## VALUATION OF BONDS AND PREFERENCE SHARES

- VALUATION OF BONDS & SHARES
- Introduction
- A ssets can be real or financial; securities like shares and bonds are called financial assets while physical assets like plant and machinery are called real assets .

- The concepts of return and risk, as the determinants of value, are as fundamental and valid to the valuation of securities as to that of physical assets.
- Principle underlying valuation:
- Value of any asset is the discounted value of the future steams of benefit expected from the asset.

- Value - concept

- Liquidation Value
- Going Concern Value
- Book Value
- Replacement Value
- Market Value

- Features of a Bond
- Face Value

- Interest Rate—fixed or floating

- Maturity

- Redemption value

- Market Value

- Bonds Values and Yields
- Bonds with maturity

- Pure discount bonds

- Perpetual bonds

- Bond with Maturity
- Bond value = Present value of interest + Present value of maturity value:

- Yield to Maturity
- The yield-to-maturity ( YTM ) is the measure of a bond’s rate of return that considers both the interest income and any capital gain or loss. YTM is bond’s internal rate of return.

- YTM of a bond with maturity:

- A perpetual bond’s yield-to-maturity :

- Current Yield
- Current yield is the annual interest divided by the bond’s current/market value.

- Example: The annual interest is Rs 60 on the current investment of Rs 883.40. Therefore, the current rate of return or the current yield is: 60/883.40 = 6.8 per cent.

- Current yield does not account for the capital gain or loss .

- Yield to Call
- Yield to call is the return associated with the bonds with buy back or call provision when the call option is exercised before maturity.

- Example : Suppose the 10% 10-year Rs 1,000 bond is redeemable (callable) in 5 years at a call price of Rs 1,050. The bond is currently selling for Rs 950.The bond’s yield to call is 12.7%.

- Bond Value and Amortisation of Principal
- A bond (debenture) may be amortised every year, i.e., repayment of principal every year rather at maturity.

- The formula for determining the value of a bond or debenture that is amortised every year, can be written as follows:

- Note that cash flow, CF , includes both the interest and repayment of the principal .

- Pure Discount Bonds
- Pure discount bonds are called deep-discount bonds or zero-interest bonds or zero-coupon bonds.

- The market interest rate , also called the market yield , is used as the discount rate.

- Value of a pure discount bond = PV of the amount on maturity:

- Pure Discount Bonds
- Example: A company may issue a pure discount bond of Rs 1,000 face value for Rs 520 today for a period of five years. The rate of interest can be calculated as follows:

- Perpetual Bonds
- Perpetual bonds , also called consols , has an indefinite life and therefore, it has no maturity value. Perpetual bonds or debentures are rarely found in practice.

- Perpetual Bonds
- Suppose that a 10 per cent Rs 1,000 bond will pay Rs 100 annual interest into perpetuity. What would be its value of the bond if the market yield or interest rate were 15 per cent?

- The value of the bond is determined as follows :

- Bond Values and Changes in Interest Rates
- The value of the bond declines as the market interest rate (discount rate) increases .

- The value of a 10-year, 12 per cent Rs 1,000 bond for the market interest rates ranging from 0 per cent to 30 per cent .

- Bond Maturity and Interest Rate Risk
- The intensity of interest rate risk would be higher on bonds with long maturities than bonds with short maturities .

- The differential value response to interest rates changes between short and long-term bonds will always be true. Thus, two bonds of same quality (in terms of the risk of default) would have different exposure to interest rate risk .

- Bond Maturity and Interest Rate Risk
- Bond Duration
- In finance, the duration of a financial asset measures the sensitivity of the asset's price to interest rate movements. Duration is a measurement of how long, in years, it takes for the price of a bond to be repaid ( i.e. recovery of PV of cash flows ) by its internal cash flows. It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations. The units of duration are years, and duration is always between 0 years and the time to maturity of the bond, with duration equal to time to maturity if and only if the bond is a zero-coupon bond.

- Macaulay duration
- Macaulay duration , named for Frederick Macaulay who introduced the concept, is the weighted average maturity of a bond where the weights are the relative discounted cash flows in each period.

- Macaulay Duration (D) =

- Duration of Bonds
- Let us consider the 8.5 per cent rate bond of Rs 1,000 face value that has a current market value of Rs 954.74 and a YTM of 10 per cent, and the 11.5 per cent rate bond of Rs 1,000 face value has a current market value of Rs 1,044.57 and a yield to maturity of 10.6 per cent. Table shows the calculation of duration for the two bonds.

- Volatility
- The volatility or the interest rate sensitivity of a bond is given by its duration and YTM. A bond’s volatility, referred to as its modified duration , is given as follows:

- T he volatilities of the 8.5 per cent and 11.5 per cent bonds are as follows:

- If YTM increases by 1%, this will result in 3.87% decrease in the price of the 8.5% bond and a 3.69% decrease in the price of 11.5% bond.

- Valuation of Shares
- A company may issue two types of shares:

- ordinary shares and

- preference shares

- Features of Preference and Ordinary Shares

- Claims

- Dividend

- Redemption

- Conversion

- Valuation of Preference Shares
- The value of the preference share would be the sum of the present values of dividends and the redemption value.

- A formula similar to the valuation of bond can be used to value preference shares with a maturity period:

- Value of a Preference Share-Example
- Valuation of Ordinary Shares
- The valuation of ordinary or equity shares is relatively more difficult.

- The rate of dividend on equity shares is not known; also, the payment of equity dividend is discretionary .

- The earnings and dividends on equity shares are generally expected to grow, unlike the interest on bonds and preference dividend.

- Dividend Capitalisation
- The value of an ordinary share is determined by capitalising the future dividend stream at the opportunity cost of capital

- Single Period Valuation:

- If the share price is expected to grow at g per cent, then P 1 = P o (1 + g) &

- P o = (DIV 1 + P 1 )/(1 + k e )

- We obtain a simple formula for the share valuation as follows:

- Multi-period Valuation
- If the final period is n , we can write the general formula for share value as follows:

- Growth in Dividends

- Normal Growth

- Super-normal Growth

- Earnings Capitalisation
- Under two cases, the value of the share can be determined by capitalising the expected earnings:

- When the firm pays out 100 per cent dividends; that is, it does not retain any earnings.

- When the firm’s return on equity (ROE) is equal to its opportunity cost of capital.

- Equity Capitalisation Rate
- For firms for which dividends are expected to grow at a constant rate indefinitely and the current market price is given

- Caution in Using Constant-Growth Formula
- Estimation errors

- Unsustainable high current growth

- Errors in forecasting dividends

- Valuing Growth Opportunities
- The value of a growth opportunity is given as follows:

- Price-Earnings (P/E) Ratio: How Significant?
- P/E ratio is calculated as the price of a share divided by earning per share.

- Some people use P/E multiplier to value the shares of companies.

- Alternatively, you could find the share value by dividing EPS by E/P ratio, which is the reciprocal of P/E ratio.

- Price-Earnings (P/E) Ratio: How Significant?
- The share price is also given by the following formula:

- The earnings price ratio can be derived as follows:

- Price-Earnings (P/E) Ratio: How Significant?
- Cautions:

- E/P ratio will be equal to the capitalisation rate only if the value of growth opportunities is zero.

- A high P/E ratio is considered good but it could be high not because the share price is high but because the earnings per share are quite low.

- The interpretation of P/E ratio becomes meaningless because of the measurement problems of EPS.