur at
the beginning of the period
• For both present and future value of an
annuity due
• Annuity due = Ordinary annuity × (1+r)

DR.LAKSHMI KALYANARAMAN        17
Perpetuity – Example 6.7
• Perpetuity formula: PV = C / r
• Current required return:
40 = 1 / r
r = .025 or 2.5% per quarter
• Dividend for new preferred:
100 = C / .025
C = 2.50 per quarter

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Table 6.2

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