Chapter 4 – Valuation of Securities
[ad_1]SECTION A – MULTIPLE CHOICE QUESTIONS
- Which types of assets are usually easiest to value?
(a) Real assets
(b) Financial assets
(c) Tangible assets
(d) Intangible assets - Which of the following features of a Treasury bond never changes over the life of the bond?
(a) Coupon rate
(b) Term to maturity
(c) Yield
(d) Both (a) and (b) - Which of the following is a long‐term debt security?
(a) Promissory note
(b) Commercial paper
(c) Treasury note
(d) Debenture - For which of the following securities is repayment guaranteed by a third party?
(a) Debenture
(b) Bank bill
(c) Commercial paper
(d) Treasury bond - Which of the following is true if a coupon bond is trading at a discount?
(a) The price is less than the yield.
(b) The yield is greater than the coupon rate.
(c) The price is less than the coupon rate.
(d) The coupon rate is greater than the yield. - Which of the following investors normally have the right to vote at a company’s AGM?
(a) Ordinary shareholders
(b) Preference shareholders
(c) Debtholders
(d) Both (a) and (b) - Which of the following groups of investors have a contractual claim to receive a return on their investment?
(a) Ordinary shareholders
(b) Preference shareholders
(c) Debtholders
(d) All of the above
La Trobe University 4
SECTION B – SHORT ANSWER QUESTIONS - What does the term “opportunity cost” mean in finance? How is the opportunity cost used?
- What is the easiest approach to valuating a firm? Why is this easier than the alternative?
- What are the fundamental differences between debt and equity?
- What is meant by the term “discount security”? List three different short‐term discount securities, indicating
the likely issuer of each.
La Trobe University 5 - Rank the three discount securities from Question 11 from most credit risk to least credit risk, and explain why
you have ranked them in this way. - Distinguish between the terms “bond”, “note”, “debenture” and “consol”.
- Describe the relationship between the price, face value, coupon rate and yield of a bond.
- What must be true for bond to trade at a premium, at a discount or at par?
La Trobe University 6 - Company ABC has ordinary shares and cumulative preference shares outstanding. The dividend payable to
preference shareholders is $2 per share. The only dividends paid in 2013 were preference dividends of $1 per
share. The company’s fortunes improved in 2014, and they declared a $2 per share dividend to preference
shareholders and a $1 per share dividend to ordinary shareholders. Is the company permitted to do this?
Why/why not? - Why are preference shares described as “hybrid securities”?
La Trobe University 7
SECTION C – ESSAY QUESTIONS - Explain the differences between debt, preference shares and ordinary shares.
La Trobe University 8
SECTION D – CALCULATION QUESTIONS - What is the price of a promissory note with 90 days to maturity, a face value of $750 and a yield of 11% p.a.?
- What is the value of a 180 day $1000 bank bill that was issued 30 days ago and that is trading at a yield of 8.8%
p.a.?* - What is the yield of a 270 day $2000 Treasury note and which is trading at a price of $1939.04?*
- What is the price of a zero‐coupon bond with a face value of $1000 and 3 years to maturity, if it is priced to
yield 6% p.a.?* - What is the value of a zero‐coupon bond with a face value of $500 and 5 years to maturity, if other bonds with
a similar risk are trading at a yield of 7% p.a.?*
La Trobe University 9 - What is the yield of a zero‐coupon bond with a face value of $2500, 4 years to maturity and a current price of
$1858.13?* - What is the value of a $1000 bond that pays an 8% annual coupon and has 9 years to maturity, if the debt cost
of capital is 6.5%? - What is the price of a $1000 Treasury bond that pays a 5.5% coupon and has 6 years to maturity, if it is priced
to yield 6.5%? - You bought a Woolworths share on 1 January 2013 for $44.50 and sold it one year later for $48.50. During
the year, Woolworths paid a dividend of $2.50 per share. What is the dividend yield, the capital gain yield and
the total yield?
La Trobe University 10 - You bought a CBA share on 1 January 2013 for $67.25 and sold it one year later for $64.75. CBA paid dividends
of $1.75 per share on 1 March 2013 and $2.00 per share on September 2013. What is the dividend yield, the
capital gain yield and the total yield? - A preference share pays a fixed dividend of $1.25 per share. The equity cost of capital is 11% p.a. What is the
value of the share? - An ordinary share is expected to pay dividend of $1.25 per share next year, after which it is expected to grow
at a constant rate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share? - An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a constant
rate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?*
La Trobe University 11 - An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a rate of
5% p.a. for the next three years, after which it is expected to grow at a constant rate of 2% p.a. in perpetuity.
