 It is interest expense that creates the interest tax shield for a levered firm. Now to determine the value of interest tax shield for the purpose of determining overall value of the firm, we need to compute the present value of all the streams of the annual interest tax yields, how it can be determined, we can see it with the help of an example. We know that a levered firm pays cash flows to its investors more than the cash flows provided to its investors by an unlevered firm and these are the cash flows in the form of interest tax shields that a levered firm can give to its investors but an unlevered firm cannot. So this means that the levered firms cash flows to the investors are the sum of the unlevered cash flows to the investors plus the interest tax shields. This equation can be pictured with the help of a diagram where we see the cash flows of an unlevered firm in the form of a bit depicted in a block colored in green and in the next we have unlevered earnings in blue and the corresponding tax in the pink but if the firm is levered then this tax is split into two forms. A considerable portion is paid to the investors in the form of interest tax shield so that a part of tax paid to the investors of the levered firm in the form of interest tax shield which is not available to the investors of an unlevered firm. This means that the interest payment which are paid to the firms investors reduces the firm's tax obligations and this reduction in the tax obligation which is a gain for the investors of the firm date reduction or saving is termed as the interest tax shield. We know that the cash flows of a levered firm are equal to the sum of the cash flows of an unlevered firm plus the interest tax shield and the law of one price says that if it is true then the same must be true for the present value of these cash flows so modifying little the mm1 proposition with the presence of taxes it can be said that a levered firm's total value exceeds over the unlevered firm's value owing to the present value of the interest tax shield this means that the value of levered firm is equal to the sum of value of unlevered firm and the present value of the interest tax shield. Now this tax saving or the interest tax shield benefit depends upon the amount of debt the amount of interest payment and the debt period. Now how to determine the value of interest tax shield we have an example where we have loan value of 2 billion dollars annual interest payment of 100 million dollars time period of the debt is 10 years and marginal tax rate is 35 percent we have real risk free rate of interest of 5 percent so the interest tax shield will be the product of annual interest payment multiplied by the corporate tax rate so corporate tax rate is 35 percent and the annual interest payment is 100 million dollar the interest tax shield comes to 35 million dollar these are the annual interest shields if we want to determine the present value of these interest shields we need to apply the formula of annuity and that annuity formula is applied here where we have to multiply the annual interest tax shield with the present value of interest factor of annuity at 5 percent for 10 years at this gives us the value of 270 million that 270 million dollar is the present value of the interest tax shield. Note that we have not used the amount of debt in this computation of present value of interest tax shield because from a counting point of view the loan amount is not deductible only the interest expense is allowed to deduct from the earnings and what will happen if we want to determine the interest tax shield with the existence of permanent debt till now we are assuming that the interest tax shields based on interest rates tax rates the amount of debt and the period of debt are certain but in practice these are rarely certain rather these are generally uncertain because firms interest payments vary due to changes in three things like firms policy on its outstanding debt rate of interest on the firm's debt and the risk of firms default in paying interest payment to the debt holders also a firm's marginal tax rate can also influence due to the changes in the firm's tax code or the tax rate and the firm's income bracket so these are the factors that can have a considerable effect on the interest tax shield of a particular firm generally firms try to retain a debt on permanent basis and they like to pay interest there on an annual basis so this means that they exist a permanent sort of debt the firm like to maintain in its balance sheet more realistically taking example of short term debt a firm likes to pay its short term debts with newer issuance of another short term debt this means that this principal amount of short term debt will never be paid rather it will be refinanced once the existing debt is likely to be matured this means that effectively it is a permanent debt generally a large firm a large firm's balance sheet carry permanent debt as in the form of certain amount of debt every year and from year to year it is carried on as a firm's business policy this is known in fact this the firm borrows new debt to pay the existing all or the older debt the assumption behind this debt policy is that the firm maintains a fixed amount of debt on its balance sheet rather than the amount that varies from year to year or from on its every debt contract now we have an example to understand the valuation of interest tax shield in the presence of permanent debt we assume that a firm borrows risk-free debt stabilized by the capital D in order to keep it permanently in its balance sheet the firm's marginal tax rate is the C and the risk-free interest rate is equal to RF now the yearly interest tax shield is the product of corporate tax rate risk-free rate RF and the amount of debt which is D now if we determine the present value of this interest tax shield we need to determine the amount of to discount the amount of interest over the risk-free rate this means that we need to develop a formula carrying the corporate tax rate with the multiplication of annual interest expense and divided by the risk-free rate now the interest is the product of RF or the risk-free rate and the capital D now so cancelling the RF the resulting amount is equal to the C or the capital rate and the debt so simply the present value of interest tax shield on permanent debt is equal to the product of the corporate tax and the amount of debt the this computation assumes that the debt is risk-free and the RF or the risk-free rate is constant throughout the debt period and if we assume that the debt is fairly priced in the open market then the market value of debt is the product of the present value of the interest expenses or the future interest payments now if a firm has constant marginal tax rate then the value of the interest tax shield for a permanent rate debt will be equal to the present value of the corporate tax rate as a product of the future interest payment this means that the present value of the interest tax shield on permanent debt is the product of the corporate tax rate and the future interest payment and by solving this equation we can reduce it to the product of corporate tax rate and the amount of debt or the D now the implication of this new equation is that the product of corporate tax rate and the debt shows magnitude of the interest tax shield this means that for a 30% corporate tax rate this means that for every $1 in the newer amount of debt the firm value will be increased by every 35 cents