Question Five Amco Pty Ltd just paid a dividend of $0.20 per share. Looking forward, this dividend is expected to grow at 15% per annum for three years, then at 10% per annum for the next three years, after which it is expected to grow at a 5% per annum forever (assume all dividends are paid at the end of the year). i. What is the price you would pay for the share if your required rate of return is 10% per annum? The price of a share is given by the present value of the expected dividend stream. d + + d d d ds d (1+r) (1+r) (1+r) ' (1+r)* ' (1+r) (1+r)' (r-g) d6 + + + (1+r) The expected dividend stream, using expected growth rates, is: Thus the price of a share is: d = 0.2(1.15)=0.23 d = 0.23(1.15) = 0.2645 d = 0.2645(1.15)=0.3042 d = 0.3042(1.10) = 0.3346 d = 0.3346(1.10) = 0.3681 d=0.3681(1.10) = 0.4049 d = 0.4049(1.05)= 0.4251 0.23 0.2645 0.3042 0.3346 0.3681 0.4049 0.4251 P = + + + + + + (1+0.10) (1+0.10) (1+0.10) (1+0.10) (1+0.10)5 (1+0.10)6 (0.10-0.05) = $6.14 (1+0.10) -6 ii. Would the price change if you expected to hold the share for only three years? No, the price would not change if you expected to hold the share for only three years. Since the price over three years is the present value of the cash flows relating to the share, the solution is the present value of the three years of dividends plus the price at year 3. Therefore, the price remains $6.14. From above the expected price at the end of period 3, P3 = $7.30. Thus the price of the share is the present value of the sum of the dividends to be received and the price prevailing at the end of period 3. d d2 d3+P3 Po = + + (1+re) (1+re) (1+re) 0.23 0.2645 0.30427.30 = + + (1+0.10) (1+0.10) (1+0.10)3 = $6.14