1. Valuation of Bond and Stock
CHAPTER 5
Valuation of Bond and Stock

2. What is a bond?
A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.

3. Key Features of a Bond
Par value – face amount of the bond, which is paid at maturity (assume $1,000).
Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.
Maturity date – years until the bond must be repaid.
Issue date – when the bond was issued.
Market rate of interest is the current interest rate available at the market. (suppose, r)

4. Valuation of Bond
Value of bond equals to the present value of all future payments of interest and the principal amounts. Since all the interest figures are equal so it is the same as the present value of annuity and the future value can be converted in the present value as:

5. Example 1. Bond valuation
A 10% and 10 year bond was issued on August 17, 2006 that pays interest on July 1 and December 1. If the current interest rate is 12%, what is the current price?
It pays interest for 20 times, and out of them how many had already been paid?
So, t=(20-7)=13
VB=$50 (PVIFA, n=13, i=6%)+PV(1000)
=[50*(8.8527)] =$ 1 2 3 4 5 6 7

6. Valuation of Stock Method 1: Zero Growth
Share price is the present value of all future dividends.
Where, D is dividends and k is the cost of capital.
Zero growth means dividends remain at the same level forever,

7. Method 2: Constant Growth
If dividends grow at a constant rate for ever, then: D1=D0(1+g), similarly, D2=D1(1+g)=D0(1+g)2
In that case:
Example: ABC Co. paid Tk.15 as the dividend of the current year. The dividends are expected to grow at constant rate of 4 percent forever. The cost of equity is 11 percent. What should be the price today?

8. Investment Decision Investment decision can be:
To buy: If market price is less than theoretical price
To sell: If market price is more than theoretical price
No change: If market price is equal to theoretical price
For example: In the previous example, if the current market price of ABC stock is Tk.205 then the investment decision is to buy ABC stock. If the market price is Tk.230, then the investment decision is to sell the stock. If the market price is Tk then neither buy nor sell.

9. Case 3: No-constant Growth
The constant growth model is not applicable when ‘g’ is quite high. No-constant growth or super growth model is then the only choice to estimate stock price.
1. Calculate the present value of dividends of super growth rate separately, sum it up,
2. Calculate the future price of the stock based on constant growth rate,
3. Make the present value of the price,
4. Add the two streams of present value.
Example: If dividend grows at a super rate for 3 years and then, at a constant rate for perpetuity, then:
Po=PV(D1)+PV(D2)+PV(D3)+PV(P3),
where, P3=D4/(k-g)

10. Problem: No-constant Growth model
Suppose, a high growth mobile firm paid a dividend of
Tk. 22 in the current year. It is expected that dividend will
grow at the rate of 20% for the next 3 years and then at a
constant rate of 3% for ever. If the cost of equity or the
required return of the firm is 15% then what should be the
price of the stock today?
Summarized Answer:
Po=PV(D1)+PV(D2)+PV(D3)+PV(P3)
=PV(26.4)+PV(31.68)+PV(38.02)+PV(39.16/( )) =
=286.46

11. Detail worksheet of the Answer (contd.)
Div
PV (Div) 1
D1=Do(1+gs)=22(1.2)=
26.4
D1/(1+k)=26.4/1.15= 2
D2=D1(1+gs)=26.4(1.2)=
31.68
D2/(1+k)2=31.68/(1.15)2 = 3
D3=D2(1+gs)=31.68(1.2)=
38.016
D3/(1+k)3=38.016/(1.15)3 = 4
D4=D3(1+g)=38.016(1.03)=
39.156
PV(D1)+PV(D2)+PV(D3)=
Po=PV(D1)+PV(D2)+PV(D3)+PV(P3)
Where, P3=D4/(k-g)=39.156/( )=
and, PV(P3)=P3/(1+k)3=326.3/(1.15)3=214.55
P0=PV(D1)+PV(D2)+PV(D3)+PV(P3)= =286.46

12. CHAPTER 8
COST OF CAPITAL

13. Cost of Capital Cost of Debt=kd=r(1-t)
Example: The cost of debt of 10% bond with corporate tax of 40% is 6%.
Cost of ordinary stock=ks=D1/Po+g
Example: The current price of Ciba share is Tk.255 that paid Tk.13 as the current year dividend. The ROE of the firm is 16%, and the retention rate is 25%. So the cost is [13(1.04)/255] +.04 =9.30%

14. Cost of Ordinary Stock
The cost of equity or ordinary stock can also be estimated by the CAPM method: ks=Rf+[E(Rm)-Rf] ß
Example: Suppose, the risk free rate is 3.5% and the expected rate of market return is 8%. Now if Ciba has a beta of 1.3 then the cost of equity capital or ordinary stock is 9.3%.

15. Cost of Preferred Stock
Cost of preferred stock=D/Po
Example: If the preference share of a firm pays 8% dividends that has a current market price of Tk.110. Then the cost of preference share capital is 7.27%.

16. WACC Source Amount Weight Cost Wi.ki Equity 200 .4 .093 .0372 Debt .06
Weighted Average Cost of Capital is the weighted average of individual sources of capital. With the following capital structure, the WACC of Ciba is 7.57%.
Source
Amount
Weight
Cost
Wi.ki
Equity
200 .4
.093
.0372
Debt
.06
.024
Pref. Cap.
100 .2
.073
.0145
Total
500 1
.0757