70 Financial Management
5. Define a yield curve. What are the reasons for an upward sloping yield curve? What is an inverted yield curve?
6. What is default risk and default risk premium? What is the relation between the default risk and credit
ratings of bonds (or debentures)?
7. What is the difference between the valuation of a bond and of a preference share? Illustrate.
8. What is the meaning of the term yield-to-maturity for bonds and preference shares? Is it appropriate to talk
of a yield-to-maturity on a preference share that has no specific maturity date?
9. What is an ordinary share? What are its features? How does it differ from a preference share and a debenture?
10. Explain in detail the method of valuing an ordinary share.
11. What is the perpetual growth model? What are its assumptions? Is this model applicable in a finite case?
12. Why are dividends important in determining the present value of a share? How would you account for the
positive market value of a company’s share, which currently pays no dividend?
13. What is the difference between the expected and the required rate of return in the context of ordinary
shares? When would this difference banish?
14. Illustrate with the help of an example the linkage between share price and earnings. What is the importance
of the price-earnings (P/E) ratio? What are its limitations?
15. What is meant by growth opportunities? How are they valued? Illustrate with an example.
QUIZ EXERCISES
1. You have just bought a 10 per cent, `1000 bond with 7-year maturity. The interest is payable annually.
How much should you pay for the bond if your required rate of return is (a) 12 per cent; (b) 9 per cent?
2. A 10 per cent, `1000 bond is currently selling for `950. It has a remaining life of five years. If your
required rate of return is 11 per cent, will you buy the bond? Assume that interest is payable (a) annually;
(b) semi-annually.
3. A company has issued a 12 per cent, `1000 bond repayable after 10 years, at 10 per cent premium. Your required
rate of return is 13 per cent. Will you buy the bond if interest is payable (a) annually; (b) semi-annually.
4. A zero-interest bond of `1000 will pay `2,500 after seven years. What is the bond’s yield?
5. A 10 per cent, `1000 bond is selling for `900. It has a remaining life of 8 years. What is the bond’s yieldto-maturity?
6. A company’s expected dividend next year `5 per share. The dividend is expected to grow at 8 per cent per
annum for ever. The equity capitalization rate is 12 per cent. What should be the value of the company’s share?
7. A share is currently selling for `120. The expected dividend after a year is `12. The perpetual dividend
growth rate is expected to be 8 per cent. What is the equity capitalization rate?
8. PQ Limited paid a dividend of `10 per share. It is expected to grow at 8 per cent for five years and at 4 per
cent thereafter, forever. Calculate the price of the share if the equity required rate of return is 10 per cent.
9. You bought a share for `100 a year ago. During the year, you received a dividend of `6. The share is now
selling for `120. What is your dividend yield and capital gain?
10. The price of a company’s share is `160, and the value of growth opportunities is `60. If the company’s
equity capitalization rate is 15 per cent, what is the earnings-price ratio? How much is EPS?
11. A company’s current price of share is `100 and the expected dividend per share is `8. If its capitalization
rate is 15 per cent, what is the dividend growth rate?
PROBLEMS
1. Suppose you buy a one-year government bond that
has a maturity value of `1,000. The market interest
rate is 8 per cent. (a) How much will you pay for
the bond? (b) If you purchased the bond for `904.98,
what interest rate will you earn on your investment?
2. The Brightways Company has a perpetual bond that
pay `140 interest annually. The current yield on this
type of bond is 13 per cent. (a) At what price will
it sell? (b) If the required yield rises to 15 per cent,
what will be the new price?
3. The Nutmate Limited has a ten-year debenture that
pays `140 annual interest. `1,000 will be paid on
maturity. What will be the value of the debenture
if the required rate of interest is (a) 12 per cent, (b)
14 per cent and (c) 16 per cent?
4. What will be the yield of a 16 per cent perpetual
bond with `1,000 par value, when the current price is
(a) `800, (b) `1,300 or (c) `1,000?
Valuation of Bonds and Shares
5. You are considering bonds of two companies. Taxco’s
bond pays interest at 12 per cent and Maxco’s at 6
per cent per year. Both have face value of `1,000 and
maturity of three years. (a) What will be the values
of bonds if the market interest rate is 9 per cent? (b)
What will be the values of the bonds if the market
interest rate increases to 12 per cent? (c) Which bond
declines more in value when the interest rate rises?
What is the reason? (d) If the interest rate falls to
6 per cent, what are the values of the bonds? (e) If
the maturity of two bonds is 8 years (rather than 3
years), what will be the values of two bonds if the
market interest rate is (i) 9 per cent, (ii) 6 per cent
and (iii) 12 per cent?
