 In continuation of earlier lesson on firms choice of its capital structure, let's see the relationship of risk and return with the firms leverage policy. We have seen that the value of leverage equity which was $500 in our earlier example, it did not exceed the expected value of leverage equity that was $573. Why this is so? This is because the leverage increases the risk of the equity of a firm and that is a reason the investors in the levered equity required higher rate of return to compensate the higher risk related to the levered equity. So discounting the levered equity cash flows at the unlevered equity discount rate is inappropriate. We can see that a table here which shows the return to equity with and without leverage. We can see in the red circle that the expected rate of return for the levered equity is 25% and it is 15% for the unlevered equity. The difference of 10% higher for the levered equity holders is because of the leverage that has increased riskiness for the equity holder of this particular firm. The relationship between risk and return depends upon the sensitivity of our securities return to the economy's systematic risk and this systematic risk is measured in terms of beta. So this beta represents the riskiness of the firm's returns to the macroeconomic factors in the market economy. To understand this beta we have a comparative table here where we have return sensitivity that is the systematic risk and we have the risk premium accordingly. We see that the debt has zero systematic risk so the debt has zero risk premium. Surprisingly we see that the levered equity has twice of systematic risk as of the unlevered equity. So accordingly the risk premium for the levered equity is also as twice as of the risk premium of unlevered equity. This means that the leverage increases the riskiness of the equity when there is no risk of a firm's default. This means that debt may be cheaper at its own yet it raises the cost of equity for the firm. Now if we determine in this particular case the equity cost of capital for the firm and we assume that for strong economy and the weaker economy both have equal likelihood then the expected cost of equity in this particular case is equal to 15% and that 15% is equal to the unlevered company's cost of overall capital that we had seen in our earlier lesson. If you understand the effect of leverage on the cost of equity capital we have an example here. Suppose that continuing from our previous example the company decided to borrow 200 dollars then what will be the equity value and the expected return in this particular case. We know that the value of a firm is equal to the cash flows of the firm that a firm raises from the debt and equity securities. So if we have the cash flow of the firm equal to 1000 dollars as in our previous example the 200 dollars on debt cash flows if we deduct from our cash flows of the project the equity cash flows come to the amount of 800 dollars. So next year's cash flows related to the debt at the rate of 5% rate of interest comes to 210 dollars for equity holders we have two things to compute the cash flows related to the levered equity and the return on this levered equity and in case of stronger economy we have cash flows of levered equity equal to 1190 dollars and the return in this particular case is 48.75 dollars and for strong weaker economy we have levered equity cash flows at 690 dollars and in this particular case the levered equity return comes to negative 13.75 and if we determine the expected return on levered equity using the return on equity from stronger and weaker economy the value comes to 17.5% and that is the return on levered equity return of levered equity. So we can also see that the return sensitivity of the equity equal to 62.5% and this has the sensitivity with the on levered equity at the rate of 125% of the on levered equity. Similarly, we can see the risk premium of 12.5% and it has the same sensitivity of risk premium with the on levered equity and that is again 125%. So we see that the riskiness and the return of the levered equity are the same. So this means that there is an appropriate compensation for the risk in this particular case. Now we can also determine the firm's weighted average cost of capital using the data we have in this particular scenario. Whereas the weighted average cost of capital is equal to the sum of the product of proportional date or equity with their respective cost. And if we put the values here in the model of WEG, the value comes to 15% and that 15% is again equal to the on levered cost of equity that we had seen in our earlier lesson which was 15%.