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. If the share is held for three years, what shall be its present value?
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% (ii) If the share is held for three years, what shall be its present value? If the share is held for three years, the investor receives dividends for years 1, 2, and 3, and then sells the share at the end of year 3. The present value of the share today (P 0 ) will be the sum of the present value of these three dividends and the present value of the share price at the end of year 3 (P 3 ). 1. Present Value of Dividends for Years 1, 2, and 3 (from part i): PV of D 1 = ₹2.11 PV of D 2 = ₹2.22 PV of D 3 = ₹2.35 Total PV of Dividends (Years 1-3) = ₹2.11 + ₹2.22 + ₹2.35 = ₹6.68 2. Present Value of Share Price at the end of Year 3 (P 3 discounted to Year 0): The share price at the end of Year 3 (P 3 ) represents the present value of all future dividends from Year 4 onwards, discounted back to Year 3. To find its present value at Year 0, we discount P 3 further back to Year 0. Following the logic from part (i), the present value of all dividends from Year 4 to Year 6 (₹2.37 + ₹2.39 + ₹2.41) and the present value of the terminal value at Year 6 (₹63.39), all discounted to Year 0, sum up to ₹70.56. This ₹70.56 represents the present value at Year 0 of the share's value at the end of Year 3 (P 3 ), which is then sold. 3. Total Present Value of the Share (P 0 ): P 0 = (Total PV of Dividends Years 1-3) + (PV of P 3 at Year 0) P 0 = ₹6.68 + ₹70.56 = ₹77.24 Thus, the value of the share is ₹77.24, which is the same as if the share is held indefinitely. This is expected, as the present value of a share should not depend on the holding period if it is sold at its intrinsic value.
Topics: Dividend Valuation Models
Related Questions in this Topic
- A company is currently paying a dividend of ₹2 per share. The dividend is expected to grow at 15% annually for three yea...
- Current price of share of a company is ₹60 and dividend per share is ₹4. If its capitalisation rate is 12%, what is the ...
- The following annual figures relate to M Ltd. ₹ Sales (with two months' credit) 36,00,000 Materials consum...
- PQ established the following spread on the AB Corporation's stock: Purchased one 3-month call option with a premium of ...
- The following particulars about four corporate securities (shares) are available: Security Today's Price (₹) Predic...