Pure Play Model

Hi friends,

My question is very specific and I have been pondering on a certain point which is very specific.

Just for recapitulation, suppose I am the owner of a firm and I want to start a business in a project which belongs to a field where my group has not ventured into before. Before starting out, I need to find out the Beta(risk) of the new project (so that I can set my return expectations, find out the cost of capital using CAPM, etc)

As per the Pure Play Model to estimate the Beta, we first consider a firm which works purely in the field of the project (i.e. does not do work in other fields) . I take the Beta of that firm as an estimate. If that firm has leverage(has taken on debt) we deleverage the beta (remove the effect of the equity multiplier). With this deleveraged beta, we estimate our project’s beta by multiplying the effect of leverage in our firm.

My question pertains to the Equity multiplier. Why is it [1/1+{(1-t)d/e}] and not simply [1/1+ (d/e)] ? Can anyone prove mathematically (please don’t quote Ramada’s original work of 1972; I don’t have the tenacity to go through it 😛 ) or illustrate with a simple numerical example why the former is chosen over the latter as the equity multiplier ? I have read the explanation for the differentiating (1-t) term in the curriculum and as well as the Schweser notes. Although I do understand why the (1-t) term is multiplied with d (debt) in the WACC(Weighted Average Cost of Capital) formula, I am failing to convince myself how exactly the (1-t) comes in the equity multiplier.

Thanks a ton to anyone who had the patience to read this! 😀 And if you can help me out then I’ll be all the more grateful! 🙂
Ron