Explain your answers with clear statements.  State your assumptions whenever you need them.

Q1. You are given with the following information of two projects planned by your company. These expected cash flows are available at the end of each year. The initial outlays for the projects are paid out by installments with regular payments as 0.26 million per year for project 1 and $0.17 million per year for project 2, respectively. These payments are paid at the beginning of each year.

Table 1: (in thousands)

Answer the following questions.

a) Suppose the cost of capital is 12%, what is the Net Present Value for each project?

b) What are the pros and cons in using the NPV decision rule for the capital budgeting?

c) Let the corporate income tax rate be 32%, the cost of debts be 6%, the cost of equity be 25% and there is no preferred stock issued by the firm. Assuming the weighted average cost of capital is given as 9% in a), what is the debt-to-equity ratio for your company?

d) Find the IRR (Internal Rate of Return) for project A and project B. What is your decision based on the IRR criterion? 

e) Suppose there is a 35% chance that the market may be bad and the cash flows for both projects when market condition is bad will change to

That is to say, the original cash flows in Table 1 only have 65% chance to happen. What is your decision for each project? What is the value contributed by the "Real Option"(that is, the possibility  to discontinue the project) for each project if you can discontinue the projects when you find out that they may not be successful when possible negative cash flows are expected?

Q2. You are given with the following information of two proposals of financing programs for your home loan. Suppose the new house costs you $600,000 (sales taxes and others are included). One program is asking you to deposit a 20% down payment on the $600,000 and it provides you with 2.6% interest rate for 15-year monthly payments of the remaining balance, the other program is a 100% financing program which gives you a 1.2% for the first 5 year plus the PMI (property mortgage insurance) as $250 per month with a balloon payment as $580,000.(That is, a lump-sum payment at the end of 5th year). The mortgage rate increases to 4.6% afterward for a 30-year mortgage if the balloon payment is not paid and refinancing is applied (That is, the extended program is for 30 years not for the 25 years leftover). Let there be no prepayment penalty. That is, you may pay off the loan should you have some extra cash later on. The brokerage fees and commissions are already taken into account in all the numbers given. Answer the following questions:

a) What is the monthly payment for each program in the first 5 years? Which one is more favorable to you if your monthly income is $6,000 before tax? (Notice that most lenders will require the borrower to have ratio between mortgage payment and monthly income no greater than 33%).

b) Suppose 4 years later, the market price of your house is $760,000. The tax rate on gains/losses on house sales is 6%. Will you consider selling this house and buy a  bigger one if your income has gained to $8000 per month? What is the annualized rate of return net of your financing cost in your housing investment for each financing program?      

c) Suppose there is a 10% income tax on your gain in selling your house, how much is the after-tax return now for each financing program?

Q3. You have the following information for the company "a-Spirit". The "beta" coefficient for "a-Spirit" is 1.24 based on the past information. The 5-year average of 30-day T-bill rate is 3%, the average market return of (say, S&P 500 index) in the same period is 12%. Answer the following questions:

a) What is the required return for "a-Spirit"? Why do we call it "required" return?

b) Suppose the current dividend for "a-Spirit" is $4.62 per share with possible expected growth rate as 6% per year from now on, what is your assessment for the value of a-Spirit's stock?

c) Suppose the current market price for the "a-Spirit's stock is $22 per share. Let the capital market be efficient as ideally assumed. That is, the current stock price is equal to the stock fair value. What is the required return for this stock now if the information in (b) still applies? What is the "beta" associated with this stock now?

d) "a-Spirit" has the following capital structure: the firm issued 5 million shares of common stock with the stock price given in c), the firm also issued 1.5 million shares of preferred stock with $2.3 preferred dividend per share, currently, a-Spirit has $90 millions in debts with interest rate as 6%. Suppose the current preferred stock price is $8 per share. The corporate tax rate is 30%. What is the (after-tax) weighted average cost of capital for "a-Spirit"?

e) What is meaning of "Weighted Average Cost of Capital"? Why do we usually apply it as the discount rate for expected future cash flows in capital budgeting decisions?

Q4. Let the information on your portfolio be given as follows. You have three funds in the basket. The "beta's" among them that are estimated by using S&P 500 index are given as follows; β₁ = 0.42, β₂ = 1.26, β₃ = 0.92. Answer the following questions;

a) Why do we need these "beta's" to construct the portfolio?

b) If the risk-free rate is given as 2%, what are the required returns for fund 1 and fund 2 if the market rate of return is expected to have 12%?

c) Is it possible to construct a risk-free (or zero-beta) portfolio by combining asset 1 and asset 2? If yes, what is the required return for this portfolio? If the transaction cost for this portfolio requires 2.5% of commission, will you do it?

d) If you'd like to form a portfolio with fund 1 and fund 2 that mimic fund 3, what are the weights of this portfolio? What are the assumptions needed for the construction of such portfolio?