Chapter 3 (fm)
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Valuation of Bonds and Shares
Valuation of Bonds and Stocks The concept of risk and return are determinants of valuation of securities and physical assets. Finance manager needs to understand the variables which influence security prices, which is logical and necessary consequence of efficient capital markets.
Concepts of Value • Present Value is the most valid and true concept of value. • Book Value (BV): BV reflects historical cost rather than value. BV of a debt is the outstanding amount. BV of a share = Net worth divided by number of shares outstanding. • Replacement Value: Amount a company would be required to spend if it were to replace existing asset in the current condition. • Liquidation Value: The amount a company could realize if it sold its assets, after terminating its business. • Going Concern Value: The value a company could realize if it sold its business as an operating business. • Market Value (MV): It is the current value at which an asset or security is being sold or bought in the market. MV > BV for profitable & growing concerns. If capital markets are efficient and in equilibrium MV = Present Value of a Share.
Features of Bonds/Debentures A bond is a long – term debt instrument/security. Main features include: • Face Value/Par Value: A bond (debenture) is generally issued at a par value of Rs. 100 or Rs. 1000. Interest is paid on FV. • Interest Rates: Interest rates are known. Interest Rate is tax deductible. Coupons are detachable certificates of interest. • Maturity: A bond/debenture is issued for a specified time period. • Redemption Value: The value that a bondholders gets on maturity. A bond may be redeemed at par/premium/discount. • Market Value: The price at which it is bought/ sold is called MV.
Bond Values & Yields • PV of bonds is the expected cash flow, i.e. interest payments + repayment of principal. • The appropriate capitalization/discount rate depends upon risk of the bond. • The risk of government bond < PSU bonds < bonds issued by companies (debentures). • A lower discount rate is applied for lower risk.
(A) Bonds with Maturity • The principal of a bond with a maturity is payable after maturity period. • By comparing the present value of a bond with current market price, it can be determined whether the bond is overvalued or undervalued. • BV = PV of interest + PV of Maturity Value • Since interest payment are constant over the life of the bond, the annuity formula to value interest payments can be used.
Yield to Maturity (YTM): Internal rate of return or the measure of a bond’s rate of return that considers both interest income and any capital gain or loss.
YTM of 5 year bond, paying 6% rate of interest on FV Rs. 1000 and currently selling for Rs. 883.40 is 10% as shown below.
YTM = 10% by trial & error. A simple measure for YTM is
For the above example, YTM = 80/800 = 10%
• It is the Yield annual & interest Current Yielddivided to Callby
bond’s current value. For the above example, 60/883.40 = 6.8%. The current yield does not account for capital gain or loss. • Companies issue bonds with buy back or call provision. Thus a bond can be called or redeemed before maturity. The yield on such bonds is called yield to call, which is similar to yield to maturity. Suppose the 10%, 10 year, Rs. 1000 bond is redeemable in 5 years at a call price of Rs. 1050. The bond is currently selling at Rs. 950.
YTC = 12.7%
YTM= 11.3%
Bond Value and Amortization of • A Bond (debenture) may be amortized every year Principal
(the principal is repaid every year rather than at maturity). The cash flow is uneven. • CF is cash flow including both interest and principal.
CF is cash flow including both interest and principal.
B) Pure Discount Bonds • Also called Deep Discount Bonds/ Zero Interest Bonds / Zero Coupon Bonds. • It provides for payment of a lump sum amount at a future date in exchange for the current price of the bond. • The difference between the FV of bond and purchase price gives return or YTM to the investor. • For example, a company issues a deep – discount bond of Rs. 1000 FV at Rs. 520 today for a period of 5 years. • Purchase Price = Rs. 500 • Maturity Value = Rs. 1000 • Maturity Period = 5 Years • YTM = 14% (by trail & error) as shown:
IDBI issued deep – discount bonds of Rs. 5,00,000 FV in 1998 at a price of Rs. 12,750 to be redeemed after 30 years. Implicit interest rate would come out to 13%]
The PV of the amount on maturity is the bond value
(In case, current market yield on similar bonds is 9%).
(C) Perpetual Bonds/Consols • Bond which has indefinite life and thus no maturity value. • The bond is simply discounted value of the infinite stream of interest flows. • 10% Rs. 1000 bond will pay Rs. 100 annual interest in perpetuity.
If Market Yield is 10%, Bo = Rs. 1000 If Market Yield is 20%, Bo = Rs. 500 Market yield and value of Bond are inversely related.
Bond Maturity & Interest Rate Risk: There is an inverse relationship between interest rate & bond value. Investors of bonds are exposed to interest rate risks: The intensity of risk is bigger on bonds with long maturities than with short maturities as one can sell and re – invest the money in case of bonds with shorter maturities in case the interest rates are going up.
