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MBA & MBA – Banking and Finance (Term-IV) Course : Security Analysis and Portfolio Management Unit II: Valuation of Securities Valuation of equity shares Motives for investing in equity Ownership and Control Periodic gain and appreciation SINGLE-PERIOD VALUATION MODEL It is the case where the investor expects to hold the equity share for one year. The present value of the equity share will be: Po = D1 (1+r) + P1 (1+r) Where Po = present value of the equity share D1 = dividend expected a year hence P1 = price of the share expected a year hence r = rate of return required on the equity share PROBLEMS Prestige’s equity share is expected to provide a dividend of Rs 2.00 and fetch a price of Rs 18.00 a year hence. What price would it sell for now if investors’ required rate of return is 12 percent? The stock of ABC Limited is expected to provide a dividend of Rs 4.00 and fetch a price of Rs 40 a year hence. What price would it sell for now if the investor’s required arte of return is 15%? ZERO GROWTH MODEL It is assumed in this model that the dividend per share remains constant year after year for ever. Po = D + D + (1+r) (1+r)2 D + (1+r)n On simplification, it becomes: PO = D r PO= Present Value/Intrinsic Value D = Dividend per share r = required rate of return …...∞ PROBLEM An equity stock is expected to earn dividend at the rate of Rs. 6 per share annually for ever. What is the worth of the stock today if the investors’ required rate of return is 10%. CONSTANT GROWTH MODEL In this model, the basic assumption is that dividends will grow at the same rate (g) for an indefinite period. P0 = D(1+g) + D(1+g)2 + D(1+g)3 +…+ D(1+g)N …∞ (1+r) (1+r)2 (1+r)3 P0 = D1 r–g P0 = Present value of stock D = Dividend paid during last year D1 = Dividend expected one year hence r = Required rate of return g = rate of growth of dividend (1+r)N PROBLEMS The ABC company’s next year dividend per share is expected to be Rs 3.50. the dividend in subsequent years is expected to grow at a rate of 10% per year forever. If the required rate of return is 15% per year, what should be its price? The share of a certain stock paid a dividend of Rs. 2.00 last year. The dividend is expected to grow at a constant rate of 6 per cent in the future indefinitely. The required rate of return on this stock is considered to be 12 per cent. How much should this stock sell for now? Assuming that the expected growth rate and required rate of return remain the same, at what price should the stock sell 2 years hence? TWO STAGE GROWTH MODEL The growth stages are divided into two, namely – a period of extraordinary growth (or decline) and a constant growth period of infinite nature. The extraordinary growth period continues for some period followed by the constant growth rate. Present Value of stock = Present Value of dividend during above-normal growth period + Value of stock price at the end of above-normal growth period discounted back to present TWO STAGE GROWTH MODEL (contd) P t D (1+g ) O = 0 s ∑ t=1 (1+rs)t N + DN+1 X 1 (rs –gn) (1+rs)N P0 = Present Value/Intrinsic Value D0 = dividend of the previous period gs = above normal growth rate gn = normal growth rate rs = required rate of return N = period of above normal growth PROBLEMS Sigma Company limited paid a cash dividend of Rs. 0.71 per share last year. The dividend is expected to increase by 15 percent a year for ten years and thereafter at 10 percent a year indefinitely. If a stockholder’s required rate of return is 16 percent, what is the fair price of this Company’s stock? Determine the intrinsic value of an equity share, given the following data: Last year dividend (D0) : Rs. 2.00 Growth rate for the next 5 years : 15 percent Growth rate beyond 5 years : 10 percent The required rate of return is 18 percent. The Commonwealth Corporation’s earnings and dividends have been growing at a rate of 12 per cent per annum. This growth rate is expected to continue for 4 years. After that the growth rate will fall to 8 per cent for the next 4 years. Beyond that the growth rate is expected to be 5 per cent forever. If the last dividend per share was Rs. 1.50 and the investors’ required rate of return on the stock of Commonwealth is 14 per cent, how much should be the market value per share of Commonwealth Corporation’s equity stock? PROBLEMS Vardhaman Limited’s earnings and dividends have been growing at a rate of 18 per cent per annum. This growth rate is expected to continue for 4 years. After that the growth rate will fall to 12 per cent for the next 4 years. Thereafter, the growth rate is expected to be 6 per cent forever. If the last dividend per share was Rs. 2.00 and the investors’ required rate of return on Vardhman’s equity is 15 per cent, what is the intrinsic value per share? The equity stock of Max Limited is currently selling for Rs. 32 per share. The dividend expected next is Rs 2.00. The investors’ required rate of return on this stock is 12 percent. Assume that the constant growth model applies to Max Limited. What is the expected growth rate of Max Limited? Fizzle Limited is facing gloomy prospects. The earnings and dividends are expected to decline at the rate of 4%. The previous dividend was Rs 1.50. If the current market price is Rs 8.00, what rate of return do investors expect from the stock of Fizzle Limited? MULTIPLE YEAR HOLDING PERIOD If the holding period of the stock is more than one year, the following formula is used: P=[ n] [(e )(d/e)] (1+g) 0 ∑ n=1 (1+r)n N + [ (P/E)(e0) (1+g)N+1] (1+r)N g = annual expected growth in earnings, dividends and price e0 = most recent earnings per share d/e = dividend pay out r = required rate of return P/E = price-earnings ratio N = holding period in years PROBLEMS Following is the data relating to a stock of Olsen Company for five years: Annual expected growth in earnings, dividends and price= 6% Recent Earnings per Share = Rs 1.886 Dividend payout = 50% Required rate of return = 10% Price-Earnings Ratio = 12.5 Holding period in years = 5 Calculate the present value of the stock using the Multiple year holding period model. PROBLEMS The Grace and Co has common shares outstanding in the market with price earnings ratio of 15. The annual expected growth in earnings, dividends and price is 7 percent. The earnings per share is Rs. 2.5, the dividend payout is 60% and the investor wants to hold the stock for 4 years. The required rate of return is 15 percent. What would be the present value?