The document contains 13 problems related to valuation of securities such as stocks and bonds. Key details include calculating stock prices given dividend growth rates, required rates of return, bond yields and prices given coupon rates and maturities. The problems require using concepts like present value, dividend discount model, yield to maturity and understanding how interest rate changes affect bond prices.

1. Valuation of Securities

2. Problem - 1
• ABC currently pays a dividend of Rs 3 per
share which is expected to grow at an
annual rate of 14% for 3 years and 11%
for the next 3 years after which it will grow
at 4% per annum forever. What amount
should be paid for the stock if the rate of
return required by the equity investors is
16%.

3. Solution - 1
Year Dividend Formula Dividend PV of Dividend (@16%)
1 3*1.14 3.42 2.95
2 3*1.14*1.14 3.9 2.9
3 3*1.14*1.14*1.14 4.44 2.85
4 3*1.14*1.14*1.14*1.11 4.93 2.72
5 3*1.14*1.14*1.14*1.11*1.11 5.47 2.6
6 3*1.14*1.14*1.14*1.11*1.11*1.11 6.07 2.49
Total Present Value of Dividend for
next 6 Years
16.51

4. Solution – 1 (Contd.)
Dividend at the end of Year 7 6.07 * 1.04 6.31
Market Price at the end of year 6 6.31/(0.16-0.04) 52.58
Present Value of Market Price at the end of Year 6 at 16% 52.58/(1.16)6
21.58
Total Value of the Stock 16.51+21.58 38.09

5. Problem - 2
• The shares of ABC are currently priced at
Rs.25. The Risk Free Rate of Return is
8% and the market return is 20%. With the
company having paid Rs.2 as the current
dividend and the company having a
growth rate of 8%, what is the value of the
share if its Beta is 0.7

6. Solution – 2
Expected Rate of Return 8 + 0.7 (20-8) 16.4
Dividend for the Next Year 2 * 1.08 2.16
Value of the Stock given the growth and Rate of Return 2.16/(0.164-0.08) 25.71
Current Share Price in the Market 25
Conclusion Marginally
Underpriced

7. Problem - 3
• The profit after Tax for a firm is Rs.20,000.
The dividend payout ratio is 50%. If the
growth rate of earnings is 4% and the
scrip trades at 2.5 times its EPS in the
market, what is the required rate of return
by equity share holders if the number of
outstanding shares is 5000.

8. Solution – 3
EPS 20000/5000 4
Market Price of the Share 2.5*4 10
Dividend Payout Ratio 50%
Dividend Paid Out 4*50% 2
Dividend for Next period 2 * 1.04 2.08
Required Rate of Return 2.08/10 + 0.04 24.8%

9. Problem - 4
• An Automobile Company
recently paid a dividend of
Rs.3 per share and it is a fairly
risky company with a cost of
equity of 25%. A summary of
Dividends and Earnings per
share is given to the right
• Any new investment is
expected to yield a return
comparable to the cost of
equity. What is the estimation
of growth rate based on
dividends?
Year Dividends Earnings
2007 3 5.5
2006 2.8 4.5
2005 2.7 5
2004 2.4 4
2003 2.3 3.5

10. Problem - 5
• The Standard Deviation of XYZ stock is
24% and its correlation coefficient with the
market portfolio is 0.5. The expected
return on the market is 16% with a
standard deviation of 20%. If the risk free
rate of return is 6% find the required rate
of return on XYZ stock

11. Solution – 5
Beta Cov (A,M)/Var(M)
Other formula for Beta using Correlation coefficient r r*SD(A)/SD(M)
Beta from the problem 0.5*0.24/0.2 0.6
Rate of Return 6 + 0.6 (16-6) 12%

12. Problem - 6
• A Financial institution issues two types of
bonds with one and three years maturity
respectively. The first pays Rs.10,000 a
year hence is now selling for Rs.8,929.
The second which pays Rs.100 next year,
Rs.100 after two years and Rs.1,100 at
the end of third year is now offered at
Rs.997.18. Find the implied interest rates
of these two bonds.

13. Solution – 6
Present value for Bond 1 10000/(1+k)
Given present value 8929
K for Bond 1 10000/8929 – 1 12%
Given Present value for Bond 2 997.18
Calculated present value from future returns 100/(1+k) + 100/
(1+k)2
+ 1100/
(1+k)3
Doing a Trial and Error the value of K for Bond 2 is 10.1%

14. Problem - 7
• A bond with a face value of Rs.100
provides 12% annual return and pays
Rs.105 at the time of maturity which is 10
years from now. If the investors required
rate of return is 13%, at what price should
the company issue the bond?

