-
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15
VALUATION OF DEBT AND
EQUITY
Introduction
Debt Valuation
- Par Value
- Long Term versus Short Term
- Zero Coupon Bonds
- Yield to Maturity
- Investment Strategies
Equity Valuation
- Growth Stocks
- P/E Ratios
Issuers of Debt or Equity
People as Gamblers
Summary
Introduction
‘Buy low, sell high’ is what all investors in shares and bonds aim to do. The key
question is when are shares or bonds high or low in their value? Placing a value on
an investment can be looked at as a two step procedure. The first step is to evaluate
the present value of the cash flows of the investment. The second step is to adjust
this value for the riskiness of these projected flows. In this chapter we will cover
the first step in the valuation process - that of placing value on investments based on
expected cash flows. The second step of adjusting for risk will be covered in the
next chapter. For the sake of this chapter, it is assumed that all projected cash flows
are 100% certain to occur.
Companies finance their holding of assets by using either debt or equity. Debt can
take many forms including bonds, debentures, zero coupon bonds, some types of
preferred shares and convertible debentures. These are just a few examples. The
basic building block of debt is an agreement between lender and borrower of a
presently specified cash flow over a future period of time. The specific terms of the
contract are designed to meet the unique needs of both the lender and the borrower.
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Financial Management and Decision Making
Equity, on the other hand, makes no promises about the amount of cash flowing
from the company to the investor in the future. Equity simply gives the holder a
‘piece of the action’ in the company. Sometimes equity carries restrictions on
voting rights or transferability. The basic understanding of equity holders is that
they will reap the rewards of the actions of the company. Most equity holders
owning common shares in a company also benefit by having limited liability in the
company’s activities. If the company is liquidated, most common equity holders
only stand to lose at most the value of their equity.
In this chapter the valuation of debt and equity from the point of view of the
investor will be examined first. Since the role of the financial manager is to
maximise shareholders’ wealth, the second aspect to be examined will be how
(indeed ‘if’) the financial manager can increase the value of the firm through
various capital raising instruments. In this way it will be possible to compare the
differences in viewpoint between investing and the issuing of debt and equity.
Debt Valuation
A debt agreement is a contract between the lender and the borrower. This contract
can include items such as the amount of money to be repaid at a specific date in the
future, the amount and timing of the payments to be made to the lender in the
interim, whether or not the debt can be recalled and at what costs, whether or not
the debt can be turned into equity, and any other contractual agreement to which the
lender and borrower agree. Once the terms of the debt agreement are understood,
determining the value of debt is a straightforward present value calculation. Most
debt issues, called bonds, have the following components:
1. Maturity, or the date in the future when the debt agreement concludes.
2. Face Value, sometimes called Par Value, or the amount of money for which the
bond will be redeemed at maturity. The most common face value is $1,000.
3. Coupon Rate, or a percentage of the face value which is paid to the debt holder
on a regular (annual, semi-annual) basis through to maturity.
A present value calculation can be made when these features of a bond are known.
Remember that the market value of an asset is determined by expressing the flows
of money through time in terms of present value. Since the amount and timing of
the future cash flows are specified in the bond agreement, calculating the present
value of the bond now becomes straightforward. Given periodic specified cash
flows into the future, the present value of these flows is determined by taking the
present value of these flows using a discount rate which is the presently prevailing
interest rates.
PV (of a bond) = PV of all future cash flows
Example
1. What is the value of a bond with a $1,000 face value, 8% annual coupon rate
having 7 years to the maturity date if prevailing interest rates are 10%?
A time line of the flows of this arrangement shows what needs to be done to
arrive at the present value of the bond.
