ACC515 Topic 6

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Topic 6

Valuation of Bonds and shares

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Learning Objectives

• Explain why we need to understand valuation

• Give various definitions for the term ‘value’

• Explain the process of valuing an asset

• Understand how to value bonds, preference shares and ordinary shares

• Appreciate the concept of an investor’s expected rate of return and be able to compute the expected rate of return on bonds, preference shares and ordinary shares

• Understand the relationship between a company’s earnings and the value of its ordinary shares

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Definitions of value

• Book value

• Liquidation value

• Going-concern value

• Market value

• Intrinsic value

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Market efficiency and behavioural finance

• An efficient market is a market in which the value of all assets and securities at any instant in time fully reflect all available information

market value = intrinsic value

• Recall Topic 5

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Valuation: The process

Value is determined by three elements:

Amount and timing of the asset’s expected cash flows

Riskiness of these cash flows

The investor’s required rate of return

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Basic factors determining an asset’s value

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The basic valuation model

where Ct = The cash flow to be received in year t

R = The investor’s required rate of return

V = The intrinsic or present value of an asset

(10- 1)

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Bond valuation

• Bonds pay fixed coupon payments at fixed intervals and pay the par value at maturity

0 1 2 n

$I $I $I+$M

Simply discount the cash flows at the investor’s required rate of return.

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Bond valuation

where $I = The coupon interest payment in year t

$M = The maturity value

Rb = The investor’s required rate of return

Vb = The intrinsic or present value of the bond

(10-2)

(10-2a)

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Bond valuation

Example (annual coupon):

Suppose our firm decides to issue 20-year bonds with a

par value of $1,000 and annual coupon payments. The

return on other bonds of similar risk is 12%, so we decide

to offer a 12% coupon interest rate.

What would be a fair price for these bonds?

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Bond valuation

3 2 1 0 20 19 …

120

120

120

120

120 … 1000

PV ?

PV = PMT { [ 1 – ( 1 + i )-n ] / i } + FV / ( 1 + i )n

= 120 x [{ 1 – (1.12)-20 } / 0.12] + 1000 / 1.1220

= $1000.00

… or using tables:

PV = PMT x PVIFAi,n + FV x PVIFi,n

= 120 x PVIFA12%,20 + 1000 x PVIF12%,20

= 120 x 7.469 + 1000 x 0.104

= $1000.28

Share dividend

The periodic cash flows from an investment in shares are dividends.

Three possible scenarios for the dividend:

1. Constant Dividend (no growth / zero growth)

2. Growth in Dividend (constant growth)

3. Variable Dividend Growth

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Preference shares

• Are a form of equity

• Have no fixed maturity

• Investors are paid a fixed dividend

• Constant dividend = perpetuity

• Can be:

• cumulative/non-cumulative

• redeemable/irredeemable

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Preference share valuation

Example:

XYZ preference shares pay a $4.12 dividend per year. If

our required rate of return on XYZ preference shares is

9.5%, what would we consider a fair price for these shares?

Answer: Vp = D / Rp

= 4.12 / 0.095

= $43.37

Vp = Annual dividend (D)

Required rate of return (Rp) (10-5)

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Valuation of ordinary shares

• Variable-income securities

• Dividends depend on earnings

• Dividend amounts are not fixed

• Represent equity or ownership

• When valuing ordinary shares, the growth factor, g, is

used

g = ROE x r

where ROE = the return on equity

r = the percentage of company profits retained

(10-6)

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Single holding period VE = PV of dividend (D1)

+ PV of expected market price (P1)

VE = + D1

( 1 + RE )

P1

( 1 + RE )

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Example:

You expect XYZ shares to pay a $5.50 dividend at the end of the year. The share price is expected to be $120 at that time. If you require a 15% rate of return, what would you pay for the share now? Answer:

VE = $5.50 + $120 (1 + 0.15) (1+ 0.15)

= $109.13

0 1

?

5.50 120

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Multiple holding periods

Is this model practical?

(10-7)

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Constant growth model

Assumes ordinary dividends will grow at a constant rate into the future

D1 = the dividend at the end of year 1 RE = the required rate of return on ordinary shares g = the constant, annual dividend growth rate

(10-9) VE = D1 / (RE - g)

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Example:

XYZ shares recently paid a $5.00 dividend. The dividend is expected to grow at 10% per year indefinitely. What would we be willing to pay if our required rate of return on XYZ shares is 15%? Answer:

D1 = D0( 1 + g ) = $5.00 x 1.10 = $5.50 VE = D1 / ( RE – g ) = $5.50 / ( 0.15 – 0.10 ) = $110

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Expected rates of return

• The discount rate that equates the present value of the future cash flows with the current market price

• For bondholders:

• ERR = yield to maturity (YTM)

• For preference shareholders:

• ERR = dividend yield

• For ordinary shareholders:

• ERR = dividend yield + dividend growth rate

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Calculating expected rates of return

Example (for a preference shareholder):

If we know the preferred share price is $40, and the

preferred dividend is $4, what is the expected return?

Answer: Substituting in Equation 10-11

Rp = D/ P = $4 / $40 = 0.10 = 10%

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Example (for an ordinary shareholder):

We know a share will pay $3 dividend in one year’s time,

has a current price of $27, and an expected growth rate for

the future of 5%. What is the market’s implied rate of

return?

Answer: Substituting in Equation 10-9

RE = D1 / P + g

= $3 / $27 + 0.05

= 0.1611

= 16.11%

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Example (for a bondholder):

Suppose we paid $898.90 for a $1,000 par 10% coupon

bond with 8 years to maturity and semi-annual coupon

payments. What is our yield to maturity?

Answer: By trial and Error

i = 6% per 6 months

YTM = 2 x 6 = 12% p.a.

ACC515 Topic 6

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