Chapter Six Valuing Shares and Bonds 6 1

Chapter Six Valuing Shares and Bonds 6 -1

Chapter Objectives • Outline the features of bonds. • Calculate the value (price) of a bond assuming annual and semi-annual coupons. • Understand the implications of interest rate risk for the value of a bond. • Calculate the value of an ordinary share under different dividend growth scenarios. • Explain the components of required return. 6 -2

Debt Securities • Debt securities are issued when an organisation wishes to borrow money from the public on a long-term basis. • Bonds are issued by the government. • Debentures are secured and issued by a corporation. • Notes are unsecured debt securities issued by a corporation. • More recently, these are all known as bonds. 6 -3

Types of Bond The 4 Primary Types of Bonds • Government Bonds (Treasuries) • Agency Bonds (Agencies) • Municipal Bonds (Munis) • Corporate Bonds (Corporates) 6 -4

Types of Bond Government Bonds (Treasuries) Ø It is the debt securities that issued and backed by the center government. Ø The safest investments in the world. Ø 4 distinct categories such as treasury bills (maturing in less than one year) , treasury notes (maturing in one to 10 years), Treasury Bonds (maturing in 10 to 30 years), Treasury Inflation Protected Securities (maturities of 5, 10, and 30 years). 6 -5

Types of Bond Agency Bonds (Agencies) Ø Debt securities that issued by institutions that were originally created by the Government. Ø Pay regular fixed-interest payments until maturity and have terms of two or more years. Ø Discount notes have maturities of less than one year. 6 -6

Types of Bond Municipal Bonds (Munis) Ø Local governments often borrow money by issuing bonds, similar to the center Government, but on a smaller scale. Ø Free from center, state and local government income taxes. Ø Two main types of municipal bonds, general obligation bonds and revenue bonds. Ø Most municipal bonds mature from 1 to 30 years. 6 -7

Types of Bond Corporate Bonds (Corporates) Ø Debt securities that issued by the corporations to raise money for investment. Ø A short-term corporate bond is less than 5 years; intermediate is 5 to 12 years, and long term is over 12 years. 6 -8

Bond Features • Coupon payments are the stated interest payments. Payment is constant and payable every year or half-year. • Face value (par value) is the principal amount repayable at the end of the term. • Coupon rate is the annual coupon divided by the face value of a bond. • Maturity is the specified date at which the principal amount is payable. 6 -9

Bond Yields • When interest rates rise, the present value of the bond’s remaining cash flows declines, and the bond is worth less. When interest rates fall, the bond is worth more. • An inverse relationship exists between market interest rates and bond price. • The inverse relationship between interest rates and values is one of the fundamental concepts of finance theory. It is applicable to any cash flow that is being valued today. 6 -10

Bond Yields • Yield to maturity (YTM) is the market interest rate that equates a bond’s present value of interest payments and principal repayment with its price. • Given the yield to maturity or ‘yield’, we can calculate the present value of the cash flows as an estimate of the bond’s current market value. • There is an inverse relationship between market interest rates and bond price. 6 -11

Bond Price Sensitivity to Interest Rates (YTM) Bond price $1 800 Coupon = $100 20 years to maturity $1000 face value $1 600 Key Insight: Bond prices and YTMs are inversely related. $1 400 $1 200 $1 000 $ 800 $ 600 Yield to maturity, YTM 4% 6% 8% 10% 12% 14% 16% 6 -12

Bond Value 6 -13

Example 1—Bond Value • A bond with a face value of $1000 and a coupon rate of 6 per cent has 10 years to maturity. What is the market price of this bond if the market interest rate is 12 per cent? 6 -14

Example 2—Bond Value • Assume now that the bond’s coupons are paid half-yearly. 6 -15

Bond Values • If the market interest rate is the same as the coupon rate, the bond’s value is the same as the face value. • If the market interest rate rises above the coupon rate, the bond’s value falls below the face value. The bond is then said to be a discount bond. • If the market interest rate falls below the coupon rate, the bond’s value rises above the face value. The bond is then said to be a premium bond. 6 -16

Interest Rate Risk • Interest rate risk is the risk that arises for bond holders from changes in interest rates. • How much interest rate risk a bond has depends on how sensitive its price is to interest rate changes. This depends on two things: – All other things being equal, the longer the time to maturity, the greater the interest rate risk. – All other things being equal, the lower the coupon rate, the greater the interest rate risk. 6 -17

Interest Rate Risk and Time to Maturity Interest rate 5% 10 1 year 30 years $1 047. 62$1 768. 62 1 000. 00 15 956. 52 671. 70 20 916. 67 502. 11 6 -18