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Chapter 15: Valuation of Debt and Equity
Year
Cash Flow
Coupon Payment
Face Value
293
1
2
3
4
5
6
7
80
80
80
80
80
80
80
1,000
The present value is:
PV = $80 x Annuity Factor10% over 7 years
+ $1,000 x Discount Factor10% over 7 years
= $80 x 4.8684 + $1,000 x .5132
= $389.47 + $513.20
= $902.67
This means that if you agreed to receive $80 per year over the next 7 years as
well as $1,000 at the end of the seventh year, you would be willing to pay
$902.67 in today’s dollars for that cash flow given that interest rates are 10%.
2. What would this bond be worth if prevailing interest rates were only 5%?
PV = $80 x Annuity Factor 5% over 7 years
+ $1,000 x Discount Factor 5% over 7 years
= $80 x 5.7864 + $1,000 x .7107
= $1,173.61
It is important to note that the value of the bond is inversely related to the level of
prevailing interest rates. This relationship is not intuitively clear but when interest
rates fall, the value of a bond goes up since the present value of the future cash
flows is discounted by a lower percentage. There are, therefore, two sorts of
income that the holder of a bond (the lender) can realise. The first and most
obvious income arises from the coupon payment and the final maturity payment.
The second source of income is capital gain (or loss) if the prevailing interest rates
fall (or rise) and the bond is sold prior to its maturity date.
Par Value
Issuers of bonds often try to set the coupon rate exactly equal to the prevailing
interest rates. What is the value of the bond in the previous example if the
prevailing interest rate is 8%?
PV = $80 x 5.2064 + $1,000 x .5835
= $1,000
In other words, when the coupon rate is equal to the prevailing interest rate the
value of the bond is its face value. While companies may wish to sell their bonds at
par, it is difficult to go through all of the printing and underwriting procedures prior
to the issuing of the bonds and estimate exactly the level of prevailing rates on the
date of issue. It is worth pointing out that bond issues are typically in the
millions($) while interest rates are measured in basis points with 100 basis points
equalling 1%. Therefore, a 1 basis point movement in interest rates can have a
significant effect on the value of the bond issue.
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Financial Management and Decision Making
Long Term
versus Short
Term
In the above example the value of the bond increased 30% from $902.67 to
$1,173.61 (or $270.94) as interest rates decreased from 10% to 5%. However,
what additional effect will the time to maturity have on the value of the bond? For
example, given a bond with an 8% coupon rate, $1,000 face value, and 20 years to
maturity, how much will it change in value as interest rates move from 10% to 5%?
at 10%, PV = $80 x 8.5136 + $1,000 x .1486
= $829.69
at 5%,
PV = $80 x 12.4622 + $1,000 x .3769
= $1,373.88
The 5% drop in interest rates resulted in a 65.6% ($544.19) increase in value of the
longer term bond. In the earlier example of a 7 year bond, the same change in
interest rates resulted in a 30.02% increase in value. Longer term bonds are more
volatile than shorter term bonds when there is a change in interest rates.
As an investor in bonds anticipates an impending decline in interest rates, bonds
with longer maturities will gain more value than the shorter maturities. At the same
time, longer term bonds will also result in more of a loss if interest rates rise.
Zero Coupon
Bonds
In order to take advantage of differing tax treatment on interest income and in order
to gain more leverage on moving interest rates the zero coupon bond has emerged.
It is simply a bond with a 0% coupon rate.
Example
What is the change in value of a zero coupon bond of 20 years with a $1,000 face
value as interest rates drop from 10% to 5%.
at 10%, PV =
=
at 5%, PV =
=
$1,000 x Discount Factor 10% over 20 years
$148.60
$1,000 x Discount Factor 5% over 20 years
$376.90
This change of $228.30 represents a 153.6% increase over the original amount
invested. This is more than double the volatility of the previous example of a 20
year bond with an 8% coupon rate.
Realisation of interest expenses and income for taxation purposes varies by country
and by the entity involved. It is common to realise interest income (expense) in
each taxation period even if no money changes hands. This means that the issuers
of the debt can realise tax deductible interest expense without needing to pay out
any actual cash. Tax exempt holders of these bonds, or holders in countries whose
tax treatment does not require tax to be paid until money changes hands, will not
have to pay tax on this non cash flow until money actually does change hands.
