1. CHAPTER 6
BOND VALUATION

2. Learning Objectives Describe a bond
Describe the various types of bonds
Calculate intrinsic value, current yield and yield to maturity
Describe zero coupon bonds
Describe a convertible bond
Calculate conversion rate, conversion value and conversion premium
Describe bond investment strategies
Describe the different types of bond risks

3. What is a bond? Bonds are long-term loans
Issuers pay bond holders rate of interest (COUPON)
Interest payable either on a semi-annual or yearly basis until bond matures

4. Basic Types of Bonds

5. Features of Bonds Factors Subcategories Details Coupon Fixed
Typically payable semi-annually, but some
are paid on a quarterly or monthly basis
Float
Reset periodically to a specified prevailing
market rate
Zero coupon bond
Payable at maturity
Price
Face value
Newly issued bond
Premium
When the price of the bond is above its
face value
Discount
When a bond price is below its face value
Yield –
Yield is the return on investment
Maturity
Short term
Less than 1 year
Long term
More than 1 year
Redemption features
Call
Provisions that allow the issuer to repay the investor's
principal at a specified date before maturity
Put
Provisions that allow the investor the option of
requiring the issuer to repurchase the bonds at
specified times prior to maturity

6. BOND VALUATION
Bond investors apply principle of risk-return trade-off to value a particular bond
When a bond is exposed to high risk, investors will expect higher return
Issuers assess the risk involved in their investment to estimate the required return of bond investors before they issue new bonds
Bond values are determined by either its promised yield (income from interest payment) or its expected return (capital gain).
Investor’s required rate of return has three components: real rate of return, an expected inflation premium and a risk premium
IV.docx

7. BOND VALUATION
All bonds are valued according to the present value of their future cash flow streams
Example
Nasri buys a ten-year bond that pays 6% coupon per annum and has a discount rate or a yield of 8%. The par value of the bond is RM100. Calculate the bond price.
Year 1 2 3 4 5 6 7 8 9 10
Cash flow RM
100
Coupon
Principal + coupon

8. BOND VALUATION Year Cash flow AF/DF @ 8% PV 1 – 10 6 6.71 40.3 10 100
The alternative approach is
Year
Cash flow 8% PV
1 – 10 6
6.71
40.3 10
100
0.4632
46.32
PV =
RM86.62
Note: Market value of the bond price is lower than the par value (RM100) because the coupon rate (6%) is lower than the market interest rate (8%).
TRY: COUPON 10%  Value of Bond RM113.40
COUPON 8%  Value of Bond RM100

9. BOND Price behaviour 1
The following conclusions were drawn on coupon rates, market rates and bond prices.
When the required rate of return is equal to the coupon rate, a bond will sell at its par value.
When the required rate of return is more than the coupon rate, a bond will sell at a discount.
When the required rate of return is less than the coupon rate, a bond will sell at a premium.

10. Different Maturity Periods Bonds Price Behaviour 2
Refer to the above example. The maturity period is increased to 20 years.
Bond price (BPc) = RM6 (PVIFA8%, 20) + RM100 (PVIF8%, 20)
= RM6 (9.818) + RM100 (0.215)
= RM RM21.50
= RM80.41
when maturity period was increased from 10 years to 20 years, a bond yields a lower price (it goes down from RM86.56 to RM80.41).

11. Semi-annual Interest Payments
Bond price formula modified for semi-annual interest payments.
Interest or coupon payment (I) divided into two parts. The interest is altered to I/2.
Market interest rate or required rate of return (i) divided by 2, i/2.
Maturity period (n) converted to a number of periods.There are ten six-month periods in five years (5 × 2 = 10). Now the maturity period becomes n × 2.
The modified bond price formula is:
Bond price (BPc) = I/2 (PVIFA i/2, n × 2) + P (PVIF i/2, n × 2)
Interest payment = I/2
Required return = i/2
Number of periods = n × 2
Recalculate previous example using semiannual payments: RM86.41

12. MEASURES OF YIELD Example
A bond’s yield is the investor’s required rate of return
Each investor expects to earn a different rate of return according to their risk preference
The required rate of return for an investor is the discount rate that equates the present value of the future interest payments plus the value at maturity date with the current market value of the bond
Current Yield
Current yield is the rate of return that bond holders receive as a reward for their initial investment and for taking a certain amount of risk.
Example
Hassan buys a four-year bond with a coupon rate of 5%. If the market price of the bond is the same as its face value, then the rate of return will be the bond’s coupon rate.

