# PowerPoint file Business Valuation by mikeholy

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```									Business Valuation

PREPARED BY
KELDON BAUER, PHD
FOR FIL 240
Introduction

 The valuation of all financial securities is based on
the expected PV of future cash flows.

E CF 1  E CF 2       E CF n 
P0  E CF0                       
1  k  1  k 2
1  k n
n
E CF t 
    1  k 
t 0
t
Introduction

n
E CFt 
P0     1  k 
t 0
t

 E[CFt] = Expected cash flow at time t.
 k = The required return (based on economic conditions
& riskiness).
 Value increases as cash flow increases or k decreases.
Bond Valuation

 Two major components
 Interest payments (an annuity).

 Principal (future lump-sum).

n

 1  k   1  k 
Interest      Par
ValueB                     t          n
t 1
B          B

= PV of Annuity + PV of Par Value
Bond Valuation - Example 1

 The value of a 15 year \$10,000 bond, paying
semi-annual payments of \$500, when market
rate is 10%.

VB  PV of Annuity + PV of Par Value
         1    
1-
 1+ 0.05 30 
= 500 
         10,000 1 
           30 
      0.05              1  0.05 
              
              
              
 7,686.23  2,313.77  10,000
Bond Valuation - Example 2

 The value of a 7 year \$10,000 bond, paying
semi-annual payments of \$500, when market
rate is 10%.

VB  PV of Annuity + PV of Par Value
         1   
1-
 1+ 0.05 14 
= 500 
         10,000 1 
           14 
      0.05             1  0.05 
              
             
             
 4,949.32  5,050.68  10,000 - Same as before!
Bond Valuation - Example 3

 The value of a 7 year \$10,000 bond, paying
semi-annual payments of \$500, when market
rate is 8%.

VB  PV of Annuity + PV of Par Value
         1   
1-
 1+ 0.04 14 
= 500 
         10,000 1 
           14 
      0.04             1  0.04 
              
             
             
 5,28156  5,774.75  11,056.31 - More than before!
.
Bond Valuation - Example 4

 The value of a 7 year \$10,000 bond, paying
semi-annual payments of \$500, when market
rate is 12%.

VB  PV of Annuity + PV of Par Value
         1   
1-
 1+ 0.06 14 
= 500 
         10,000 1 
           14 
      0.06             1  0.06 
              
             
             
 9,070.50  4,647.49  9,070.50 - Less than before!
Some Conclusions

 Return or loss on bonds comes from two
components.
Interest Payment (Current Yield) = (Interest Payment)/VB
Change in Face Value (Capital Gain) = (VEnding - VBeginning)/VBeginning
Current Yield - Example

 The value of a 7 year \$10,000 bond, paying
semi-annual payments of \$500, when market
rate is 8%.

 Interest Payment 
                       
Current Yield = # of Payments per year                   
Value of Bond t 

500
2            9.04%
11,056.31
Capital Gains Yield - Example

 The value of a 7 year \$10,000 bond, paying
semi-annual payments of \$500, when market
rate is 8%.
 Value t+1  Value t 
Capital Gains Yield =  # of Payments per year                       
     Value t         
10,948.56  11,056.31
2                          104%
.
11,056.31
Total Yield - Example

 The value of a 7 year \$10,000 bond, paying
semi-annual payments of \$500, when market
rate is 8%.

Total Yield = Current Yield + Capital Gains Yield
 9.04%  104%  8.00%  market rate
.
Some Conclusions

 When market rate = kB the bond sells at par or face
value.
 When market rate < kB the bond sells at a premium.
   When interest rates go down, bond prices go up.
 When market rate > kB the bond sells at a discount.
Some Conclusions

 As time to maturity approaches zero, market value
approaches face value.
   If a 15 year, 10% coupon bond at 5% 10% and 15% market rates
were sold on the market, the values of the bond would be as
shown in the following graph.
Value of a 10% Coupon Bond
1,600
Market Rate =5%
1,400
1,200
Market Value

Market Rate =10%
1,000
800
Market Rate =15%
600
400
200
0
-1      1        3       5      7     9   11   13   15
Time
Some Conclusions

 As time to maturity approaches zero, market value
approaches the face value of the bond.
Yield to Maturity (YTM)

 Yield to Maturity (YTM): The effective interest rate
earned on the bond.
 Your calculator can calculate it directly.
   Input the n, PV (Market Value), PMT (semi-annual payments),
FV (Par Value), and have it compute i (then adjust).
YTM - Example

 What is the yield-to-maturity of a bond with
current market value of \$950.51, a par value of
\$1,000 (which is returned in seven years),
making a coupon payment of \$45 every six
months?