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Chapter 15: Valuation of Debt and Equity
295
Zero coupon bonds are suitable for the investor seeking extreme leverage on
changing interest rates given that the tax implications of non cash realisable income
are acceptable. Issuers of zero coupon bonds take the advantage of the non cash
interest expense, but receive less up front money on the issue.
Yield to
Maturity
Given the current price (present value) of a bond, its coupon rate, and its face value,
it is possible to determine the discount rate that must be used on the future cash
flows so that the present value of the future cash flows is exactly equal to the price
of the bond. This discount rate is known as the bond’s yield to maturity,
sometimes called the internal rate of return, and is found using an iterative process
using varying discount rates. A discount rate is chosen to see how close the present
value of the future cash flows comes to the bond’s current price. If the calculated
value is higher (lower) than the current price, a higher (lower) discount rate is
selected and the process repeated until the present value of the future cash flows
equals the current price.
Example
What is the yield to maturity of a $1,000 face value bond having a 5% annual
coupon rate maturing in 10 years whose price is $860?
$860 = $50 x Annuity Factor y% over 10 years
+ $1,000 x Discount Factor y% over 10 years
where y is the yield to maturity.
If y of 8% is used, the right side of the equation is
$50 x 6.7101 + $1,000 x .4632 = $798.71
which is less than the price of $860. To increase the right side of the equation, a
lower interest rate must be tried. Using y of 6% gives
$50 x 7.3601 + $1,000 x .5584 = $926.41
which is higher than the price of $860. The yield to maturity must be higher than
6% and trying 7% gives
$50 x 7.0236 + $1,000 x .5083 = $859.48
Therefore, the yield to maturity of the bond is very close to 7%.
Extrapolation, as described in the Capital Investment chapter, can be used to better
estimate the exact discount rate but where large sums of money are involved
extrapolation should be avoided. A computer should be used to calculate the yield
to an acceptable degree of accuracy.
Investment
Strategies
When making a decision to invest, a further understanding of the needs and desires
of the investor is necessary. If the money invested is needed at a specific point of
time in the future, then investment in bonds is essentially a trading in maturity dates
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Financial Management and Decision Making
and coupon rates in anticipation of changes in interest rates. It has been shown that
bonds with lower coupon rates or with longer maturity dates change their present
value more with a change in interest rates, than do bonds with higher coupon rates
or shorter maturities. If bonds are bought and held to maturity - not traded, or
traded only for other bonds with the same maturity date - then the yield to maturity
is fixed at the time of purchase regardless of the intervening changes in interest
rates.
Consider the initial example of a bond which cost $902.67 when interest rates were
10% and which increased in value to $1,173.61 when interest rates dropped to 5%.
What benefit is there to realising this gain of $270.94 if it is to then be reinvested
into a bond with the same coupon rate and maturity date? It will cost exactly
$270.94 more to buy this bond with the newly prevailing interest rates. Anticipation
of changes in interest rates will cause bond investors to alter their average maturity
dates. If a rise in rates is anticipated, the maturity dates will be shortened. If a
decline in interest rates is anticipated, the average maturity date will be lengthened.
(Transaction costs in the form of commissions to brokers must also be considered.
With higher transaction costs, the amount of movement in prevailing interest rates
must be higher before capital gains profits can be made).
Equity Valuation
The ownership of shares in a company entitles the owner to the dividend payments
and other benefits the company directors might recommend, as well as giving the
shareholders the right to sell the shares sometime in the future. It should be noted
again that all cash flows discussed here are considered risk free. The value of a
share is thus the present value of the future cash flows resulting from owning the
share. Given that:
P0
Pt
Dt
r
g
=
=
=
=
=
price of share in time period 0 (PV)
price of share at end of year t
dividend to be given at the end of year t
the required rate of return on the share
the expected growth rate of the share (also of earnings and
dividends),
then if the share is to be held for one year:
P0 =
D1 + P1
(1 + r)
P1 =
D 2 + P2
D 3 + P3
etc
; P2 =
(1 + r)
(1 + r)
But
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Chapter 15: Valuation of Debt and Equity
297
Therefore, substituting for P1 and P2 etc:
P0 =
D1
(1 + r)
1
+
D2
(1 + r)
2
+
D3
(1 + r)
3
+ . . .
