Hi everyone, our coverage of advanced valuation models focuses on three models. The dividend discount model, the discounted cash flow model, also referred to as a discounted free cash flow model, and the residual income model. Today, we will learn how to apply the residual income model. Ideally, we would like to determine a company's stock price, or market value of equity directly from the balance sheet. But it's not simple to do so, since most of the items on the company's balance sheet are not reported using market or intrinsic values. However, we can use the book value of equity as a starting point, and then add in the additional or residual value that is created when the company's earnings exceed its required rate of return. So in essence, we can estimate a company's market value of equity as its book value of equity, plus any extra value that is created. The general principle is that extra value is created whenever a company's earnings exceed the required return on its book value of equity. From a big picture standpoint, a company's goal is to generate earnings over and above some normal economic return. This normal economic return can be estimated as a return that the net assets of the business is expected to earn, given the company's required rate of return. Put differently, residual income is the amount of earnings that is left over after subtracting a required return on the company's book value of equity. This rate of return is a company's cost of equity, and if the firm earns more on its book value of equity, then the firm's market value of equity should exceed the book value. So the concept here is very plain and simple. Let's begin our walkthrough of how to implement the model. To apply the model, we must first generate an estimate of the company's book value of equity per share at the end of each year. We will do this by rolling forward the beginning book value of equity, and then adding in a forecasted amount for earnings per share, minus a forecasted dividends per share amount. This calculation will give you an estimate of the book value of equity per share at the end of the year. We will use the estimated book value of equity amounts to derive forecasts of the required return on the book value of equity. We can then derive forecasts of residual income by benchmarking the forecasted earnings per share to the required return on the book value of equity. Like our other valuation models, we should generate forecasts of residual income over a 3 to 5 year horizon. And then apply a growth rate to the final forecasted amount to derive an estimate of continuing value into perpetuity. We will then discount the forecasted residual income amounts and the continuing value to present value. To illustrate this further, the current book value of equity will be your starting point. We will then add the present value of our forecasted residual income amounts. This present value is comprised of two components. The present value of future residual income over a short horizon, and the present value of the continuing value into perpetuity. We will now formalize these steps into the following model. As depicted in the equation, the intrinsic or market value of equity at present time is equal to the current book value of equity, plus the discounted stream of future residual income, plus the discounted continuing value. We use the company's estimated cost of equity to discount the residual income forecasts over our horizon, as well as a terminal continuing value. So let's go through this step by step in more detail. First, we will identify the book value of equity in the most recent balance sheet, and convert this to a per share amount. The next step is to forecast earnings and dividends per share over or forecast horizon. We will use these forecasts to generate forecasts of future book values per share by taking the current book value per share, and adding our forecasts of earnings and dividends per share. Next, we will calculate future residual income per share by taking the earnings per share forecast, and subtracting out the required return on the book values of equity at the beginning of each forecast year. In step five, we will calculate a continuing value using the final year forecast of residual income, and a terminal growth rate. In steps six and seven, we will discount the forecast of residual to present value, and discount the continuing value to the present value. Lastly, we will sum the amounts from steps 1, 6, and 7 to arrive at the market value of equity. We will now go through a detailed example to put these steps altogether. My forecast horizon is five years from 2007 to 2011, and my amounts are depicted in dollars per share. The required rate of return or the cost of equity is 9%, and the terminal growth rate is 4.5%. The ending book value of equity from the 2006 balance sheet is $14 per share. This is essentially total shareholder's equity, divided by the number of common shares outstanding. That ending balance becomes the beginning book value of equity per share for 2007. I will then add my forecast of earnings per share, and dividends per share to arrive at a forecasted book value per share of $16.25 at the end of 2007. I will roll forward this book value forecast to get the beginning book value for 2008. I will again, add my forecast for earnings and dividends per share to arrive at a forecasted book value per share of $19.17 at the end of 2008. I will use the same roll forward process to generate the ending book values for 2009, 2010 and 2011. When I have these amounts, the next step is to compute my residual income forecast for each of the five years. So let's go back to 2007. My earnings per share forecast is $2.96, and from that I will subtract a required return of a dollar, and $0.26 on my book value of equity at the beginning of the year. I arrive at the dollar, and $0.26 cents by taking the beginning of year book value of $14, and multiplying that amount by the estimated cost of equity of 9%. When I subtract the $1.26 from the earnings per share forecast, I will get a residual income amount of $1.70 per share. The process for 2008 and onwards will be the same. For example, in 2008, I will compute a required return on the book value by taking the forecasted book value of equity of $16.25 at the beginning of the year, and multiplying that amount by 9%. I will get an amount of $1.46, which I will then subtract from my earnings per share forecast of $3.80. The residual income forecast for 2008 will therefore be $2.34. Once I have the stream of forecasted residual income per share, the next step is to convert each amount to present value by multiplying the amount by the discount rate at a cost of equity of 9%. We can use present value tables to arrive at the discount rates, or compute the rate as 1.09 to the power end. I will then sum all the present value amounts to arrive at a total present value of $7.36 for the forecasted residual income amounts. My next step is to compute the continuing value for the terminal residual income per share, and convert this to present value. Recall that my terminal residual income amount is $2.11 per share in 2011, and that the estimated terminal growth rate is 4.5%. So I will compute the continuing value as $2.11 times, 1, plus the 4.5% growth rate, and divide that by the discount rate of 9%, minus the growth rate of 4.5%. This gives me a continuing value of $48.96 per share. I will further divide this value by the discount rate in 2011 of 1.5386 to arrive at a present value of $31.82 per share. Next, I will sum the total present value of the forecasted residual income amounts, to the present value of the continuing value to arrive at a total equity value of $53.18 per share. So the estimated price per share for this company at the beginning of 2007 is $53.18. So to wrap up, the residual income model has several steps to arrive at an equity valuation estimate. These steps incorporate forecasts of earnings, dividends, and shareholders equity at the beginning of the year. So overall the model is comprehensive, it is not focused on just dividends as in the dividend discount model. It is also not focused just on cash flows, as in the discounted free cash flow model. Thus, the residual income model is a pretty solid valuation model for us to use.