VALUATION OF BONDS AND STOCKS
Two Approaches of Valuation Process:
1. Top-down, three-step approach
2. Bottom-up, stock valuation, stockpicking approach
Top-down, three-step approach
Analysis of Alternative Economies
and Security Markets
Analysis of Alternative
Industries
Analysis of
Individual
Companies
and Stocks
Page 1
Security Valuation
VALUATION OF BONDS AND STOCKS
Valuation of Bonds
Types of Bonds:
1. Pure Discount or Zero-Coupon Bonds
2. Coupon Bonds
3. Consols or Perpetuities
t1
t2
t3
t4
Zero-Coupon Bonds
tn
F
Coupon Bonds
C
C
C
C
F+C
Consols
C
C
C
C
C
Valuation of Zero-Coupon Bond
PV 
Page 2
… …
F
(1  r ) Τ
Security Valuation
C
C
Valuation of Bonds
Valuation of Coupon Bond
PV  C  Ar 
T
F
(1  r ) T
Valuation of Consol
PV 
C
r
Coupon Rate Vs. Market Rate (Discount Rate)
Discount Rate > Coupon rate
 Sell at Discount
Discount Rate < Coupon rate
 Sell at Premium
Page 3
Security Valuation
Valuation of Common Stocks
Two kinds of Cash Flow from a Stock:
1. Dividend
2. Sales Price (when sold)
Approaches to Equity Valuation
Discounted Cash Flow
Techniques
Relative Valuation
Techniques
 Present Value of
Dividends (Dividend
Discount Model)
 Price/Earning Ratio
(P/E)
 Present Value of
Operating Free Cash
Flow
 Present Value of Free
Cash Flow to Equity
Page 4
Security Valuation
 Price/Cash Flow
Ratio (P/CF)
 Price/Book Value
Ratio (P/BV)
 Price/Sales ratio (P/S)
Valuation of Common Stocks
Case 1: Constant Dividend (Zero Growth Dividend), Hold for T
Years
P0  Div  Ar 
T
PT
(1  r )T
Case 2: Zero Growth Dividend, Perpetuity
P0 
Div
r
Case 3: Constant Growth Dividend, Perpetuity
P0 
Div
rg
Where, r > g
Case 4: Differential Growth Dividend, Perpetuity
Div T 1
T
r  g2
Div (1  g ) t
P0  

(1  r ) t
(1  r ) T
t 1
Page 5
Security Valuation
Valuation of Common Stocks
Differential Growth
g1> g2
Dividend
Per Share
Low Growth
(g2)
Constant
Growth
High
Growth (g1)
Zero Growth
g=0
Time
Example 1
For the last three years Aftab Automobiles was paying
dividend of Tk. 16 per share. The amount is expected to
be same for the coming three years also. After three
years, the sales price is expected to be Tk. 360 per share.
If the required rate of return is 10% what would be the
price of Aftab share today?
P0  16  A0.10 
3
360
(1  0.10)3
= 16  2.4869 + 270.47
= Tk. 310.26
Page 6
Security Valuation
Valuation of Common Stocks
Example 2
For the last three years Aftab Automobiles was paying
dividend of Tk. 16 per share. The amount is expected to
be same for the infinite period. The expected holding
period is also unforeseeable. If the required rate of
return is 10% what would be the price of Aftab share
today?
P0 
16
.10
= Tk. 160
Example 3
ACI Ltd. will pay a dividend of Tk. 4 per share a year
from now. Financial analysts believe that dividends will
rise at 6 percent per year for the foreseeable future.
Required rate of return is 15%.
P0 
4
.15  .06
= Tk. 44.44
Page 7
Security Valuation
Valuation of Common Stocks
Example 4
Keya Cosmetics Ltd. (KCL) will pay dividend of Tk. 4 per share
one year from today. During the next four years, the dividend
will grow at 15 percent per year (g1 = 15%). After that, growth
(g1) will be equal to 10 percent per year. Calculate the present
value of KCL share if the required rate of return is 15%.
Here, r = g. So, growing annuity formula cannot be used.
Present Value of 1st Five Years’ Dividend
Years
Growth
Expected
PV factor at
PV of
Rate (g1)
Dividend
15%
Dividends
1
0.15
4.00
0.8696
3.48
2
0.15
4.60
0.7561
3.48
3
0.15
5.29
0.6575
3.48
4
0.15
6.08
0.5718
3.48
5
0.15
7.00
0.4972
3.48
Present Value of 1st Five Years’ Dividend
Page 8
Security Valuation
17.40
Valuation of Common Stocks
Example 4 (contd.)
From the 6th year the dividend growth rate will be 10%.
P5 
7.7
.15  .10
= Tk. 154
Present value of P5 at 0 period is
P0 
154
(1  0.15)5
= Tk. 76.56
Present value of all dividends
17.40 + 76.56 = Tk. 93.96
Page 9
Security Valuation
Valuation of Common Stocks
Present Value of Operating Free Cash Flows
n
Vj  
t 1
OFCFt
(1  WACC j ) t
Where,
Vj = Value of Total Firm
OFCFt = Operating free cash flow in period t prior to the
payment of interest to the debt holders but
after deducting funds needed to maintain the
firm’s asset base (capital expenditures)
PV of Equity = Vj - Debts
Infinite Period Constant Growth DDM
Vj 
OFCF1
WACC j  gOFCF
Page 10
Security Valuation
Valuation of Common Stocks
Present Value of Free Cash Flows to Equity
n
Vj  
t 1
FCFEt
(1  k j )t
Where,
Vj = Value of the Stock of Firm j
Kj = Cost of Equity
FCFEt = The firm’s free cash flow to equity in period t.
The amount is derived after paying capital
expenditure, debt and preferred services.
Relative Valuation Approach
Page 11
Security Valuation