Dn
(1 + r) n
+ . . .
If D1 = D2 = .... = Dn and if n approaches infinity, it has already been shown that
this is the formula for a perpetuity whose value can be written as:
P0 =
D1
r
If the dividend is growing at rate g where g is less than r, then this is a growing
perpetuity with the value:
P0 =
D1
r− g
While it may seem strange to assume that the company will continue to pay out a
dividend forever, it is not an unreasonable assumption since the present value of
dividends paid out only 50 years hence at a required rate of return of 20% has a
present value of only .0001 times the future amount of the dividend. Thus, future
dividend payments have less and less impact on the present value price.
However, the value of the share is independent of future values of the share and is
only dependent upon the dividend amount, the dividend growth rate and the
required rate of return. What does this imply about the capital gain in the value of
the share? It implies that any capital gain can always be defined in terms of future
dividend income and subsequent growth.
Examples
1. XYZ Company is expecting to pay out a dividend of $2.50 per share at the end
of the year. XYZ is of the opinion that $2.50 is a reasonable dividend payout
and does not plan on increasing that amount ever even if earnings rise. If your
required rate of return for investing in XYZ is 18%, how much would you be
willing to pay for one share of XYZ?
2.50
.18
= $13.89
P0 =
2. New directors of XYZ change the payout policy and announce that they would
allow the dividends to grow at 9% per year. Their announcement convinces you
that they can sustain this growth rate well into the future. What would you now
be willing to pay for one share of XYZ?
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Financial Management and Decision Making
2.50
(.18− .09)
= $27.78
P0 =
This illustrates the fact that the amount of the dividend has a large effect on the
price of the share - as dividend prospects go, so goes the price of the share. Some
firms pay out a fixed percentage of earnings as a dividend in which case the price of
the share is affected directly by earnings of the company. It is also interesting to
note that companies with high growth rates are more price sensitive to changes in
the required rate of return, r, than low growth companies.
Example
1. If r increases from 10% to 11%:
(a) in a company with a 2% growth rate and an expected dividend of $5.00, the
share value decreases by 11%.
5.00
(.10− .02)
= $62.50
P0 =
compared with
5.00
(.11− .02)
= $55.56
P0 =
(b) in a company with an 8% growth rate and an expected dividend of $5.00,
the share value decreases by 33%.
5.00
(.10− .08)
= $250.00
P0 =
compared with
5.00
(.11− .08)
= $166.67
P0 =
2. Compare the effect of a 1% reduction in the expected rate of return on a share
with a 9% growth rate, to the effect of the same reduction on a share with a 3%
growth rate. If the required rate of return drops 1% from 18% to 17% then:
2.50
(.18− .09)
= $27.78 as earlier
P0 =
2.50
(.17 − .09)
= $31.25
P0 =
compared with
This is $3.47, or 12.5% higher than before the reduction in the required rate of
return.
If the growth rate is only 3% then before the change in the required rate of
return:
2.50
(.18− .03)
= $16.67
P0 =
compared with
2.50
(.17 − .03)
= $17.86
P0 =
his change of $1.19 is only a 7% change in the price of the share.
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Chapter 15: Valuation of Debt and Equity
299
Therefore, it has been shown that the value of the share will change as the amount
of dividends, the prevailing discount rate, and the growth rate of the dividends
change. While each of these three will result in a change in share price value, it is
not at all uncommon for all three of these valuation parameters to change together making the valuation process more difficult.