Yield Curve and Default Risk • Yield Curve shows the relationship between yields to maturity of bonds and debentures to their maturities. Yield Curve is upward sloping, implying long – term yields are higher than short term yields. • Default Risk and Credit Rating: Risk that a company will default on its promised obligation to bondholders is default risk. Govt. bonds entail lower risk.
Features of Preference Shares
• Claims: Preference shareholders have a claim on assets and income prior to ordinary shareholders. • Dividend: Dividend rate is fixed for Preference shareholders. Dividends paid on preference & equity shares are not tax deductible. • Redemption: Both redeemable & irredeemable preference shares can be issued in India. • Conversion: Convertible Preference shares can be issued which are converted to equity shares at a stated date.
Value of Preference Shares • Value of Preference Shares = • Present Value of Dividend + Present Value of Maturity Value • Po = Present value of Preference Shares; PDIVt is preference dividend in period t; Kp = Required Rate of Return on Preference shares; Pn = Maturity value of Preference share
Value of Irredeemable Preference Shares: Present value of irredeemable preference share with Rs. 100 as issued price, dividend of Rs. 9. Current Yield is 11%.
Yield on Preference Share • If price of Preference Share = Rs. 81.82 and Dividend of Rs. 9, what is the current yield/return to investors? • 81.82 = 9/ Kp • Kp = 0.11 or 11%
Valuation of Ordinary Shares • The valuation of equity shares is relatively more difficult due to two factors: 2. The rate of payment of dividend is unknown and payment of dividend is discretionary. Cash flow is uncertain. 3. Earnings & dividends on equity shares are expected to grow. Variable Dividend makes calculations difficult.
Dividend Capitalization: • Expected cash inflows consists of future dividends & value of ordinary shares is determined by capitalizing future dividends stream at opportunity cost of capital. (The return investors expect to earn from an investment of equivalent risk).
Single Period Valuation • Present value of a share (Po) is determined by PV of dividend per share at the end of first year, DIV1 + PV of expected price after 1 year, P1, Opportunity cost/Expected Rate of return, Ke
If DIV1 = 2, P1 = 21 & Ke = 15% Po = (2 + 21)/1.05 = Rs. 20 g = (P1 – Po)/ Po g is expected growth/capital gain. For the aforesaid example, g = (21 – 20)/20 = 5% Rearranging, P1 = Po(1 + g)
Multi – Period Valuation • When the investor in above example, sells shares to second investor, the new investor obtain stream of dividends and liquidation price of share in year 2. • For example, DIV2 = Rs. 2.10 P2 = 22.05 • • Po can be calculated by :
Thus, the general formula for a share is as follows:
If n approaches to infinity
GROWTH DIVIDENDS • The expected dividends in practice could increase, decrease or remain same. Due to retention policies the earnings and dividends of companies grows over time. • The retained earnings are reinvested in business which, if, number of shares does not change, will increase EPS and expand stream of DPS.
Normal Growth • If a totally equity financed firm retains a constant proportion of earnings (b) and reinvests it at internal rate return/return on equity (ROE) dividends with grow (g) at a rate • g = b × ROE
Normal Growth
Perpetual Growth Model
If Ke > g, DIV1 > 0 and Ke & g remain constant and perpetual.
Supernormal Growth In case, a company is experiencing high demand for its products dividends may grow at supernormal growth rate and subsequently at normal rate. Share Value = PV of dividends during supernormal growth period + PV of dividends during indefinite normal growth period
Earnings Capitalization • When a firm pay out 100% dividends and does not retain any earns. b = 0, g = rb = 0 • When a firm’s ROE = Ke as firm lacks real growth opportunities. r = Ke g = rb = Ke b • Thus, true growth depends on existence of growth opportunities for reinvestment of retained earnings at a rate higher capitalization, Ke thereby creating NPV over and above investment required.
Linkages between Share Price, Earnings & Dividends • When investor buy shares there are two considerations: - dividends and capital gains. • They may buy growth shares or income shares. • Growth shares offer greater opportunities for capital gains dividends yields are low as retention rate is high. • Income shares pay higher dividends but lower prospects for capital gains.
1. For example, if a company follows a b = 40%, r = 20% and g = 8%, EPS1 = Rs. 6.67, Ke = 12%. Po = Rs. 100
2. For example, if for the same company in case the b = 0, DIV = EPS Po = Rs. 55.58 = Rs. 55.58
Thus, the difference between Rs. 100 and Rs. 55.58 is the value growth opportunities. Retention of earnings adds value since it generates cash flow.
Price–Earnings Ratio (P/E Ratio) • Price of a share divided by EPS = P/E Ratio and its reciprocal is called earnings – price ratio or earnings yield (E/P). • Further, estimation of EPS may be meaningless because of measurement problem of EPS. • Earnings may include non – cash items like depreciation. • Thus it is difficult to interpret EPS meaningfully and rely on P/E ratio as a measure of performance.
