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**Chapter Organisation 6.1 Bond Valuation 6.2 Common Stock Valuation**

Summary and Conclusions

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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.

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Bond Value

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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?

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

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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.

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**The Longer the Time to Maturity, the Greater the Interest Rate Risk**

Bond 1 Face Value = $ 1000 Coupon Interest = 10% Maturity = 5 years 12% = $ 927.9 14% = $ 862.6 There is 7% change in value of the bond as a result of 2% change in market interest rate Bond 2 Face Value = $ 1000 Coupon Interest = 10% Maturity = 10 years 12% = $886.9 14% = $791.3 There is 10% change in value of the bond as a result of 2% change in Market Interest Rate

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**The Lower the Coupon Rate, the Greater the Interest Rate Risk**

Bond 1 Face Value = $ 1000 Coupon Interest = 8% Maturity = 5 years 12% = $ 855.8 14% = $ 794 There is 7.5% change in value of the bond as a result of 2% change in market interest rate Bond 2 Face Value = $ 1000 Coupon Interest = 10% Maturity = 5 years 12% = $ 927.9 14% = $ 862.6 There is 7% change in value of the bond as a result of 2% change in market interest rate

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**Calculating Yield to Maturity (YTM)**

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. 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).

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**Bond Price Sensitivity to Interest Rates (YTM)**

$1 800 Coupon = $ 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%

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**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 $ YTM = 9%

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**Common Stock 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 are all future dividends. Dividend growth is an important aspect of share valuation.

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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.

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**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.

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**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?

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**Share Price Sensitivity to Dividend Growth, g**

2% 4% 6% 8% 10% 50 45 40 35 30 25 20 Share price ($) Dividend growth rate, g D1 = $1 Required return, R, = 12% 15 10 5

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**Share Price Sensitivity to Required Return, r**

6% 8% 10% 12% 14% 100 90 80 70 60 50 40 Share price ($) Required return, R D1 = $1 Dividend growth rate, g, = 5% 30 20 10

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**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 (D1/P0). The growth rate (g) can be interpreted as the capital gains yield, and is the rate at which the value of the investment grows.

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**Components of Required Return**

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**Summary and Conclusions**

Bonds are issued when an organization 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.

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