Calculating Yield to Maturity (YTM) • Yield to maturity (YTM) is the rate implied by the current bond price. • Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity. • If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign). 6 -19

Example―Calculating YTM • Consider a bond with a 8 per cent annual coupon rate, 10 years to maturity and a par value of $1000. The current price is $935. 82. – Will the yield be more or less than 8 per cent? Enter: 10 N Solve for → I/Y 9. 00 -935. 82 1 000 PV FV 80 PMT YTM = 9% 6 -20

Bond Price Reporting • Each working day an estimated $7– 8 billion of securities is traded in Australian money and fixed interest markets. • Information on notes, bonds, and debentures issued by large companies and government bodies are reported in newspapers (e. g. Australian Financial Review) and by financial agencies (e. g. Bloomberg). • A typical reporting system lists the issuer, the coupon, maturity date, quantity in millions, the YTM bid and offer, and the last traded yield. 6 -21

Ordinary Share Valuation • Share valuation is more difficult than debenture valuation for a number of reasons: – uncertainty of promised cash flows – shares have no maturity – observing the market rate of return is not easy. • However, there are cases in which the present value of future cash flows for a share can be derived and thus the share’s value determined. 6 -22

Ordinary Share Valuation • The market value of a share is the present value of all expected net cash flows to be received from the share, discounted at a rate of return that reflects the riskiness of those cash flows. • The expected net cash flows to be received from a share all future dividends. • Dividend growth is an important aspect of share valuation. 6 -23

Zero Growth Dividend • Shares have a constant dividend into perpetuity, with no growth in dividends. • A share in a company with a constant dividend is much like a preference share. • The value of a share is then the same as the value of an ordinary perpetuity. 6 -24

Example: • If ARAMCO is expected to pay cash dividends of $8 per share and ARAMCO has a 10% required rate of return, what is the value of the stock? P 0 = D/r = 8/0. 10 = $80 Here D = $8 and r = 10% = 0. 10 Copyright 2007 Mc. Graw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4 e, by Ross, Thompson, Christensen, Westerfield & Jordan 6 -25

Constant Growth Dividend • Dividends grow at a constant rate each time period. Therefore we have a growing perpetuity. • The constant dividend growth model determines the current price of a share as its dividend next period divided by the discount rate less the dividend growth rate. 6 -26

Example—Constant Growth Dividend Company ABC has just paid a dividend of 30 cents per share, which is expected to grow at 3 per cent per annum. What price should you pay for the share if the required rate of return on the investment is 12 per cent? 6 -27

Non-constant Growth Dividend • The growth rate cannot exceed the required rate of return indefinitely but can do so for a number of years. • Allows for ‘super normal’ or ‘erratic’ growth rates over some finite length of time. • The dividends have to grow at a constant rate at some point in the future. 6 -28

Example—Non-constant Growth Dividend • A company has just paid a dividend of 30 cents per share and that dividend is expected to grow at a rate of 10 per cent per annum for the next three years, and at a rate of 3 per cent per annum forever after that. • Assuming a required rate of return of 14 per cent, calculate the current market price of the share. 6 -29

Solution—Non-constant Growth Dividend 6 -30

Solution—Non-constant Growth Dividend (continued) 6 -31

Solution—Non-constant Growth Dividend (continued) 6 -32

Share Price Sensitivity to Dividend Growth, g Share price ($) 50 45 D 1 = $1 Required return, R, = 12% 40 35 30 25 20 15 10 5 0 2% 4% 6% 8% 10% Dividend growth rate, g 6 -33

Share Price Sensitivity to Required Return, r Share price ($) 100 90 80 D 1 = $1 Dividend growth rate, g, = 5% 70 60 50 40 30 20 10 Required return, R 6% 8% 10% 12% 14% 6 -34

Components of the Required Return • The total return, r, has two components: – Dividend yield – Capital gains yield • The dividend yield is a share’s cash dividend divided by its current price (D 1/P 0). • The growth rate (g) can be interpreted as the capital gains yield, and is the rate at which the value of the investment grows. 6 -35

Components of Required Return 6 -36

Summary and Conclusions • Bonds are issued when an organisation wishes to borrow money from the public on a long-term basis. • An inverse relationship exists between market interest rates and bond price. • The market value of a share is the present value of all expected net cash flows to be received from the share, discounted at a rate of return that reflects the risk of those cash flows. • Dividend growth is an important aspect of share valuation. 6 -37