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Valuation of Securities

Q.1. A bond of Rs. 1,000 bearing a coupon rate of 12% is redeemable at per in 10 years. Find out the value of the bond if:
(i) Required rate of return is 12% or 10% or 14%.
(ii) Required rate of return is 12% and the maturity period is 8 years or 12 years.
(iii) Required rate of return is 12% and redeemable at Rs. 950 or at Rs. 1,050 after 10 years.
Ans. (i) 1,000, 1123.40, 895.92. (ii) 907.68 // 887.20. (iii) 983.90 // 1016.10.

Q.2. A bond of Rs. 1,000 bearing a coupon rate of 12% p.a. payable half-yearly is redeemable after five year at par. Find year at par. Find out the value of the bond given that the required rate of return is 14%.
Ans. 929.

Q.3. A bond of Rs. 10,000 bearing coupon rate 12% and redeemable in 8 years at par being at Rs. 10,600. Find out the YTM of the bond.
Ans. 10.92%.

Q.4. A firm pays a dividend of 20% on the equity shares of face value of Rs. 100 each. Find out the value of the equity share given that the dividend rate is expected to remain same and the required rate of return of the investor is 15%. 
Ans. 133.33.

Q.5. A firm is paying a dividend of Rs. 1.50 per share. The rate of dividend is expected to grow at 10% for next three years and 5% thereafter infinitely. Find out the value of the share given that the required rate of return of the investor is 15%. 
Ans. 21.

Q.6. A firm pays a dividend of Rs. 1.50 with a growth rate at 7%. The risk-free rate,If’ is 9% and the market rate of return, km’ is 13%. Presently, the firm has a B, beta factor of 1.50. However, due to a decision of the finance manager, B is likely to increase to 1.75. Find out the present as well as the likely as the likely value of the share after the decision.
Ans. Ke – 15%, Po - 18.75% Ke – 16%. Po - 16.67.

Q.7. A Rs. 1,000 bond matures in 20 years and offers a 9% coupon rate. The required rate of return is 11%. Compute the bonds’s value. 
Ans.  840.67.

Q.8. A Rs. 5,000 with a 10% coupon rate matures in 8 years and currently sells at 97%. Is this bond a desirable investments for an investor whose required rate of return is 11%.
Ans. P.V 4,743, Sale Price – 5000 x 97% = 4,850.

Q.9. The Elu Co. is contemplating a debenture issue on that following terms:

Face Value = Rs. 100 per Debenture
Term to Maturity = 7 years
Coupon rate of Interest:
Years 1-2 = 8% p.a.
3 – 4 = 12% p.a.
5 – 7 = 15% p.a.

The current market rate of interest of 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. Determine the issue price. Assume the redemption on debenture at a premium of 5%.
Ans. 82.93

Q.10. Zed Ltd. has just paid a dividend of Rs. 13 per share. As a part of its major reorganization of its operations it has stated that it does not intend to pay any dividend for the next two years. In three time it will commence paying dividend at Rs. 10 per share and the Directors have indicated that they expect to achieve dividend growth at 12% p.a. thereafter.
If the reorganization does not take place, dividend will be paid in the next two years and the expected dividend growth will remain at the present level of 6% p.a. The firm’s cost of equity is 18% (i.e., the return expected by the equity investors) and will be unaffected by the reorganization. Calculate the value of firm’s shares in both the situations.
Ans. If g is 6% Then Po = 114.83, if g is 12% - 1666.67 but P.V. – 119.70.

Q.11. A firm has paid dividend at Rs. 2 per share last year. The estimated growth of the dividends from the company is estimated to be 5% p.a. Determine the estimated market price of the equity share if the estimated growth rate of dividends (i) rises to 8% and (ii) falls to 3%. Also find out the present market price of the share, given that the required rate of return of the equity investors is 15.5%.
Ans. 20 / 28.80 / 16.48.

Q.12. A company has a book value per share of Rs. 137.80. Its return on equity is 15% and it follows a policy of retaining 60% of its earnings. If the opportunity cost of capital is 18%, what would be the price of the share today?
Ans. g = 9%, and Po = 91.90.

Q.13. A mining company’s iron ore reserves are being depleted, and its cost of recovering a declining quantity of iron ore are raising each year. As a sequel to it the company, earnings and dividends are declining, at a rate of 8% per year. If the previous year’s dividend, (Do) was Rs. 10 and the required rate of return is 15%, what would be the current price of the equity share of the company? 
Ans. Price = Rs. 40.

Q.14. The current price of a company share is Rs. 70. The company is expected to pay a dividend of Rs. 4.20 per share increasing with an annual growth rate of 5%. If an investor’s required rate of return is 105, should he buy the share 
Ans. Ke is 11%, the share may be parched.

Q.15. ABC company had sold 1,000 12% perpetual debentures 10 years ago. Interest rates have since then son that, debentures of this company are now selling at 15% yield basis.
(i) Determine the current indicated / expected market price of the debentures. Would you buy the debentures for Rs. 700?
(ii) Assume that the debentures of the company are selling at Rs. 825. If the dentures have 8 years to run to maturity, compute the approximate effective yield an investor would earn on his investment?

Ans. Expected Market Price is Rs. 800. Effective Yield is approx. 16%.

Q.16. A company is currently paying a dividend of Rs. 2.00 per share. The dividend is expected to grow at a 15% annual rate for three years then at 19% rate for the next three years, after which it is expected to grow at a 5% rate forever, (a) What is the present value of the share if the capitalization rate is 9%? 
Ans. PO = 77.20.

Q.17. A large-sized chemical company has been expected to grow at 14% per year for the next 4 year and then to grow indefnitely at the rate 5%. The required rate of return on the equity shares is 12%. Assume that the company paid a dividend of Rs. 2 per share last year (Do =2). Determine the market price of the shares today. 
Ans. Price = Rs. 40.62.

Q.18. A chemical has been growing at a rate of 18% per year in recent. The abnormal growth is expected to continue for another 4 years; then it is likely to grow at the normal rate (gn) of 6%. The required rate of return on the shares of the investment community is 12%, and the dividend paid per share last year was Rs. 3 (Do = Rs. 3). At what price, would you, as an investor, be ready to buy the shares of this company (t = 0), and at the end of the years 1, 2, 3, 4 respectively? Will there be any extra advantage by buying shares at t = 0, on in any of the subsequent four years, assuming all other things remain unchaged?
Ans. P4 is Rs. 102.82, Po Rs. 79.12 i.e., P4 + PV of D1 to D4. Similarly, P1 = Rs. 85 approx, P2= Rs. 91 approx and P3 = Rs. 97 approx. No extra advantage of buying shares at these price.

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