6. Three bonds have face value of `1,000, coupon rate
of 12 per cent and maturity of 5 years. One pays
interest annually, one pays interest half-yearly, and
one pays interest quarterly. Calculate the prices of
bonds if the required rate of return is (a) 10 per cent,
(b) 12 per cent and (c) 16 per cent.
7. On 31 March 2003, Hind Tobacco Company issued
`1,000 face value bonds due on 31 March 2013. The
company will not pay any interest on the bond until
31 March 2008. The half-yearly interest is payable
from 31 December 2008; the annual rate of interest
will be 12 per cent. The bonds will be redeemed at 5
per cent premium on maturity. What is the value of
the bond if the required rate of return is 14 per cent?
8. Determine the market values of the following bonds,
which pay interest semi-annually:
Bond
Rate
A
B
C
D
9.
Interest
16%
14%
12%
12%
Required Rate
Period (Years)
15%
13%
8%
8%
Maturity
25
15
20
10
If the par values of bonds are `. 100 and if they
are currently selling for `95, `100, `110 and `115,
respectively, determine the effective annual yields of
the bonds? Also calculate the semi-annual yields?
10. A 20-year, 10 per cent, `1,000 bond that pays interest
half-yearly is redeemable (callable) in twelve years at
a buy-back (call) price of `1,150. The bond’s current
yield-to-maturity is 9.50% annually. You are required
to determine (i) the yield-to-call, (ii) the yield-to-call
if the buy-back price is only `1,100, and (iii) the
yield-to-call if instead of twelve years, the bond can
be called in eight years, buy-back price being `1,150.
11. A fertiliser company holds 15-year, 15 per cent bond
of ICICI Bank Ltd. The interest is payable quarterly.
The current market price of the bond is `875. The
company is going through a bad patch and has
accumulated a substantial amount of losses. It is
negotiating with the bank for the restructuring of
debt. Recently the interest rates have fallen and there
is a possibility that the bank will agree for reducing
the interest rate to 12 per cent. It is expected that
the company will be able service debt to the reduce
71
interest rates. Calculate stated and the expected
yields-to-maturity?
12. You are thinking of buying BISCO’s preference share
of `100 par value that will pay a dividend of 12 per
cent perpetually. (a) What price should you pay for the
preference share if you are expecting a return of 10
per cent? (b) Suppose BISCO can buy back the share
at a price of `110 in seven years. What maximum
price should you pay for the preference share?
13. The share of Premier Limited will pay a dividend
of `3 per share after a year. It is currently selling at
`50, and it is estimated that after a year the price
will be `53. What is the present value of the share
if the required rate of return is 10 percent? Should
the share be bought? Also calculate the return on
share if it is bought, and sold, after a year.
14. An investor is looking for a four-year investment. The
share of Skylark Company is selling for `75. They
have plans to pay a dividend of `7.50 per share each
at the end of first and second years and `9 and `15
respectively at the end of third and fourth years. If
the investor’s capitalization rate is 12 percent and the
share’s price at the end of fourth year is `70, what
is the value of the share? Would it be a desirable
investment?
15. A company’s share is currently selling at `60. The
company, in the past, paid a constant dividend of
`1.50 per share, but it is now expected to grow at
10 per cent compound rate over a very long period.
Should the share be purchased if required rate of
return is 12 per cent?
16. The earnings of a company have been growing at
15 per cent over the past several years and are
expected to increase at this rate for the next seven
years and thereafter, at 9 per cent in perpetuity. It
is currently earning `4 per share and paying `2 per
share as dividend. What shall be the present value
of the share with a discount rate of 12 per cent for
the first seven years and 10 per cent thereafter?
17. A company retains 60 per cent of its earnings, which
are currently `5 per share. Its investment opportunities
promise a return of 15 per cent. What price should be
paid for the share if the required rate of return is 13
per cent? What is the value of growth opportunities?
What is the expected rate of return from the share
if its current market price is `60?
18. The total assets of `80,000 of a company are financed
by equity funds only. The internal rate of return on
assets is 10 per cent. The company has a policy of
retaining 70 per cent of its profits. The capitalization
rate is 12 per cent. The company has 10,000 shares
outstanding. Calculate the present value per share.
19. A prospective investor is evaluating the share of
Ashoka Automobiles Company. He is considering three
scenarios. Under the first scenario the company will
maintain to pay its current dividend per share without
any increase or decrease. Another possibility is that
72 Financial Management
the dividend will grow at an annual (compound) rate
of 6 per cent in perpetuity. Yet another scenario is
that the dividend will grow at a high rate of 12 per
cent per year for the first three years; a medium rate
of 7 per cent for the next three years and thereafter,
at a constant rate of 4 per cent perpetually. The last
year’s dividend per share is `3 and the current market
price of the share is `80. If the investor’s required
rate of return is 10 per cent, calculate the value of
the share under each of the assumptions. Should the
share be purchased?