The equity cost of capital is 11% p.a. What is the value of the share?* - An ordinary share is expected to pay a dividend of $3 per share for the next 10 years. After 10 years the
dividend is expected to grow at a constant rate of 3.5% p.a. in perpetuity. The required rate of return is 14%
p.a. What is the value of the share?*
La Trobe University 12
Hint, tips, advice and guidance
SECTION D – CALCULATION QUESTIONS - What is the value of a 180 day $1000 bank bill that was issued 30 days ago and that is trading at a yield of 8.8%
p.a.?
Note that the value of any security is always based on the time remaining until maturity. - What is the yield of a 270 day $2000 Treasury note and which is trading at a price of $1939.04?
This is based on the formula for the price of a discount security, but we know the price. You need to rearrange
the formula to solve for the yield. - What is the price of a zero‐coupon bond with a face value of $1000 and 3 years to maturity, if it is priced to
yield 6% p.a.?
The yield is the return you will get, based on the known future cash flows, if you pay the current price, so “priced
to yield” is just a way of telling you what the yield is. - What is the value of a zero‐coupon bond with a face value of $500 and 5 years to maturity, if other bonds with
a similar risk are trading at a yield of 7% p.a.?
Securities with the same risk should be trading at the same yield, so this is a way of telling you what the yield
will be on this bond. - What is the yield of a zero‐coupon bond with a face value of $2500, 4 years to maturity and a current price of
$1858.13?
This is based on the formula for the price of a zero‐coupon bond, but we know the price. You need to rearrange
the formula to solve for the yield.
25.
26.
27.
28.
29.
30. - An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a constant
rate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?
This similar to the previous question, except that the formula for the price of a share (based on the formula for
the present value of a growing perpetuity) requires the first dividend in the numerator, and we are not given
the first dividend. We are given dividend that has just been paid (which is not a future cash flow and is not part
of the value of the share). You need to calculate the first dividend based on the most recent dividend and the
growth rate, before you can use the formula.
La Trobe University 13 - An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a rate of
5% p.a. for the next three years, after which it is expected to grow at a constant rate of 2% p.a. in perpetuity.
The equity cost of capital is 11% p.a. What is the value of the share?
You need to calculate the next three dividends, using the information provided, and then separately discount
each of them to a present value. They need to be added together and form part of the price of the share. Then
you need to calculate the fourth dividend (note that this based on one growth rate for three years and then a
different growth rate in the fourth year). This is the first dividend in the growing perpetuity that begins with
Dividend 4, so you use it in the numerator of the formula for the present value of a growing perpetuity. The
answer you get from that formula applies one period before the first payment – i.e. it applies to year 3, so it
needs to be discounted by three years and then added to the present value of the first three dividends. - An ordinary share is expected to pay a dividend of $3 per share for the next 10 years. After 10 years the
dividend is expected to grow at a constant rate of 3.5% p.a. in perpetuity. The required rate of return is 14%
p.a. What is the value of the share?
This is similar in principle to the previous question, but the easiest way to calculate it is to treat the first 10
dividends as an annuity. Then treat the dividend in year 11 – which you will need to calculate – as the first
dividend of a growing perpetuity, the value of which must be discounted by the appropriate number of years
to a present value.
La Trobe University 14
Solutions
SECTION A – MULTIPLE CHOICE QUESTIONS - Which types of assets are usually easiest to value?
(a) Real assets
(b) Financial assets
(c) Tangible assets
(d) Intangible assets - Which of the following features of a Treasury bond never changes over the life of the bond?
(a) Coupon rate
(b) Term to maturity
(c) Yield
(d) Both (a) and (b) - Which of the following is a long‐term debt security?
(a) Promissory note
(b) Commercial paper
(c) Treasury note
(d) Debenture - For which of the following securities is repayment guaranteed by a third party?
(a) Debenture
(b) Bank bill
(c) Commercial paper
(d) Treasury bond - Which of the following is true if a coupon bond is trading at a discount?
(a) The price is less than the yield.
(b) The yield is greater than the coupon rate.
(c) The price is less than the coupon rate.
(d) The coupon rate is greater than the yield. - Which of the following investors normally have the right to vote at a company’s AGM?
(a) Ordinary shareholders
(b) Preference shareholders
(c) Debtholders
(d) Both (a) and (b) - Which of the following groups of investors have a contractual claim to receive a return on their investment?