Growth
Stocks
There are some share values that grow at very fast rates. In many cases g is
significantly higher than r for any reasonable level of expected return. This does
not mean that these stocks have infinite value. Firstly, it is impossible for any share
to grow at a high compound rate for a long period of time since the value of the
company will eventually exceed the value of the total economy in which the
company finds itself. Secondly, there is a limit to the total amount of available
equity investment in the economy. These two finite quantities, amount of available
assets and amount of available equity, create upper limits to the size a firm can
achieve. While it is true that firms can and do grow at rates of 50% per year for
eight or ten years, this growth simply must come back to realistic levels - less than r
- over a reasonable period of time. To calculate the value of these shares, it is
necessary to estimate the length of time that significant growth will continue before
settling down to sustainable levels.
Example
ABC’s earnings are currently $100 per share with a 20% payout ratio. It is
anticipated that ABC will grow at 20% per year for the next three years and then
continue to grow at 12% well into the future. If your expected rate of return for
ABC is 25%, what is the value of one share of ABC?
First calculate the cash flows:
Year
0
1
2
3
4
Earnings
Dividends
-
$120.00
$24.00
$144.00
$28.80
$172.80
$34.56
$193.536
$38.707
Therefore:
P0 =
24.00
(125
. )1
+
28.80
(125
. )2
+
34.56
(125
. )3
 38.707
1 
+ 
×

(125
. )3 
(.25− .12)
. )3 ]
= 19.2 + 18.432 + 17.695 + [297.746 / (125
= $207.77 per share
where the far right hand term of the above equation is the present value of a
growing perpetuity which begins in the fourth year.
The important principle which must be remembered is that the value of any share is
exactly equal to the present value of the expected stream of future cash flows. If
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Financial Management and Decision Making
this stream of cash flows is expected to vary, the computations required may
become more complex, but the principle remains unchanged.
P/E Ratios
The P/E ratio, or the ratio of price to earnings, is a measure of how many times
current earnings the shareholders are willing to pay to buy one share of the
company. It is possible to compare P/E ratios for different companies. Average
P/E ratios have varied from a low of around 6 to a high of around 20. If average
P/E ratios in the market are around 15, a share with a P/E ratio of 5 is relatively
inexpensive while one with a P/E of 70 is relatively expensive. However, P/E ratios
should not be used as a guide to a correct price, rather they can give clues as to
relative values of firms in the same industry.
The riskiness of the firm cannot be divorced from the company’s share price - try
though we may. High P/E shares are perceived by shareholders to be less risky
and(or) have greater future potential than low P/E shares since shareholders are
willing to pay more for the expected future cash flows, thus implying confidence in
the underlying strength of the company and in those future cash flows occurring. As
the shareholders feel less sure of future cash flows, they are willing to pay less, thus
lowering the P/E.
Example
You are considering selling your holding in a privately held financial services
company. The problem is that your partners do not know how to put a ‘fair’ value
on the shares in the company. It is known that current earnings per share are
$10,000 per year. From the share market it is observed that people who are buying
and selling equity in companies in the same business have P/E ratios ranging from
12 to 16. What could be considered a ‘fair’range for the value of a share?
If the P/E is 12, the price per share would be:
12 x $10,000, or $120,000
If the P/E is 16, the price would be $160,000.
Therefore, a starting point for discussion between the partners would be a price per
share of $120,000 to $160,000.
P/E ratios cannot provide concrete values of companies, but they can act as guides
to relative values when comparing prices of similar shares.
Issuers of Debt or Equity
An underlying principle followed by financial managers when financing the assets
of their firms is one of financial matching. This principle holds that the money
raised for assets should match in length of time the purpose for which it will be
used. For example, a piece of equipment expected to last for ten years could be
financed with a ten year bond. An annual need for two month money could be
financed with a short term loan from the bank. A permanent investment in fixed
assets or working capital would be best financed by equity capital.
