 To determine the worth of interest tax shields, we need to compute present value of all the future streams of the interest tax shields a firm receives every year. Now let's see how interest tax shield will behave for a firm that has a target debt equity ratio for a firm that is a levered firm and there exist the corporate taxes. In for a for such a firm, the leverage allows tax benefits for its vague because it reduces the cost of debt or the of the firm with tax deductibility of the interest expense the effective after tax cost of debt can be computed by multiplying the corporate rate and multiplying by the interest rate with the differential of 1 minus the corporate tax rate and for a firm without taxes its vague is simply the sum of the return that is available to its investors in line with the riskiness of the firm's assets. This means that return or the vague for such firm is equal to the proportional cost of equity and the debt. Now if there exist some corporate taxes then the vague after tax will be computed and to determine the after tax vague or the our vague we need to multiply 1 minus corporate tax rate with the proportional rate of the cost of debt of the firm this way the cost of debt of the firm will be reduced by the corporate tax rate and the resulting overall cost of capital or the vague will be termed as the after tax vague of the firm. The our vague are the after tax vague is the firm's effective cost of capital once the benefit of interest tax shields are adjusted into the cost of debt of the firm. Now there exist also some relationship between the after tax vague and the firm's pre-tax vague and that relationship can be understood with the help of an equation where our vague is the difference between the pre-tax vague and the interest tax shield. So higher the interest tax shield the lesser would be the after tax vague and accordingly. If the taxes affirms target leverage ratio does not affect its vague because the that is the reason that any firm with higher leverage can better exploit the more tax advantage of debt in order to lower its cost of capital or the vague. Now how the vague will move with and without corporate taxes to understand this issue we have a diagram on the screen where the red curve shows the equity cost of capital and the thick blue curve shows the after tax cost of debt capital and the debt cost of capital is simply the blue dotted line and by using the interest tax shield it is reduced to a certain amount as we can see in the form of thick blue line. And where we see the pre-tax vague or the unlivered cost of capital that is simply the firm's required rate of return which is based on the riskiness of its assets and that we see in the form of a constant which has horizontal yellow dotted line but whereas the effective cost of debt or the after tax cost of capital or vague is concerned it declines with the interest tax shield and that we see here in the form of thick yellow line which is showing decreasing trend. Now high interest tax shield will behave where the firm has a target debt equity ratio. We see that many of the firms like to maintain a specific debt equity ratio instead of maintaining a constant amount of debt every year. This policy allows a firm to grow its debt or shrink its debt in line its size. By adjusting debt over the time allows debt equity ratio to maintain at a certain level this means that this policy also allows the firm to maintain its debt equity ratio at a constant level and such firm's value or the VL can be determined by discounting its pre cash flows over the firm's cost of capital and whereas the present value of interest tax shield for such livered firm is concerned it is based on the discounting of the differential pre cash flows of a livered firm by discounting them over the firm's cost of capital whereas this firm's cost of capital will be treated as the unlivered cost of capital and by differential interest tax differential cash flow means the difference between the livered firms cash flows and the unlivered firms cash flows. Now we have an example to determine the interest tax shields where we have expected future free cash flows of 4.2 million dollars free cash flows growth rate is 4 percent equity cost of capital is 10 percent equity debt cost of capital is 6 percent and the corporate tax rate is 35 percent the debt equity ratio that the firm is maintaining is 0.5. What will be the value of interest tax shield as I have earlier said that the value of interest tax shield is basically the present value of the interest tax shield and to determine this present value of interest tax shield we need to determine the difference between the value of a livered firm and the value of an unlivered firm here we have the value of livered firm equal to 107 dollars and the unlivered firm value is 91 dollars so the difference of 16 million is termed as the present value of the interest tax shield. Now going into further how we determine the value of livered firm in this particular scenario livered firms present value can be determined by discounting its free cash flows over the difference between its VEC and the growth rate and we get the answer of 107 million dollars to determine the present value of the unlivered firm we need to divide or discount the free cash flows over its unlivered cost of capital and the growth rate so the free cash flows of the firm are divided over the difference between unlivered VEC and the firms growth rate that we have 91 million dollars so in this way the differential cash flows for both of the firms give the present value of the interest tax shield.