Cost of capital after = 0.092/(1+.1375) =8.09%2. Computed change in firm value incorrectlyCost of equity after = 10.48%3. Did not use after-tax cost of debtCost of debt after = 4.5%4. Other math errors.
Sheet1Page 310.48% (1-X) + 4.5% (X) = 8.09%Solving for X,X = 40%32.6086956Problem 3Duration of assets =7Common errorsExisting Debt =1(duration of this debt = 4 years)1. Misread the problem to read change by instead ofNew Debt =3change to.(1/(1+3)) (4) + (3/(1+3)) X = 7! Since the asset mix does not change, the duration remains 72. Tried to change asset duration (why?)Solving3. Set up new debt incorrectly (had two unknowns withDuration of new debt =8one equation)Proportion on new debt that has to be 2 year debt =25%(.25(2) + .75(10) = 8)4. Other errors.Spring 2001Problem 1a. Current Cost of Equity =10.72%! 5% + 1.04*5.5%! If you decide to use the effective tax rate, the rationaleCurrent cost of debt =3.90%has to be that you do not have enough operating income to cCurrent cost of capital =8.47%! 10.72% (.67) + 3.9% (.33)However, this will mean that the effective tax rate should be If you did this, I gave you full credit.b. New debt to capital ratio =50%New debt to equity ratio =100.00%! I gave full credit if you read the increase as 0.25%Unlevered Beta =0.8of the existing interest rate (I did take off half a pointNew Beta =1.28if you read it as 25%New cost of equity =12.0400%! You lost a point if you did not unlever and relever betasNew after-tax cost of debt =4.05%New Cost of capital=8.05%c. Number of shares bought back =21.7391304! Since the price at which you were buying back the stock wac. Change in annual financing cost =$6.30cannot divide by the total number of shares outstanding.Change in firm value =$78.26Change per share =$0.58! Transfer of wealth to stockholders selling back stock = (11.Problem 2Market value of the firm =2000! 1000/.5Dollar debt at optimal of 25% =500! Don't increase the size of thDuration of debt at optimalLet X be the proportion of the debt that is 5-year debt at optimalX (4) + (1-X) (8) = 7X = .25The firm has to have $ 125 million in 5-year debt and $ 375 million in 10-year debtIt needs to pay off $ 275 million of 5-year debt and $ 225 million of 10 year debt.Spring 2002Problem 1Part a: Current cost of capitalBeta =1.15Math error: -0.5Cost of equity =9.85%forgot to after-tax cost of debt: -0.5Cost of capital =9.23%! Debt ratio = 10%Part b: New cost of capital
Sheet1Page 4Unlevered beta =1.078125! Forgot to adjust cost of equity : -1New levered beta =1.35535714! Don't forget to unlever and relever! Math errors: -0.5New cost of equity =10.67%New cost of capital =8.73%Part cBorrow money over next 5 years and pay dividends! Closely held, outperformed: Not target of a takeover - No immediacyIts stockholders like dividends, because it has paid large dividends in the past! ROC < Cost of capital : Don't investIts projects earn less than its cost of capital! History of paying dividends: Pay more dividendsProblem 2Cost of capital before =9.00%Cost of capital after 8.00%Change in firm value =800! Forgot to consider the effect of growth : -1 pointIncrease in dollar debt to get to 25% =1000Number of shares bought back =12.5Number of shares left =37.5! Did not adjust the number of shares for buyback : -1Increase in value per share =21.3333333