15. Solution – 7
Interest every year 12
No of years of Interest 10
Present value of all the interests for the next 10 years 12/1.13 + 12/1.132
+ ----------+
12/1.1310
Maturity value paid out 105
Present value of the maturity amount 105/1.1310
Total Present value of the Bond 96.087

16. Problem - 8
• A company is offering a bond with the
issue price Rs.100, coupon rate of 12%
with maturity period of 5 years. If the bond
is to be redeemed at par and the investor
faces a 30% tax on income and 10%
capital gains tax. Find the effective yield to
maturity for the investor

17. Solution – 8
Interest every year 12
No of years of Interest 5
Tax on the Interest every year 30% = 3.6
Effective Interest after tax every year 8.4
Present value of all the interests for the next 5 years (A) 8.4/(1+i) + 8.4/
(1+i)2
+ ----------+
8.4/(1+i)5
Maturity value paid out 100
Present value of the maturity amount (B) 100/(1+i)5
Total Present value of the Bond A+B
Solving A+B = 100
By Trial and Error method i = 8.4%

18. Problem - 9
• A company is contemplating a debenture issue
on the following terms.
• Face Value = Rs.100 per debenture
• Coupon rates: Years 1-2 (5% p.a), Years 3-4
(13% p.a), Years 5-7 (16% p.a)
• Current market rate of interest on similar
debentures is 15% p.a. The company proposes
to price the issue so as to yield a compounded
return of 16% p.a to the investors. Find the issue
price assuming redemption on debenture at a
premium of 10%.

19. Solution - 9
Year Coupon PV Formula PV of Dividend (@16%)
1 5 5/1.16 4.31
2 5 5/1.162
3.71
3 13 13/1.163
8.33
4 13 13/1.164
7.17
5 16 16/1.165
7.61
6 16 16/1.166
6.56
7 16 16/1.167
5.66
Total
Present
Value of
Coupons
for next 7
Years
43.35

20. Solution – 9 (Contd.)
Redemption Amount at the end of Year 7 100*1.1 110
PV of the redemption amount 110/1.167
38.94
Present Value of Debenture 38.94+43.35 82.29

21. Problem - 10
• A bond of face value Rs.1,000 is currently
quoting in the market at Rs.1,062. The coupon
rate of the bond is 14% payable semi annually.
The remaining maturity of the bond is 5 years
and the principal is repayable at two equal
installments at the end of 4th
and 5th
year from
now. The yield to maturity of the bond is 12.16%.
What would be the new price of the bond if the
YTM for similar type of bonds increases by 2%?

22. Solution – 10
Increase in Market Rate (YTM) 2%
New YTM 12.16 + 2 14.16%
Interest payable until 4 years (8 Installments) 70
PV of those 8 Installments 70/(1.0708) + 70/
(1.0708)2
+
----------+ 70/
(1.0708)8
Principal paid at the end of 4th
year 500
PV of that Principal 500/ /(1.0708)8
Interest payable in 4.5th
Year (9th
Installment) 35
PV of that Interest =35/ /(1.0708)9
Principal paid at the end of 5th
year + 10th
Installment Interest 500 + 35 = 535
PV of that Principal + Interest 535/ /(1.0708)10
Total Present value of the Bond 995.29

23. Bond Valuation – Key Facts
• Whenever the Expected Rate of Return, rd, is equal to the coupon rate, a fixed-
rate bond will sell at its par value.
• Interest rates do change over time, but the coupon rate remains fixed after
the bond has been issued. Whenever the Expected Rate of Return rises above
the coupon rate, a fixed-rate bond’s price will fall below its par value. Such a
bond is called a discount bond.
• Whenever the Expected Rate of Return falls below the coupon rate, a fixed-rate
bond’s price will rise above its par value. Such a bond is called a premium
bond.
• Thus, an increase in interest rates will cause the prices of outstanding bonds to
fall, whereas a decrease in rates will cause bond prices to rise.
• For bonds with similar coupons, the differential sensitivity to changes in
interest rates always holds true—the longer the maturity of the bond, the
more its price changes in response to a given change in interest rates.

24. Problem – 11 – A quick Recap
• If you buy a stock for a price P0 = Rs.23, and if you expect the
stock to pay a dividend D1 = Rs.1.24 one year from now and to
grow at a constant rate g = 8% in the future, what is the
expected rate of return on such a stock?

25. Problem - 12
• The bond of Zeta Industries with a par
value of Rs.500 is currently traded at
Rs.435. The coupon Rate is 12% and it
has a maturity period of 7 years. What is
the yield to maturity?

26. Problem 13
• Consider the following three firms with different growth
rates
– Firm A with a growth rate of 0%
– Firm B with a growth rate of 6%
– Firm C a super normal growth rate of 10%
• The expected EPS and DPS of each of the above firms
are Rs 5 and Rs 4 respectively. Required rate of return
from Equity is 16%
• Find the Current Stock Price, Dividend Yield, Capital
Gain Yield and P/E Ratio