Valuation of Bonds and Stocks The concept of risk and return are determinants of valuation of securities and physical assets. Finance manager needs to understand the variables which influence security prices, which is logical and necessary consequence of efficient capital markets.
Concepts of Value • Present Value is the most valid and true concept of value. • Book Value (BV): BV reflects historical cost rather than value. BV of a debt is the outstanding amount. BV of a share = Net worth divided by number of shares outstanding. • Replacement Value: Amount a company would be required to spend if it were to replace existing asset in the current condition. • Liquidation Value: The amount a company could realize if it sold its assets, after terminating its business. • Going Concern Value: The value a company could realize if it sold its business as an operating business. • Market Value (MV): It is the current value at which an asset or security is being sold or bought in the market. MV > BV for profitable & growing concerns. If capital markets are efficient and in equilibrium MV = Present Value of a Share.
Features of Bonds/Debentures A bond is a long – term debt instrument/security. Main features include: • Face Value/Par Value: A bond (debenture) is generally issued at a par value of Rs. 100 or Rs. 1000. Interest is paid on FV. • Interest Rates: Interest rates are known. Interest Rate is tax deductible. Coupons are detachable certificates of interest. • Maturity: A bond/debenture is issued for a specified time period. • Redemption Value: The value that a bondholders gets on maturity. A bond may be redeemed at par/premium/discount. • Market Value: The price at which it is bought/ sold is called MV.
Bond Values & Yields • PV of bonds is the expected cash flow, i.e. interest payments + repayment of principal. • The appropriate capitalization/discount rate depends upon risk of the bond. • The risk of government bond < PSU bonds < bonds issued by companies (debentures). • A lower discount rate is applied for lower risk.
(A) Bonds with Maturity • The principal of a bond with a maturity is payable after maturity period. • By comparing the present value of a bond with current market price, it can be determined whether the bond is overvalued or undervalued. • BV = PV of interest + PV of Maturity Value • Since interest payment are constant over the life of the bond, the annuity formula to value interest payments can be used.
Yield to Maturity (YTM): Internal rate of return or the measure of a bond’s rate of return that considers both interest income and any capital gain or loss.
YTM of 5 year bond, paying 6% rate of interest on FV Rs. 1000 and currently selling for Rs. 883.40 is 10% as shown below.
YTM = 10% by trial & error. A simple measure for YTM is
For the above example, YTM = 80/800 = 10%
• It is the Yield annual & interest Current Yielddivided to Callby
bond’s current value. For the above example, 60/883.40 = 6.8%. The current yield does not account for capital gain or loss. • Companies issue bonds with buy back or call provision. Thus a bond can be called or redeemed before maturity. The yield on such bonds is called yield to call, which is similar to yield to maturity. Suppose the 10%, 10 year, Rs. 1000 bond is redeemable in 5 years at a call price of Rs. 1050. The bond is currently selling at Rs. 950.
YTC = 12.7%
YTM= 11.3%
Bond Value and Amortization of • A Bond (debenture) may be amortized every year Principal
(the principal is repaid every year rather than at maturity). The cash flow is uneven. • CF is cash flow including both interest and principal.
CF is cash flow including both interest and principal.
B) Pure Discount Bonds • Also called Deep Discount Bonds/ Zero Interest Bonds / Zero Coupon Bonds. • It provides for payment of a lump sum amount at a future date in exchange for the current price of the bond. • The difference between the FV of bond and purchase price gives return or YTM to the investor. • For example, a company issues a deep – discount bond of Rs. 1000 FV at Rs. 520 today for a period of 5 years. • Purchase Price = Rs. 500 • Maturity Value = Rs. 1000 • Maturity Period = 5 Years • YTM = 14% (by trail & error) as shown:
IDBI issued deep – discount bonds of Rs. 5,00,000 FV in 1998 at a price of Rs. 12,750 to be redeemed after 30 years. Implicit interest rate would come out to 13%]
The PV of the amount on maturity is the bond value
(In case, current market yield on similar bonds is 9%).
(C) Perpetual Bonds/Consols • Bond which has indefinite life and thus no maturity value. • The bond is simply discounted value of the infinite stream of interest flows. • 10% Rs. 1000 bond will pay Rs. 100 annual interest in perpetuity.
If Market Yield is 10%, Bo = Rs. 1000 If Market Yield is 20%, Bo = Rs. 500 Market yield and value of Bond are inversely related.
Bond Maturity & Interest Rate Risk: There is an inverse relationship between interest rate & bond value. Investors of bonds are exposed to interest rate risks: The intensity of risk is bigger on bonds with long maturities than with short maturities as one can sell and re – invest the money in case of bonds with shorter maturities in case the interest rates are going up.
