UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGNCollege of BusinessD E P A R T M E N T O F F I N A N C EFinance 321 – Advanced Corporate Finance – Spring 2007Assignment 4 (20 points)Lectures 19-23Due May 1, 2007Assignments must be turned by classtime on May, 1, as the answer key will be posted later that day. No credit will be given for any assignment turned in after the key is posted. Each question is worth 2 points.1. Refer to the Pfizer example in section 18.1 of the text. Suppose that Pfizer moves to a 40 percent book debt ratio by issuing debt and using the proceeds to repurchase shares. Consider only corporate taxes. A. How much additional value (compared to table 18.3 (a)) is added if the assumptions in the table are correct?B. Reconstruct table 18.3(b) to reflect the new capital structure. 2. Based on the following information, leverage will add how much value to the unlevered firm per dollar of debt?3. A. Which corporate finance theory covered in chapter 18 best explains why profitable firms tend to have a lower debt equity ratio than less profitable firms in the same industry? B. Why?4. Calculate the After Tax Weighted Average Cost of Capital (WACC) for the following values. The marginal corporate tax rate is 35%. The book value of debt is $20 million and the market value of debt is $25 million. The book value of equity is $30 million and the market value of equity is $42 million. The cost of debt is 8%; the cost of equity is 16%. 5. The Boston Company has total assets of $30 million, of which $10 million are financed by debt and $20 million by equity. The EBIT is $6 million. The firm's tax rate is 34% and the interest rate on debt is 10%. Calculate the after tax cash flow. Corporate tax rate: 35%Personal tax rate on income from bonds: 35%Personal tax rate on income from stocks: 20%6. A project requires a $10 million initial investment and offers a level after-tax cash flow of $1.75 million per year for 10 years. The opportunity cost of capital is 12%. The project is tobe financed with $5 million debt and $5 million equity. The interest rate on the debt is 8% and the marginal tax rate is 35%. The debt will be paid off in equal annual installments over the project’s 10 year life.A. Calculate the Adjusted Present Value of the project.B. Calculate the APV if the firm will incur issue costs of $400,000 to raise the $5million of required equity.7. A company grants its CEO the option to buy 200,000 shares of stock at the current market price ($35 a share) anytime over the next four years. The risk free rate is 4.5% and the standard deviation of the company’s stock return is 30%. Use the Black-Scholes option pricing model to value this option grant.8. If the CEO were to increase the risk of the company and increase the standard deviation of the stock return to 35%, how much more would these options be worth? 9. Calculate the Total Average Cost of Capital (TACC) based on the approach suggested by Prakash Shimpi for the following values. The book value of debt is $20 million and the market value of debt is $25 million. The book value of equity is $30 million and the market value of equity is $42 million. The company would have to carry an additional $5 million of capital if it did not carry insurance. The cost of debt is 8%; the cost of equity is 16%; the cost of insurance for the year is $150,000. 10. Use the Excel program called VaR Example that is loaded on the class website in the Assignment section. Change the investment allocation to 50% bonds and 50% stocks, select the AAA model and when asked to pick a number use 3472 to run the program. Then hit the F9 key to select the appropriate 100 iterations of the model. Go the the Asset (end) worksheet to see the results of this model and follow the attached instructions.A. What is the 95% VaR for this portfolio?B. What is the Tail VaR for this portfolio based on the 95% level? Extra Credit(2 points)Draw the Histogram to illustrate the VaR from question 10-A.Finance 321Risk Metrics Calculations - VaR Example InstructionsThis program is designed as a learning tool for risk metrics. The goal is to show you how common risk metrics are calculated and to demonstrate how much these values can vary based on different sets of experience or different model parameters. This program uses the value of a portfolioconsisting of stocks and bonds as the key variable. This program is in the early stages of development, and you are encouraged to suggest or develop improvements for future sessions. Although you are not responsible for the details behind the calculations, if you are interested, these models are more fully described at:http://www.business.uiuc.edu/~s-darcy/Fin432/2007/Readings/ActFinScenGen.pdfThe Setup page allows the user to select the total initial investment, the investment allocation,the investment return generating model and the starting value for the run. After making these choices, and hitting ‘F9’, one hundred sets of investment returns are displayed on the the remaining worksheets. In order to have an unchanging example of how to do this, we have a worksheet labeled Fixed Example. Risk metrics are shown both numerically and graphically. The 95% VaR is listed at the top of the page. This is a negative 3,814,598, the value in row 7, column A. In 5% of the cases, the loss in value of the investment portfolio will be greater than this value (the portfolio will decline by more than 3,814,598). When using the term VaR, people will say the 95% one year VaR is $3,814,598, meaning that 95% of the time losses will not exceed that level. The Tail VaR (and the Tail Conditional Expectation) is the average portfolio change in the lowest 5%, which is calculated by averaging the values in rows 2 through 6, column A. This value is (4,442,200) in the Fixed Example, meaning that the average value of losses in the worst 5% of the cases is $4,442,200. The next worksheet, labeled Fixed Histogram, used the Excel tool Data Analysis to determine the loss frequency by particular ranges (called bins). The histogram is shown based on the change in asset values for the Fixed Example, and the 95% VaR level is indicated by a line. Here is what you need to do to calculate these risk metrics for other runs: 1. Change the investment allocation, if applicable.2. Select the model you want to use (CAS-SOA or AAA) and pick a seed (usually anything except 1) to run the program. 3. Hit the ‘F9’ key to