1. You're given with a 5-year auto loan from your credit union. Suppose the total loan you have is $32,000 and the current market interest rate is 4.6% for the short-term loans with the same creditability as yours. Answer the following questions:
a) Given that the APR (namely the Annual Percentage Rate. That is, the stated interest agreed on the loan) of the loan is 4.6% per year, what is the monthly payment if you're intended to have the loan for 5 years?
b) What is the effective annual rate if the loan is compounded monthly?
c) Suppose the credit union says that if you'd like to retire the loan earlier, say at the end of the 3rd year, you need to pay (say) $18,000 for the rest of the loan, would you take it given that you have no difficulty to generate the cash flow? Why or why not?
d) Suppose the original agreement that you signed with credit union is to have a 3-year loan and pay back the loan with $21,200 at the end of year 3, how much will be your monthly payment now?
e) Given that the present value of the loan which is $25,000 now, what is the Internal Rate of Return (IRR) for this loan? Is this rate different from the 4.6% market interest rate? Why or why not?
2. You are given with the following information of two proposals of financing programs for your home loan. Suppose the new house costs you $672,400 (sales taxes and others are included). One program is asking you to deposit a 20% down payment on the $672,400 and it provides you with 2.4% interest rate for 15-year monthly payments of the remaining balance, the other program is a 100% financing program which gives a 1.2% for the first 5 year plus the PMI (property mortgage insurance) as $150 per month with a balloon payment as $650,000, (that is, a lump-sum payment at the end of 5th year). The mortgage rate increases to 4.8% afterward for a 30-year mortgage if the balloon payment is not paid and refinancing is applied (That is, the extended program for refinancing is for 30 years and it's not for the 25 years leftover only). 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 more favorable to you if your monthly income is $6,000 before tax? (Notice that most lenders will require the borrower to have the ratio between mortgagepayment and monthly gross income no greater than 33%).
b) Suppose 4 years later, the market price of your house is $768,000. 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 $8500 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 12% income tax on your gain in selling your house, how much is the after-tax return now for each financing program?
3. You have the following information for the company "Spy". The "beta" coefficient for "Spy" is 1.05 based on the past information. The 5-year average of 30-day T-bill rate is 2%, the average market return of (say, S&P 500 index) in the same period is 14.5%. Answer the following questions:
a) What is the required rate of return for "Spy"? Why do we call it "required" rate of return?
b) Suppose the current dividend for "Spy" is $3.12 per share with possible expected growth rate as 7% per year from now on, what is your assessment for the value of Spy's stock?
c) Suppose without using the information of "beta", the current market price for the "Spy's stock is $26.50 per share. Let the capital market be efficient as ideally assumed. That is, the current stock price is equal to the stock's present value. What is the required rate of return for this stock now if the information in (b) still applies? What is the "beta" associated with this stock now?
d) "Spy" has the following capital structure: the firm issued 6 million shares of common stock with the stock price given in c) and dividend in b), the firm also issued 2 million shares of preferred stock with $1.09 preferred dividend per share, and currently, "Spy" has $90 million in debts with interest rate as 6%. Suppose the current preferred stock price is $6.72 per share. The corporate tax rate is 30% and the common stock price is as given in c), what is the (after-tax) weighted average cost of capital (after tax) for "Spy"?
What is meaning of "Weighted Average Cost of Capital (after tax)"? Why do we usually apply it as the discount rate for expected future cash flows in capital budgeting decisions?