Bond Values

 If one knows the market interest rate, the maturity,
the coupon payments, and the par value, one can
calculate the bond’s value by using one’s calculator!
Bond Values - Example

 What is the market value of a bond with current
market rate of 10%, a par value of \$1,000
(which is returned in seven years), making a
coupon payment of \$54 every six months?

Interest Rate Risk

 Two types of interest rate risk associated with bond
value.
   Price Risk
   Reinvestment Risk
 Price Risk: The risk of change in price give change in
interest.
   As interest increases, value decreases.
Price Risk - Effect of Maturity
Value of 10% Coupon Bond

1,600
1,400
1,200
Bond Value

1,000                               1-Year Bond
800
600
400                               14-Year Bond
200
0
0%   5%   10%      15%        20%       25%   30%
Market Rate
Interest Rate Risk

 Reinvestment Risk: The risk of worse reinvestment
opportunities when repaid.
   When interest rates increase reinvestment opportunities
improve.
 Note: Price and Reinvestment Risks go in opposite
directions.
Price Risk - Effect of Payment
14 Year Debt Instrument - 10% Contract Rate

2,500
2,000
Bond Value

1,500                                           Coupon Bond
Zero Coupon
1,000                                           Monthly Loan
500
0
0%      5%    10%   15%   20%   25%   30%
Market Rate
Equity Valuation - Dividend Based Models

 The first economic based valuation models assessed
the present value of expected dividends.
 Myron Gordon applied the previous equation to
expected dividends, assuming a constant growth
rate.
   Since stocks never mature, n must be allowed to approach
infinity.
Dividend Based Models

 The Gordon Constant Growth Model:

D0 1  g  D0 1  g      D0 1  g 
2                 
[1]   P0                         
1  k s  1  k s 2
1  k s 

multiplyin g both sides by
1  g 
1  k s 
[2]     1  g  P  D0 1  g 2  D0 1  g 3   D0 1  g 
1  k s  0
1  k s 2     1  k s 3     1  k s 
Gordon Constant Growth Model

 Subtracting [2] from [1]:

P0 
1  g  P  D0 1  g 
1  k s  0 1  k s 
 1  k s 1  g  D0 1  g 
 1  k  1  k   1  k 
P0                   
       s        s            s

 k s  g  D0 1  g 
 1  k   1  k 
P0          
       s         s
Gordon Constant Growth Model

 Solving for PV:

 k s  g  1  k s  D0 1  g   1  k s 
P0                               
 1  k  k  g  1  k   k  g         
       s  s               s     s       

D0 1  g    ˆ
D1
P0              
ks  g  ks  g 
Free Cash Flow Models

 Many stocks do not offer a dividend.
 If the same assumptions are made, except that free
cash flow, not dividends are being valued, the same
process can be used to derive another valuation
model:

FCF0 1  g 
P0 
k s  g 
What Affects Stock Prices?

FCF0 1  g 
P0 
k s  g 
 Stock prices should therefore depend on:
 Expected cash flow.
 Growth rate.

 The company’s required return.
What Affects Stock Prices?

 Required return is a function of the Capital Asset
Pricing Model (CAPM):

k s  RF  km  RF  s
   Therefore ks depends on:
 Interest rates.
 Systematic risk of the firm.
 Market risk aversion.
Non-Constant Growth Valuation

 Since constant growth is unlikely, we will now
consider how to value stock under non-constant
growth.
 First, project dividends (or free cash flows) as far as
practical.
 From there estimate a constant growth rate.
 Then take the PV as we discussed in an earlier
chapter.
Non-Constant Growth - Example

 If Buford’s Bulldozer is expected to pay the
following dividends, and then grow indefinitely
at 4.5% (assuming a discount rate of 14.50%),
what would its stock value be?
T im e Div idends
1      1 .25
2      2.7 5
3      1 .50
4      2.80
5      3.20
Non-Constant Growth - Example

 First we consider the price of the stock at time five.

      3.20(1  0.045) 3.344
D5 1  g
P5                                  \$33.44
k  g 0145  0.045 010
s
.               .
Non-Constant Growth - Example

 Next we sum all period cash flows.

T im e Div idends Stock Value      T otal
1      1 .25                     1 .25
2      2.7 5                     2.7 5
3      1 .50                     1 .50
4      2.80                      2.80
5      3.20       33.44         36.64
Non-Constant Growth - Example

0           1     2       3       4       5
14.5%

\$1.25    \$2.75   \$1.50   \$2.80   \$36.64

\$ 1.09
\$ 2.10
\$ 1.00
\$ 1.63
\$18.62
\$24.44 = Present Value
Other Valuation Methods

 Book Value Method.
 Liquidation Value Method.
 Price/Earnings (P/E) Multiples.

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