 We see that leverage may not affect the vague for a pump because low cost of debt may exactly be offset by higher cost of equity and as a result there is no net benefit for the pump and the vague may remain constant for the pump Now how to compute vague for multiple securities For this we have an example where we have equity of $440 debt of $500 and warrants of $60 only The cost of debt is 5% and the weighted cost of warrants or the return on warrants is 75% whereas the return of levered equity is equal to 18.18% To determine the return on levered equity we have an additional computation where we have to calculate first the expected value of payoffs on the equity and using these payoffs we have determined the return on equity which is 18.18% Now we have to determine the proportional weights of the equity debt and the warrants Then we are multiplying the individual securities return with the securities computed weight and this will give us the weighted cost of debt particular security as then in the end we sum up the weighted cost of the three securities and the resulting cost is termed as the vague and that vague for these three securities is equal to 15% Now what is levered and its relation with unlevered betas We know that a firm's unlevered beta or its assets beta is the weighted average of its equity beta and its debt beta This means that beta of unlevered firm is the sum of its proportional equity beta and its proportional debt beta Now this unlevered beta measures the market risk and this unlevered beta can also be used as proxy for other firms A change in capital structure without changing the investment pools does not change the unlevered beta of the firm because its equity beta will change to reflect the change of capital structure on its risk This means that the beta of equity will be the sum of unlevered beta plus the additional beta due to the leverage effect and this means that the beta of equity in this particular case or the levered beta may also increase with the leverage in the firm We have an example to understand this unlevered and levered betas We have equity beta of 0.8 debt equity ratio of 0.1 We have debt beta equal to 0 So how the asset beta would be We have the model of unlevered beta which is equal to the proportional equity beta and the proportional debt beta using this value In this model we have the asset or unlevered beta equal to 0.73 Now assume that we have debt equity ratio of 0.5 Increase from the earlier of 0.1 So what will be the equity beta Now we have a little change to our unlevered beta Now the equity beta or the levered beta will be equal to the unlevered beta plus the additional beta due to the debt as multiplied by the debt equity ratio Now when we are putting the values into this model the levered beta is equal to 1.09 So there is an increase in the unlevered beta due to the leverage effect This means that the levered beta de-cost of equity and the debt beta will be increased as the firm is increasing its leverage So is there any effect of cash on the firm's cost of capital Now cash and other marketable securities are treated as a risk pre-assert for the firm and because they reduces the required risk premium on the firm's assets This means that excess cash holding has an opposite effect of the leverage on risk and return on the firm's securities This means that the additional cash holding and the marketable securities are viewed as a negative debt for the particular firm If we are to determine the firm's enterprise value we can determine its enterprise value by deducting its cash holding and marketable securities from its overall value or the total value This means that we have to take in fact the net debt of the firm to determine its enterprise value and to determine this net debt we need to deduct its excess cash holding and other marketable securities from the firm's total debt Now we have an example to understand this phenomenon of cost of capital and the excess cash holding We have market capitalization of 140 billion debt 25.4 billion cash and other short-term investments by 60.4 billion equity beta 1.09 debt beta we assume 0 risk period is 2% market risk premium we assume 5% So we need to determine the enterprise value and the return of the unlevered firm To determine the enterprise value we need to deduct the net debt from the market value of the firm Market value of the firm is 140 billion Now to determine the net debt we need to deduct the cash investment of 60.4 billion from its debt value of 25.4 billion The resulting enterprise value is 105 million Now the other computation is the unlevered cost of capital for the unlevered equity cost Now we put the given values into the model of the unlevered cost of equity The resulting value is 9.25% So this means that as we are decreasing our debt then the unlevered cost of debt has also decreased