Valuation of Securities

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%.

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

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

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

Solution – 2Expected 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

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.

Solution – 3EPS 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%

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

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

Solution – 5Beta 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%

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.

Solution – 6Present 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%

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?

Solution – 7Interest 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

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

Solution – 8Interest 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%

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%.

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

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

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%?

Solution – 10Increase 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

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.

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?

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?

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