A company is currently paying a dividend of ₹2 per share. The dividend is expected to grow at 15% annually for three years, then at 10% rate for the next three years after which it is expected to grow at 5% rate forever.
CS Professional · Financial, Treasury and Forex Management · PYQS · December 2016
A company is currently paying a dividend of ₹2 per share. The dividend is expected to grow at 15% annually for three years, then at 10% rate for the next three years after which it is expected to grow at 5% rate forever. What is the present value of the share if the capitalisation rate is 9%?
Answer & Explanation:
Given: Current Dividend (D 0 ) = ₹2 Growth Rate 1 (g 1 ) = 15% for Years 1-3 Growth Rate 2 (g 2 ) = 10% for Years 4-6 Growth Rate 3 (g 3 ) = 5% forever from Year 7 onwards Capitalisation Rate (k e ) = 9% (i) Present Value of Dividends during super normal growth period (Years 1-6): Year Dividend Calculation Dividend (₹) PVF @ 9% PV of Dividend (₹) 1 D 0 (1+g 1 ) = 2(1.15) 1 2.30 0.9174 2.11 2 D 0 (1+g 1 ) 2 = 2(1.15) 2 2.645 0.8417 2.22 3 D 0 (1+g 1 ) 3 = 2(1.15) 3 3.04175 0.7722 2.35 4 D 3 (1+g 2 ) 1 = 3.04175(1.10) 1 3.345925 0.7084 2.37 5 D 3 (1+g 2 ) 2 = 3.04175(1.10) 2 3.6805175 0.6499 2.39 6 D 3 (1+g 2 ) 3 = 3.04175(1.10) 3 4.04856925 0.5963 2.41 Total PV of Dividends (Years 1-6) 13.85 Present Value of Share at the end of Year 6 (P 6 ): P 6 = D 7 / (k e - g 3 ) D 7 = D 6 (1+g 3 ) = 4.04856925 * (1 + 0.05) = 4.04856925 * 1.05 = 4.2509977125 P 6 = 4.2509977125 / (0.09 - 0.05) = 4.2509977125 / 0.04 = 106.2749428125 ≈ ₹106.31 Present Value of P 6 today = P 6 * PVF 9%, 6 Years PV of P 6 = ₹106.31 * 0.5963 = ₹63.39 Total Present Value of the Share (P 0 ): P 0 = Total PV of Dividends (Years 1-6) + PV of P 6 P 0 = ₹13.85 + ₹63.39 = ₹77.24 The present value of the share is ₹77.24.
Topics: Dividend Valuation Models
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