Where is the dividend payout ratio, is the growth rate in earnings/dividends, is the cost of g k ρ capital, and are earnings from continuing operations per share in period Furthermore, we Yt t. need the condition, > to hold. Assume we are standing at time an instant prior to the k g, t – Δt, earnings announcement at and that investors have a forecast of time t earnings, E[Yt | t, It-Δt], | denotes expectation conditional on the information set, given by E[Yt | = Is] Is, It-Δt] where E[• Realized earnings at are then given by (2) below: Yt-1(1+g). t (2) Where is the error in the forecast of Once is announced at time then the uncertainty Yt. Yt t, Ɛt over is resolved and E[Yt | = . If we now move forward and consider the expectation of Yt It] Yt Yt+1 conditional on the information available just prior to time E[Yt+1 | = t+1, It+1-Δt] = In other words, the time earnings surprise, also Yt-1(1+g)2 + (1 + g). t Ɛt Ɛt, propagates through time, growing at the same constant rate, per period. Assuming that the g earnings surprise does not change beliefs about and then the change in stock k, g, investors’ ρ, price due to the earnings surprise will be given by: (3) This represents the capitalization of the propagation of the earnings surprise through time, where future earnings are discounted at the cost of capital, k. If we now divide both sides by the firm’s pre-announcement stock price, we have an expression relating announcement period Pt-Δt, returns to unexpected earnings: (4) where is the ERC. Earlier I asserted that of differences in earnings γ investor’s perceptions quality would manifest themselves in perceptions of earnings growth, (an increasing function g of earnings quality), and earnings riskiness, (a decreasing function of earnings quality). How k
Where ρ is the dividend payout ratio, g is the growth rate in earnings/dividends, k is the cost of capital, and Yt are earnings from continuing operations per share in period t. Furthermore, we need the condition, k > g, to hold. Assume we are standing at time t – Δt, an instant prior to the earnings announcement at t, and that investors have a forecast of time t earnings, E[Yt | It-Δt], where E[• | Is] denotes expectation conditional on the information set, Is, given by E[Yt | It-Δt] = Yt-1(1+g). Realized earnings at t are then given by (2) below: (2) Where Ɛt is the error in the forecast of Yt. Once Yt is announced at time t, then the uncertainty over Yt is resolved and E[Yt | It] = Yt . If we now move forward and consider the expectation of Yt+1 conditional on the information available just prior to time t+1, E[Yt+1 | It+1-Δt] = = Yt-1(1+g)2 + Ɛt (1 + g). In other words, the time t earnings surprise, Ɛt, also propagates through time, growing at the same constant rate, g per period. Assuming that the earnings surprise does not change investors’ beliefs about k, g, and ρ, then the change in stock price due to the earnings surprise will be given by: (3) This represents the capitalization of the propagation of the earnings surprise through time, where future earnings are discounted at the firm’s cost of capital, k. If we now divide both sides by the pre-announcement stock price, Pt-Δt, we have an expression relating announcement period returns to unexpected earnings: (4) where γ is the ERC. Earlier I asserted that investor’s perceptions of differences in earnings quality would manifest themselves in perceptions of earnings growth, g (an increasing function of earnings quality), and earnings riskiness, k (a decreasing function of earnings quality). How
065-Tom%20Nohel-LDC%20Bank%20earnings%202012.docx