13. Current Yield-Price behaviour 3
Initial cash flow
Year 1
Year 2
Year 3
Year 4 RM
100 5
105
Rate of return for 1 year = RM5/RM100 = 5%. This rate is the same as the coupon payment of 5%. In addition, at the end of year 4, Hassan will get back his original investment of RM100 . (CY = C, Price = Principal)
When the market value of bonds goes up, the current yield drops because investors expect market interest rate to fall ( Price > Principal, CY < C)
In times of low market interest rate, the bond holder’s required return also declines along with the market interest rate
Using the above example, if new market price for Hassan’s bond is RM120. Hassan’s cash flows will be as follows:

14. Current yield (CY) = Annual coupon payment × 100
Initial investment
Year 1
Year 2
Year 3
Year 4 RM
120 5
105
New rate of return = × 100 = 4.17%
120
Current yield (CY) = Annual coupon payment × 100
Current market price of bond
Example
Fikri buys a four-year bond with a coupon rate of 7%. Calculate the yield when market price of the bond is:
RM90
RM100
RM115

15. Rate of return = × 100 = 7.78% 90
Rate of return = × 100 = 7%
100
Rate of return = × 100 = 6.09%
115
Conclusion
When market price of a bond is the same as its face value, then the rate of return is the bond’s coupon rate.
Bonds with a higher coupon payment yield higher return
Lower coupon payment bonds yield a lower rate.
When market price drops, bond has higher yield.
We can conclude that a bond’s current yield depends on the coupon rate as well as the market price.

16. Yield to Maturity Yield to maturity measures a bond’s total return
Yield takes into account the coupon payment (interest) as well as the changes in a bond’s market value over its life
Yield to maturity is the discount rate that makes the present value of the bond’s payment (interest and capital gain) equal to its current price ( NPV = 0)
Yield to maturity assumes that bond holders reinvest the bond’s periodic coupon payments at the same rate over time
Use trial and error method to estimate yield to maturity

17. YTM = A + [C/(C – D)](B – A)
Where
A = Lower discount rate
B = Higher discount rate
C = Net present value (NPV) of cash inflow of the lower discount rate
Example: Vantura Berhad’s bonds are selling for RM110. The bonds carry a coupon rate of 6% and mature in eight years. Calculate the yield to maturity of the bonds if interest is payable
a. On a yearly basis
b. On a semi-annual basis
There is no short-cut method to calculate the yield to maturity.

18. Yearly compounding: i. Try I = 4% Years Cash flow AF/DF @ 4%
Present value RM
-110 1
1 – 8 6
6.733
40.4 8
100
0.731
73.1
 NPV
3.5
ii. Try = 7%

19. YTM = 4% + [3.50/((3.50 – (15.97))](7% – 4%)
Years
Cash flow 7%
Present value RM
-110 1
1 – 8 6
5.971
35.83 8
100
0.582
58.2
 NPV
-15.97
YTM = 4% + [3.50/((3.50 – (15.97))](7% – 4%)
= 4.54%
YTM = A + [C/(C – D)](B – A)
Where
A = Lower discount rate
B = Higher discount rate
C = Net present value (NPV) of cash inflow of the lower discount rate

20. Semi-annual compounding
Period
Cash flow (RM)
2 %
Present value RM
(110) 1
(110.00)
1 – 16 3
13.578
40.73 16
100
0.728
72.80
NPV
3.53
YTM = 2% + [3.53/((3.53 – (40.28))](6% – 2%)
= 2.32%

21. Conclusion
Price Behaviour 4
When the market price of a bond is above its face value, the bond holders will have to accept a yield lower than the bond’s coupon rate.
When the market price drops below the principal value, the bondholders will expect a higher yield from the bond.
we can conclude that one of the factors that affects bond’s yield to maturity is the current market price of the bond.

22. CY Vs YTM They are equal if the bond sells at par.
If the bond sells at discount (premium), YTM is higher (lower) than the CY  Bond sells at discount (premium) will give capital gains (loss), thus generate higher (lower) return.
From previous example;
C = 6%, Price RM110: CY = 6/110 = 5.45%
YTM = 4.54%.
TRY C= 6%, Price = 90;
CY = 6/90 = 6.67% YTM = ??? (should be higher than CY)

23. ZERO COUPON BONDS Zero coupon bonds do not pay any interest
As time progresses, zero coupon bonds will increase in their value at a compound rate of return up to maturity date
At maturity date, the bonds will be worth more than their initial investment.
Example
Let us assume a ten-year zero coupon bond was purchased with a yield to maturity of 6%. What would be the approximate current value?
Bond price (BPc) = RM100 (PVIF 6%, 10 years )
= RM 100 × 0.508
= RM50.80

24. ZERO COUPON BONDS Example
The price of a zero coupon bond is RM75. The bond has eight years to maturity. Calculate the yield of the zero coupon bond.
Bond price (BPc) = 75 = RM100 (PVIF I, 8 years )
PVIF I, 8 = RM 75
RM 100
= 0.75