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Chapter 15: Valuation of Debt and Equity
301
When issuing debt or equity financing, the financial market will not pay more for
the shares or bonds than they feel they are worth. If comparable financial
instruments are available, then these will act as a guideline for valuing new issues. It
is not possible to expect more in present value terms for the new issues than the
present value of the future cash flows. Since the net present value to the purchaser
will always be zero, the issuer cannot expect to increase shareholders’ wealth by
issuing debt or equity financing instruments. If the NPV of raising funds were
positive for the issuer, it means that it is negative for the provider of the funds. But
since there is so much competition for raising funds, the providers of funds will not
permit themselves to be in a negative NPV arrangement. Therefore, a zero NPV for
the purchaser implies that any financial issue is a zero NPV transaction for the
issuer. This implies that the form of financing is more an exercise in marketing and
matching, than one of generating profits, since generating profits through financing
issues is impossible.
People as Gamblers
People who invest in debt and equity do so with their own personally held views
firmly in mind. Debt investors, for example, may be content to accept the market
set rate of return until the date of maturity. However, it is more likely that the debt
investor is taking a financial gamble on the impending changes in interest rates. If
the gamble is that interest rates are bound to go down, then the investor would ‘go
long’ (i.e. increase their duration, or time to maturity) and/or reduce their coupon
stream.
Equity investors also invest with a speculative view of the future. It is a rare
investor indeed who decides on the total potential cash flow stream -including the
final liquidation dividend - of any company. More likely, the investor cares little
about the dividend flow, and cares most about the amount that the share can be
resold for to another investor. Nevertheless, without potential cash flow from the
company to the investor, the share has no value.
Since the market place is full of investors who are gambling on the future direction
of their investments, it is often the case that group psychology has an effect on the
value of debt and equity. The efficient market hypothesis, discussed in more detail
in the chapter on risk and return, would describe these people as ‘noise traders’.
While it is true that noise traders can influence prices, it can be shown that the
influence of the gambler - i.e. noise trader - is always overcome by the influence of
the investor who bases their investment decisions on firm fundamental analysis of
their investment.
The dilemma is this: if the market is efficient and reflects the ‘fair’ value of the
investment ‘correctly’, then why would anyone trade in the market? The answer is
that often the market is provided with new information which alters the ‘correct’
value of the asset and the market is also influenced by the gamblers.
Thus, the challenge facing the investor is to sort out the noise and fundamentals so
that safe investments can be made.
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Financial Management and Decision Making
Summary
Ignoring risk for the time being, placing a value on shares and bonds is derived
from NPV calculations. The bond valuation process is one of bringing into the
present, the value of the future cash flows using the prevailing interest rates as the
discount factor. This form of corporate indebtedness for financing operations has
several aspects including the length of maturity, coupon amount, and face value
amount. Nevertheless, knowing prevailing interest rates, it is a straightforward
matter of converting the future cash flows into present value terms to arrive at a
market price for the bond.
Equity valuation can also be thought of as converting future cash flows into present
value terms. It is more difficult to anticipate future cash flows of equity since there
is no contractual agreement for those future flows. Anticipated dividend payouts
combined with projected growth rates determine the value of the share for a given
required rate of return. Growth companies are more volatile in price due to their
high sensitivity to required rates of return. Privately held companies - those not
traded on a share market - can be valued by considering P/E ratios of comparable
shares.
Knowing what a ‘fair’ price is for a bond or a share can thus be reduced to a
discussion of the appropriate required rate of return. Guidelines for this rate of
return can be arrived at by looking at comparable issues in the market place and
using their prevailing rates. This problem of an ‘appropriate’rate of return has been
simplified by avoiding risk, which will be discussed in the next chapter.
While this chapter discusses proper approaches to valuation, people often place
their subjective judgements on their view of ‘value’.
Glossary of
Key Terms
Face Value
The amount a bond pays at maturity.
Coupon Rate
The percentage of face value paid to the holder of a bond.
Yield to Maturity
The internal rate of return for a bond.