Yield Curve and Default Risk • Yield Curve shows the relationship between yields to maturity of bonds and debentures to their maturities. Yield Curve is upward sloping, implying long – term yields are higher than short term yields. • Default Risk and Credit Rating: Risk that a company will default on its promised obligation to bondholders is default risk. Govt. bonds entail lower risk.
Features of Preference Shares
• Claims: Preference shareholders have a claim on assets and income prior to ordinary shareholders. • Dividend: Dividend rate is fixed for Preference shareholders. Dividends paid on preference & equity shares are not tax deductible. • Redemption: Both redeemable & irredeemable preference shares can be issued in India. • Conversion: Convertible Preference shares can be issued which are converted to equity shares at a stated date.
Value of Preference Shares • Value of Preference Shares = • Present Value of Dividend + Present Value of Maturity Value • Po = Present value of Preference Shares; PDIVt is preference dividend in period t; Kp = Required Rate of Return on Preference shares; Pn = Maturity value of Preference share
Value of Irredeemable Preference Shares: Present value of irredeemable preference share with Rs. 100 as issued price, dividend of Rs. 9. Current Yield is 11%.
Yield on Preference Share • If price of Preference Share = Rs. 81.82 and Dividend of Rs. 9, what is the current yield/return to investors? • 81.82 = 9/ Kp • Kp = 0.11 or 11%
Valuation of Ordinary Shares • The valuation of equity shares is relatively more difficult due to two factors: 2. The rate of payment of dividend is unknown and payment of dividend is discretionary. Cash flow is uncertain. 3. Earnings & dividends on equity shares are expected to grow. Variable Dividend makes calculations difficult.
Dividend Capitalization: • Expected cash inflows consists of future dividends & value of ordinary shares is determined by capitalizing future dividends stream at opportunity cost of capital. (The return investors expect to earn from an investment of equivalent risk).
Single Period Valuation • Present value of a share (Po) is determined by PV of dividend per share at the end of first year, DIV1 + PV of expected price after 1 year, P1, Opportunity cost/Expected Rate of return, Ke
If DIV1 = 2, P1 = 21 & Ke = 15% Po = (2 + 21)/1.05 = Rs. 20 g = (P1 – Po)/ Po g is expected growth/capital gain. For the aforesaid example, g = (21 – 20)/20 = 5% Rearranging, P1 = Po(1 + g)
Multi – Period Valuation • When the investor in above example, sells shares to second investor, the new investor obtain stream of dividends and liquidation price of share in year 2. • For example, DIV2 = Rs. 2.10 P2 = 22.05 • • Po can be calculated by :
Thus, the general formula for a share is as follows:
If n approaches to infinity
GROWTH DIVIDENDS • The expected dividends in practice could increase, decrease or remain same. Due to retention policies the earnings and dividends of companies grows over time. • The retained earnings are reinvested in business which, if, number of shares does not change, will increase EPS and expand stream of DPS.
Normal Growth • If a totally equity financed firm retains a constant proportion of earnings (b) and reinvests it at internal rate return/return on equity (ROE) dividends with grow (g) at a rate • g = b × ROE
Normal Growth
Perpetual Growth Model
If Ke > g, DIV1 > 0 and Ke & g remain constant and perpetual.
Supernormal Growth In case, a company is experiencing high demand for its products dividends may grow at supernormal growth rate and subsequently at normal rate. Share Value = PV of dividends during supernormal growth period + PV of dividends during indefinite normal growth period
Earnings Capitalization • When a firm pay out 100% dividends and does not retain any earns. b = 0, g = rb = 0 • When a firm’s ROE = Ke as firm lacks real growth opportunities. r = Ke g = rb = Ke b • Thus, true growth depends on existence of growth opportunities for reinvestment of retained earnings at a rate higher capitalization, Ke thereby creating NPV over and above investment required.
Linkages between Share Price, Earnings & Dividends • When investor buy shares there are two considerations: - dividends and capital gains. • They may buy growth shares or income shares. • Growth shares offer greater opportunities for capital gains dividends yields are low as retention rate is high. • Income shares pay higher dividends but lower prospects for capital gains.
1. For example, if a company follows a b = 40%, r = 20% and g = 8%, EPS1 = Rs. 6.67, Ke = 12%. Po = Rs. 100
2. For example, if for the same company in case the b = 0, DIV = EPS Po = Rs. 55.58 = Rs. 55.58
Thus, the difference between Rs. 100 and Rs. 55.58 is the value growth opportunities. Retention of earnings adds value since it generates cash flow.
Price–Earnings Ratio (P/E Ratio) • Price of a share divided by EPS = P/E Ratio and its reciprocal is called earnings – price ratio or earnings yield (E/P). • Further, estimation of EPS may be meaningless because of measurement problem of EPS. • Earnings may include non – cash items like depreciation. • Thus it is difficult to interpret EPS meaningfully and rely on P/E ratio as a measure of performance.
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