25. BOND PRICE BEHAVIOUR
When the required rate of return is equal to the coupon rate, a bond will sell at its par value.
When the required rate of return is more than the coupon rate, a bond will sell at a discount
When the required rate of return is less than the coupon rate, a bond will sell at a premium

26. CONVERTIBLE BONDS
Holders of convertible bonds can exchange their bonds for a specified number of shares during a given period
Convertible bonds carry lower interest rates than non-convertible bonds due to the benefits gained when common share prices go up
In times of rising share prices, the accrued value of convertible bonds will increase, enabling the bond holders to exercise their options to convert the bonds into common shares and subsequently sell them at a higher price in the capital market
Convertible bonds earn coupon interest even when shares sell at a lower price

27. Conversion Ratio Conversion ratio = Par value of bond Conversion price
The number of shares that a bond holder will receive when he converts his bond into common shares
Example: Zulhasan holds Abad Dinamik’s convertible bond which has a face value of RM100 and a conversion price of RM20. What is the conversion ratio?
Conversion ratio = RM100/RM20 = 5 shares

28. Conversion Price
Conversion price = Face value of a bond/Conversion ratio
Arina Juara’s convertible bond has a par value of RM100 with a conversion ratio of 25 shares. Calculate the conversion price.
Conversion price = RM100/25 shares = RM4 per share
Conversion Period is a period of time during which bond holders are allowed to exercise their option to convert their bonds into common shares

29. Conversion Value
Conversion value is the market value of the underlying shares that bond holders receive when their bonds are converted into common shares
Conversion value = Current market price per share × Conversion ratio
Example: Laser Berhad’s convertible bond of RM100 carries a conversion ratio of 20 shares. Determine its conversion value if the market price per share is RM5.50.
Conversion value = RM5.50 × 20 = RM110

30. Conversion Premium (Issuer’s View)
The difference between market value of convertible bond and conversion value
Two approaches are used to calculate conversion premium.
1.Current market price base (price of a convertible bond less the conversion value)
2. Face value base
Example: The current market price of Angkasa’s convertible bond is RM120. The company has set the conversion ratio as 15 shares. Currently, Angkasa’s share is selling at RM6. Calculate the conversion premium.
Conversion value = Conversion ratio × Market price of share
= 15 × RM6 = RM90
Conversion premium = 120 – 90 = RM30

31. Example
SB Dynamic has issued a convertible bond with a face value of RM100. The bond’s conversion value is RM82. What is the conversion premium?
Conversion premium = RM100 – RM82 = RM18

32. Conversion Premium (Investor’s View)
Example
The board of directors of Telemax has issued 800,000 units of convertible bond. The market price of the bond is RM105. The conversion ratio is 20 shares and the market price of a share is RM5.
Conversion value = Conversion ratio × Market price per share
= 25 shares × RM5
= RM125
Conversion premium = RM125 – RM105 = RM25 per share
Total premium = RM25 × 800,000 = RM20,000

33. MINIMUM VALUE OF BOND
The higher between the value of bonds as debt (IV) and the value of bonds as shares (Conversion value)

34. Callable bond When bond is called, investor may
Redeem and receive principal plus call penalty (if any)
Convert and received stocks valued at its current market value
Issuer will call bonds if investor choose to convert or when current market interest rate is lower than coupon.

35. BOND INVESTMENT STRATEGIES
Investors assess their bond investment strategies to maximize investment return
Some investors will buy bonds for interest income
some may hold them for capital gain
The type of strategies that investors adopt can help cushion their investments from interest rate fluctuations.
Diversification
Income Maximization

36. RISKS IN BOND
Interest rate risk : The risk that an investment's value will change due to a change in the absolute level of interest rates, in the spread between two rates, in the shape of the yield curve or in any other interest rate relationship. Such changes usually affect securities inversely and can be reduced by diversifying (investing in fixed-income securities with different durations) or hedging (e.g. through an interest rate swap)

37. Price volatility risk The risk that the holder of a bond is exposed to based on the potential for the volatility of the price.
 Liquidity risk : Liquidity risk is the risk that you will not be easily able to find a buyer for a bond you need to sell. A sign of liquidity, or lack of it, is the general level of trading activity: A bond that is traded frequently in a given trading day is considerably more liquid than one which only shows trading activity a few times a week.

38. Credit risk: The possibility that a bond issuer will default, by failing to repay principal and interest in a timely manner
Call risk: The cash flow risk resulting from the possibility that a callable bond will be redeemed before maturity. Callable bonds can be called by the company that issued them, meaning the bonds have to be redeemed by the bondholder, usually so that the issuer can issue new bonds at a lower interest rate. This forces the investor to reinvest the principal sooner than expected, usually at a lower interest rate