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DISCOUNTED CASH FLOW VALUATION

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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
  add additional amounts? Assume a 7%
  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       
                           
                                        
                                         



                                                          13
          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


                                   18
Table 6.2




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