(a) Ordinary shareholders
(b) Preference shareholders
(c) Debtholders
(d) All of the above
La Trobe University 15
SECTION B – SHORT ANSWER QUESTIONS - What does the term “opportunity cost” mean in finance? How is the opportunity cost used?
The benefit forgone by not taking up the next best alternative investment.
Any investment must earn at least the opportunity cost in order to be a worthwhile investment. - What is the easiest approach to valuating a firm? Why is this easier than the alternative?
It is easier to value financial securities (the right‐hand side of the balance sheet) because:
Much of the time (in the case of publicly listed companies) these securities are frequently traded in
liquid markets and their market value can be determined.
Real assets are rarely traded and difficult to value.
Sometimes real assets are built for a particular purpose and cannot be sold for their true value. - What are the fundamental differences between debt and equity?
Debt Equity
Usually has a limited life Valued on the assumption they will last forever
(Exception: Consols) (Exceptions: Redeemable preference shares)
Usually pay a fixed return Return can be variable, and sometimes negative
(Exception: Floating rate notes) (Exception: Preference shares)
Contractual claim Residual claim
Less risky for the investor More risky for the investor - What is meant by the term “discount security”? List three different short‐term discount securities, indicating
the likely issuer of each.
A security with only one cash flow (the face value repayable on maturity).
As a result, it will always be sold at a discount to its face value, because of the time value of money.
Examples:
o Promissory notes (commercial paper) – issued by businesses
o Bank bills – issued by businesses, with the assistance of a bank which guarantees payment of
the face value to the holder
o Treasury notes – issued by the Federal government - Rank the three discount securities from Question 11 from most credit risk to least credit risk, and explain why
you have ranked them in this way.
Promissory notes (commercial paper) – there is no collateral and no guarantee of repayment.
Businesses can be risky investments.
Bank bills – although issued by businesses, repayment is guaranteed by a bank, which is less risky than
a business.
Treasury notes – issued by the Federal government, which is considered to be free of credit risk.
La Trobe University 16 - Distinguish between the terms “bond”, “note”, “debenture” and “consol”.
Bond – strictly speaking, any debt security, but in common practice, refers to a long‐term debt security.
Note – strictly speaking, any debt security, but in common practice (used on its own) refers to a medium‐term
security. Also, in combination with other words, can be used for short‐term debt securities (e.g. promissory
note, Treasury note).
Debenture – unsecured bonds.
Consol – a debt security that does not mature. - Describe the relationship between the price, face value, coupon rate and yield of a bond.
Price is the current value of the bond. It is a function of the yield, as described below. Face Value is
the amount that will be repaid on maturity.
Coupon Rate determines the amount of interest paid via coupon payments. Yield is the rate of return
implied by the bond’s current price. It is the return the investor will get if he or she pays the current
price and holds the bond until maturity. It represents the investor’s opportunity cost or required rate
of return. If the yield exceeds the coupon rate, the return, as a percentage of the face, is insufficient
to meet the investor’s required rate of return and investors won’t pay the face value. The price will
fall until the rate of return, as percentage of the price paid, is equal to the required rate of return. - What must be true for bond to trade at a premium, at a discount or at par?
Premium – Price > Face value, Yield < Coupon Rate. Discount – Price < Face value, Yield > Coupon Rate.
Par – Price = Face value, Yield = Coupon Rate. - Company ABC has ordinary shares and cumulative preference shares outstanding. The dividend payable to
preference shareholders is $2 per share. The only dividends paid in 2013 were preference dividends of $1 per
share. The company’s fortunes improved in 2014, and they declared a $2 per share dividend to preference
shareholders and a $1 per share dividend to ordinary shareholders. Is the company permitted to do this?
Why/why not?
No, this in not permissible. Because the preference shares are cumulative, the $1 per share that was missed
in 2013 accumulate and must be repaid, along with all future dividends, before ordinary shareholders can
receive a dividend. If there is $3 available for dividends in 2014, it must all be paid as preference dividends. - Why are preference shares described as “hybrid securities”?
Equity securities with some of the features of debt securities – usually fixed dividend and rank ahead of
ordinary shareholders in payment of dividends and distribution of the firm’s assets if the company is wound
up.
La Trobe University 17
SECTION D – CALCULATION QUESTIONS - What is the price of a promissory note with 90 days to maturity, a face value of $750 and a yield of 11% p.a.?
750 $730.19
1 1 0.11 90
365 365
P FV
y d
- What is the value of a 180 day $1000 bank bill that was issued 30 days ago and that is trading at a yield of 8.8%
p.a.?
1000 $965.10
1 1 0.088 150
365 365
P FV
y d - What is the yield of a 270 day $2000 Treasury note and which is trading at a price of $1939.04?
