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- 1. Valuation of Bonds and Shares 1
- 2. Features of a Bond• Face Value• Interest Rate—fixed or floating• Maturity• Redemption value• Market Value 2
- 3. Bond with MaturityBond value = Present value of interest +Present value of maturity value: n INTt Bn B0 = ∑ + t =1 (1 + kd ) (1 + kd ) t n 3
- 4. 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.• A perpetual bond’s yield-to-maturity: n =∞ INT INT B0 = ∑ = t = (1 + k d ) t 1 kd 4
- 5. 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: n CFt B0 = ∑ t =1 (1 + k d ) t 5
- 6. Pure Discount BondsPure discount bond do not carry an explicitrate of interest. It provides for the payment of alump sum amount at a future date in exchangefor the current price of the bondValue of a pure discount bond = PV of the amounton maturity: Mn B0 = ( 1 +k d ) n 6
- 7. Bond Duration and Interest Rate SensitivityThe bond’s price sensitivity can be moreaccurately estimated by its duration.A bond’s duration is measured as the weightedaverage of times to each cash flow (interestpayment or repayment of principal).(1+y/y) – [{(1+y) + T (c-y)}]/ [c {(1+y)T - 1}+y] 7
- 8. VolatilityThe 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: Duration Volatility of a bond = (1 + YTM) 8
- 9. 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 9
- 10. 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: n PDIV1 Pn P0 = ∑ + t =1 (1 + k p ) (1 + k p ) n t 10
- 11. Valuation of Ordinary Shares• Single Period Valuation: – If the share price is expected to grow at g per cent, then P1: – We obtain a simple formula for the share valuation as follows: DIV1 P = 0 ke − g 11
- 12. Multi-period ValuationIf the final period is n, we can write thegeneral formula for share value asfollows: n DIVt Pn P0 = ∑ + t =1 (1 + ke ) (1 + ke ) t n 12
- 13. Multi-period Valuation• Growth in Dividends Growth = Retention ratio × Return on equity g = b × ROE – Normal Growth DIV P = 0 1 ke −g 13
- 14. Multi-period Valuation In the case of super normal growth for a particular period and normal growth for the remaining periodShare value = PV of dividends during finite super-normal growth period + PV of dividends during indefinite normal growth period 14
- 15. H - MODELIn this there is super normal in the beginningwhich linearly declines to a stable rate in aparticular time say 2H years.The value of the shares is as follows. 15
- 16. Price-Earnings (P/E) RatioP/E ratio is calculated as the price of ashare divided by earning per shareUsing PE ratio the price of the share canbe calculated as follows Price = PE ratio * EPS. 16

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