20. Vikas Engineering Ltd has current dividend per share
of `5, which has been growing at an annual rate of
5 per cent. The company is expecting significant
technical improvement and cost reduction in its
operations, which would increase growth rate to 10
per cent. Vikas’ capitalization rate is 15 per cent.
You are required to calculate (a) the value of the
share assuming the current growth rate; and (b) the
value of the share if the company achieves technical
improvement and cost reduction. Does the price
calculated in (b) make a logical sense? Why?
21. Consider the following past data of four auto (two/
three-wheelers) companies.
Companies
EPS
(`)
DIV
(%)
Share Price
(`)
1. Bajaj
11.9
50
275.00
2. Hero Honda
10.2
22
135.00
3. Kinetic
12.0
25
177.50
4. Maharashtra Scooters 20.1
25
205.00
The face value of each company’s share is `10. Explain
the relative performance of the four companies.
22. The dividend per share of Skyjet Company has
grown from `3.5 to `10.5 over past 10 years. The
share is currently selling for `75. Calculate Skyjet’s
capitalization rate.
23. Rama Tours and Travels Limited has current earnings
per share of `8.60, which has been growing at 12
per cent. The growth rate is expected to continue
in future. Rama has a policy of paying 40 per cent
of its earnings as dividend. If its capitalization rate
is 18 per cent, what is the value of the share? Also
calculate value of growth opportunities.
24. A company has the following capital in its balance
sheet: (a) 12-year, 12 per cent secured debentures of
`1,000 each; principal amount `50 crore (10 million
= crore); the required rate of return (on debentures
of similar risk) 10 per cent; (b) 10-year, 14 per cent
unsecured debentures of `1,000 each; principal
amount `30 crore; interest payable half-yearly; the
required rate of return 12 per cent; (c) preference
share of `100 each; preference dividend rate of 15
per cent; principal amount `100 crore; required
rate of return 13.5 per cent; and (d) ordinary share
capital of `200 crore at `100 each share; expected
dividend next year, `12; perpetual dividend growth
rate 8 per cent; the required rate of return 15 per
cent. Calculate the market values of all securities.
25. Satya Systems Company has made net profit of `50
crore. It has announced to distribute 60 per cent of
net profit as dividend to shareholders. It has 2 crore
ordinary shares outstanding. The company’s share is
currently selling at `240. In the past, it had earned
return on equity at 25 per cent and expects to main
this profitability in the future as well. What is the
required rate of return on Satya’s share?
26. A company has net earnings of `25 million (1 crore =
10 million). Its paid-up share capital is `200 million
and the par value of share is `10. If the company
makes no new investments, its earnings are expected
to grow at 2 per cent per year indefinitely. It does
have an investment opportunity of investing `10
million that would generate annual net earnings of
`2 million (1 million = 10 lakh) for next 15 years.
The company’s opportunity cost of capital is 10 per
cent. You are required: (a) to find the share value
if the company does not make the investment; (b)
to calculate the proposed investment’s NPV; and (c)
to determine the share value if the investment is
undertaken?
27. Gujarat Bijali Ltd has earnings of `80 crore and it
has 5 crore shares outstanding. It has a project that
will produce net earnings of `20 crore after one year.
Thereafter, earnings are expected to grow at 8 per
cent per annum indefinitely. The company’s required
rate of return is 12.5 per cent. Find the P/E ratio.
28. Symphony Limited is an all-equity financed company.
It has 10 million shares outstanding, and is expected
to earn net cash profits of `80 million. Shareholders
of the company have an opportunity cost of capital of
20 per cent. (a) Determine the company share price if
it retained 40 per cent of profits and invested these
funds to earn 20 per cent return. Will the share price
be different if the firm retained 60 per cent profits to
earn 20 per cent? (b) What will be the share price if
investments made by the company earn 24 per cent
and it retains 40 per cent of profits? Will share price
change if retention is 60 per cent?
29. Sonata Company has no investment opportunities.
It expects to earn cash earnings per share of
`10 perpetually and distribute entire earnings as
dividends to shareholders. (a) What is the value of
the share if shareholders’ opportunity cost of capital
is 15 per cent? (b) Suppose the company discovers
an opportunity to expand its existing business. It
estimates that it will need to invest 50 per cent of
its earnings annually for ten years to produce 18 per
cent return. Management does not foresee any growth
after this ten-year period. What will be Sonata’s share
price if shareholders’ opportunity cost of capital is
15 per cent?