1 365 2000 1 365 4.25%
1939.04 270
y FV
P d
- What is the price of a zero‐coupon bond with a face value of $1000 and 3 years to maturity, if it is priced to
yield 6% p.a.?
3
1000 $839.62
1 1.06 n
P FV
y
- What is the value of a zero‐coupon bond with a face value of $500 and 5 years to maturity, if other bonds with
a similar risk are trading at a yield of 7% p.a.?
5
500 $356.49
1 1.07 n
P FV
y
- What is the yield of a zero‐coupon bond with a face value of $2500, 4 years to maturity and a current price of
$1858.13?
1/ 1/4 1 2500 1 7.7%
1858.13
n YTM FV
P
- What is the value of a $1000 bond that pays an 8% annual coupon and has 9 years to maturity, if the debt cost
of capital is 6.5%?
9 9
1 1 1 80 1 1 1 1000 $1099.84
1 1 0.065 1.065 1.065 n n
P CPN FV
y y y
La Trobe University 18 - What is the price of a $1000 Treasury bond that pays a 5.5% coupon and has 6 years to maturity, if it is priced
to yield 6.5%?
12 12
1 1 1
1 1
27.50 1 1 1 1000 $950.96
0.0325 1.0325 1.0325
n n
P CPN FV
y y y
- You bought a Woolworths share on 1 January 2013 for $44.50 and sold it one year later for $48.50. During the
year, Woolworths paid a dividend of $2.50 per share. What is the dividend yield, the capital gain yield and the
total yield?
1
0
Dividend yield 2.50 5.62%
44.50
Div
P
1 0
0
Capital gain yield 48.50 44.50 8.99%
44.50
P P
P
1 1 0
0
Total yield 2.50 48.50 44.50 14.61%
44.50
Dividend yield Capital gain yield 5.62% 8.99% 14.61%
Div P P
P
- You bought a CBA share on 1 January 2013 for $67.25 and sold it one year later for $64.75. CBA paid dividends
of $1.75 per share on 1 March 2013 and $2.00 per share on September 2013. What is the dividend yield, the
capital gain yield and the total yield?
1
0
Dividend yield 1.75 2.00 5.58%
67.25
Div
P
1 0
0
Capital gain yield 64.75 67.25 3.72%
67.25
P P
P
1 1 0
0
Total yield 1.75 2.00 64.75 67.25 1.86%
67.25
Dividend yield Capital gain yield 5.58% 3.72% 1.86%
Div P P
P
- A preference share pays a fixed dividend of $1.25 per share. The equity cost of capital is 11% p.a. What is the
value of the share?
0
1.25 $11.36
0.11 E
P Div
r
- An ordinary share is expected to pay dividend of $1.25 per share next year, after which it is expected to grow
at a constant rate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?
1
0
1.25 $20.83
0.11 0.05 E
P Div
r g
La Trobe University 19 - An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a constant
rate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?
0
0
1 1.25 1.05
$21.88
0.11 0.05 E
Div g
P
r g
- An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a rate of
5% p.a. for the next three years, after which it is expected to grow at a constant rate of 2% p.a. in perpetuity.
The equity cost of capital is 11% p.a. What is the value of the share?
1 0 1
2 2
2 0 1
3 3
3 0 1
4 3
4 0 1 2
1 1.25 1.05 $1.3125
1 1.25 1.05 $1.3781
1 1.25 1.05 $1.4470
1 1 1.25 1.05 1.02 $1.4760
Div Div g
Div Div g
Div Div g
Div Div g g
1 2 3 4
0 2 3 3
2 3 3
1
1 1 1 1
1.3125 1.3781 1.4470 1.4760 1 $15.35
1.11 1.11 1.11 0.11 0.02 1.11
E E E E E
P Div Div Div Div
r r r r g r
Note: When answering a question like this, you may find it necessary to write down and re‐enter the individual
dividends. If so, it is recommended that these be recorded to 4 decimal places to minimise rounding errors. - An ordinary share is expected to pay a dividend of $3 per share for the next 10 years. After 10 years the
dividend is expected to grow at a constant rate of 3.5% p.a. in perpetuity. The required rate of return is 14%
p.a. What is the value of the share?
10
11
0 10
1
10
1 to10 10 10
10 10
1 1
1 1 1 1 1
1 1
1 1 3.00 1.035 1 3.00 1 $23.63
0.14 1.14 0.14 0.035 1.14
t
t
t E E
E E E E
P Div Div
r r
Div g
Div
r r r g r
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