Example on page 15 of chapter 12 CT1 - A French investor, who is taxed at 35% on income, has just purchased 500 shares in a small education company ex-dividend. Dividends are paid annually and the next dividend is due in one month’s time. The last dividend was 8 euros per share and dividends are expected to rise by 4% pa. Calculate the price paid by the investor if the expected yield is 12% pa effective. Solution The investor does not receive the dividend due in one month because the shares are purchased ex-dividend. I understand that for ex-dividends the next dividend is not paid. Shouldn't the present value of the shares in one months time be 500(8 x 1.04^2 x (1-0.35) v^2 + 8 x 1.04^3 x (1-0.35) v ^ 3 +....) instead of 500(8 x 1.04^2 x (1-0.35) v + 8 x 1.04^3 x (1-0.35) v ^ 2 +....) Thanks in advance Bijal
Why would that be true? If the dividend in one months time is not included, and they are payed annually the investor will get the (last) dividend inflated by 2 years and discounted by one year since it will be a year after the dividend which was not payed. = 500*5.2((1.04^2)*v + (1.04^3)*v^2 + ..... = 5.2*500v(1.04^2) [1+(1.04v) + (1.04v)^2 + ...
On the same example, how does 500V^1/12(8 x 1.04^2 x 0.65v + 8 x 1.04^3 x 0.65v^2 +...) simplify to 500v^1/12[(8 x 1.04^2 x 0.65v)/1-1.04v)]? At first I thought it was by geometric progression formula but there isn't a minus sign on the top line so it can't be that. How do you get that? I understand how to work out the answer using annuities though.
If the first term sums to infinity, there is the standard GP "sum to infinity" formula. a/(1-r); |r|< 1
The last dividend was €8 and so next dividend (which is due in one month's time) is €8×1.04, which the investor doesn't receive due to ex-dividend. So, the first dividend which the investor will receive should be €8×1.04². Hope this helps.