Par Value
Also called ‘face value’, the amount a bond pays at maturity.
Selected
Readings
Brealey, R. & Myers, S., Principles of Corporate Finance, Fourth Edition,
McGraw-Hill, New York, 1991.
Brigham, E.F., Financial Management Theory and Practice, Third Edition, The
Dryden Press, 1982.
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Chapter 15: Valuation of Debt and Equity
303
Brigham, E.F. and Gardenski, L.C., Financial Management Theory and Practice,
Fifth Edition, The Dryden Press, 1988.
Francis, J.C., Investments: Analysis and Management, Fifth Edition, McGraw-Hill,
New York, 1991.
Keown, A.J., Scott, D.F., Martin, J.D., and Petty, J.W., Basic Financial
Management, Third Edition, Prentice-Hall, 1985.
Peirson, G., and Bird, R., Business Finance, Third Edition, McGraw Hill, Sydney,
1983.
Pringle, J.J. and Harris, R.S., Essentials of Managerial Finance, Scott Foresman &
Co, Glenview, Illinois, 1984.
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Financial Management and Decision Making
Questions
15.1
The value of an asset depends on several factors, what are these?
15.2
Explain the relationship between the value of an asset and the investor’s required rate of return.
15.3
Explain the difference between a bond’s face value and its market value.
15.4
What would you expect the value of an ordinary share to be in a company that pays no dividends?
15.5
Will the market price of a ten year government bond be more or less variable than that of a five year
government bond? Explain the reasoning behind your answer.
15.6
What is the main reason why knowledge of bond and share valuation is important to managerial
decision makers?
15.7
Investors buy ordinary shares in expectation of future dividends and capital gains. Is the distribution
between dividends and capital gains affected by a firm’s decision to pay out a higher proportion of its
earnings as dividends?
15.8
Do you believe that a firm operating and owned in New Zealand could grow at an annual rate of 30%
indefinitely? Explain your answer.
15.9
Two investors are considering buying shares in Robert Jones Investments. Both agree on the expected
value of the upcoming dividend and also on the expected dividend growth rate. One investor intends
holding the shares for one year while the other investor intends holding them for eight years. Will
both investors be willing to pay the same price for the shares? Explain your answer.
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Chapter 15: Valuation of Debt and Equity
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15.10
If all other factors are held constant, what would be the effect on the market value of a firm’s ordinary
shares if investors lowered their assessment of the firm’s risk?
15.11
ABC Company bonds have a coupon rate of 10%, a face value of $10,000 and mature in 15 years’
time. If investors require a return of 8%, what will be the market price of the bonds?
15.12
Percy’s Plastic Products has issued $1,000 bonds with a coupon rate of 15% (paid semi-annually). If
the bonds mature in two years’time and your required return is 10%, what price would you be willing
to pay for the bonds? Assume the semiannual return compounds to 10% annually.
15.13
Elfton Company bonds are currently priced at $9,528, have a face value of $20,000 and mature in ten
years’ time. If the market rate of return is 20%, what is the annual coupon rate? (Assume payments
are made annually.)
15.14
Smart Corp bonds, maturing in two years, are selling for $1,248.52. If the coupon rate is 24% paid
annually and the face value is $1,000, what is the required rate of return?
15.15
Preference shares in Ali’s Aluminium Yacht Company are currently selling for $3.56. If the annual
dividend on the shares is $0.72 and is expected to be paid forever, what is the required rate of return?
15.16
An investor is willing to pay $981.41 for a one year bond (face value $1,000) with a coupon rate of
10% paid quarterly. What is her expected annual rate of return?
15.17
Ordinary shares in Heady Heights Health Centre have a current market value of $3.20. The dividend
expected this year (in 364 days) is $0.08 per share. You intend to purchase a share today and sell it in
one year’s time. By how much will the share price have to appreciate if your required rate of return is
12%?
