# Discounted Cash Flow Valuation

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```					     Valuation:

Time Value of Money
&
Discounted Cash Flow
Basic Definitions
   Present Value – money now
   Future Value – money later
   Interest rate – “exchange rate” between money
now and money later
 Required return
 Cost of capital

 Discount rate

1
Future Value: Formula
   FV = PV(1 + r)t
 FV = future value
 PV = present value

 r = period interest rate, expressed as a decimal

 t = number of periods

2
Example
   Invest \$1000 for one year at 5% per year.
   What is the future value in one year?

   How much will you have two years from now?

3
Compounding
   Simple versus compound interest
   Previous example
 FV with simple interest =
 FV with compound interest =

 Interest on first interest payment =

4
Present Value
   How much do I have to invest today to have
some amount in the future?
 FV = PV(1 + r)t
 PV = FV / (1 + r)t

   Discounting - PV of some future amount

5
Value of the Interest Rate
   PV = FV / (1 + r)t
   Is it worse to have higher or lower rates for
payments you receive in the future?
   Rate = 10%              Rate = 15%

6
New Savings Account
   Invest \$500 today and \$600 in one year
   Earn 9% annually
   How much will you have in two years?

   How much will you have in 5 years if you make
no further deposits?

7
Discounted Cash Flows

8
Annuities and Perpetuities
   Annuity
   Finite series of equal payments, occurring regularly
         1      
1
(1  r ) t 
PV  C                 
       r        

                

 (1  r ) t  1
FV  C                
      r        
   Perpetuity
   Infinite series of equal payments
   PV = C / r
9
PV of an Annuity
   Annuity pays \$500/year for 3 years
   If r = 10%, what’s the value of the annuity?

10
Car Loan
   Can afford \$632/month
   Available rate: 1%/month for 48 months
   How much can you borrow today? (PV)

11
Preferred Stock
   Perpetuity formula: PV = C / r
   Preferred stock pays \$10 dividends/year
   r = 5%
   PV = ?

12

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