15.18
Percy’s Plastic Products Company last year (yesterday) paid a dividend of $0.09 per share. Dividends
are expected to grow at the past rate of 10% per annum. If investors require a return of 15% per
annum, what is the current share price?
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Financial Management and Decision Making
15.19
The ordinary shares of a company are currently trading at $10.52. A growth rate of 10% per annum is
expected and the dividend for the upcoming year (364 days hence) has been set at $0.12. What is the
expected rate of return?
15.20
Preference shares in Anderson Company are selling for $10.50 and pay an annual dividend of $0.95
which is expected to be paid forever.
Required:
a. What is the expected return on the shares?
b. If an investor has a required rate of return of 12% should he acquire preference shares in the
company?
c. At what price would the investor in (b) consider purchasing the shares?
15.21
Shares in Company A traded today at $12.60. Yesterday the company paid a dividend of $0.96. The
required rate of return for a company with a risk profile such as Company A is 13%. If dividends are
expected to grow at a constant rate in the future, and if the required rate of return remains at 13%,
what is Company A’s expected share price in six years’time?
15.22
Martin’s Magnificent Mushroom Company is currently experiencing a period of rapid growth. A
growth rate of 20% in earnings and dividends is expected for the next three years, 18% in the fourth
and fifth years, and a constant rate of 5% thereafter. Last year (yesterday) the company made a
dividend payout of $0.82 and the required rate of return is 15%.
Required:
a. What is today’s share price?
b. What will the share price be in one year’s time?
c. Calculate the dividend yield and the capital gains yield for each of years 1, 2 and 3.
15.23
The required rate of return on shares in Company Y is 15%. What is the share price if last year’s
(yesterday) dividend was $0.50 and investors expect dividends to grow at a constant annual rate of:
a. -7%
b. 0%
c. 7%
d. 14%
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Chapter 15: Valuation of Debt and Equity
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15.24
Mine Corp’s dividend last year (yesterday) was $1.50. For the next three years earnings and
dividends are expected to grow at a rate of 15% per annum. After that the dividend growth rate is
expected to slow and remain at a constant rate per annum indefinitely. If the required rate of return is
12% per annum and the current share price is $22.17, what is the expected annual growth rate after
three years?
15.25
You buy shares in a company at $3.50 each. Expected dividends for the next three years are: $0.60,
$0.63, $0.66. At the end of the three years you expect to sell the shares at $4.70.
Required:
a. Calculate the dividend growth rate (not a constant).
b. Calculate the current dividend yield.
c. Assuming that the growth rate is expected to continue, what is the expected total rate of return?
15.26
A sharebroker offers you shares in a company that paid a $0.87 dividend last year (yesterday). The
expected growth rate in dividends is 15% per annum for the next three years and 6% thereafter. If you
buy the shares you intend to hold them for three years and then sell them.
Required:
a. If the required rate of return is 10%, what is the present value of the dividend stream over the first
three years?
b. You expect the share price to be $35.00 in three years’ time. What is the present value of the
expected share price?
c. If you plan to hold the shares for three years, what is the maximum price you should pay?
d. What is the present value of the shares?
e. What is the present value of the shares if you decide to hold them for seven years?
15.27
A company has recently made an issue of $1,000 zero coupon bonds which are to be repaid in ten
years’time. If market interest rates are now 18%, what is the market value of the bonds?
15.28
A company has issued bonds that are not repayable but bear a 12% coupon rate and have a face value
of $2,000. The market rate of return is 10%.
Required:
a. What is the current market price of the bonds?
b. What would the market price be if the market return fell to 8%?
c. How would the answers to (a) and (b) be different if the bonds were to be repaid in ten years’
time?
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Financial Management and Decision Making
15.29
You wish to have $60,000 in eight years’ time in order to purchase a new car. Upon inquiring at the
local sharebroker you discover that a company has recently issued a series of zero coupon bonds that
are repayable in eight years’ time. If market interest rates are currently 15%, how much must you
invest in the bonds today?