Q1. You're given with a 5-year auto loan from your credit union. Suppose the total loan you have is $25,000 and the current market interest rate is 5.2% 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 5.2% 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) $13,000 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? (Already pay three years and two more years leftover, so find the p.v. of all next 24 monthly payments)
d) Suppose the original agreement that you signed with credit union is to have a 3-year loan and pay back the loan with $13,200 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 5.2% market interest rate? Why or why not?
Q2. You are given with the following information of two projects planned by your company. Each cash flow per year shown in Table 1 represents the cash flow at the end of each year during the project. For instance, for project A, the cash flow as 735 in first year is expected at the end of the Year 1. The initial outlays for the projects are paid out by installments with regular payments as 0.74 million at the beginning of each year for project 1 and $0.81 million per beginning of each year for project 2, respectively.
Table 1: (in thousands)
|
Project
|
Year 1
|
Year 2
|
Year 3
|
Year 4
|
Year 5
|
|
A
|
727
|
2290
|
1129
|
2037
|
2391
|
|
B
|
609
|
3239
|
1823
|
|
|
Answer the following questions.
a) Suppose the cost of capital is 14%, what is the Net Present Value for each project? Which project would you prefer? Why?
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 24%, the cost of debts (that is, the interest rate) be 7%, the cost of equity be 26% and there is no preferred stock issued by the firm. Assuming the weighted average cost of capital is given as 14% 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 40% chance that the market may be bad and the cash flows for both projects when market condition is bad will change to
|
Project
|
Year 1
|
Year 2
|
Year 3
|
Year 4
|
Year 5
|
|
A
|
350
|
720
|
-919
|
-1092
|
-1321
|
|
B
|
376
|
-1872
|
-1008
|
|
|
That is to say, the original cash flows in Table 1 only have 60% 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?
Q3. 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 mortgage payment and monthly gross income below no greater than 33%).
b) Suppose 4 years later, the market price of your house is $758,000. 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?
Q4. 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"?
e) 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?
Q5. 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; = 0.47, = 1.83 = 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 replicates fund 3's beta, what are the weights of this portfolio? What are the assumptions needed for the construction of such portfolio?
Q6. Company Wii gives you the following information for its operation. The expected income available for dividends is $42 million next year before the firm has any debts. Suppose there is a 25% corporate income tax imposed on the company. Company Wii has no debt originally. There are 6 million shares of common stocks outstanding. Let the market price for the stock be $42.5 per share before debt. Suppose that there is no expansion plan for the company to either spend on working capital vs. long-term investment or to apply the accumulated retained earning. Answer the following questions:
a) What is the possible dividend per share for the common stock before company Wii has debt? What is the cost of equity for Company Wii's stock before debt? Suppose that Company Wii now has issued some bonds with 6% coupon rate recently. Let Company Wii's total debts (with the above coupon bond) be $80 million and let this coupon rate represent the cost of debt, how much will be the value of stockholders' equities under Modigliani and Miller's proposition 2?
b) What is the cost of equity for Company Wii, if there's no preferred stock issued for this company?
c) What is the weighted average cost of capital after Company Wii has debts?
d) Suppose the risk-free rate is 2%, S&P 500 index return is 12%, what is the "beta" of Company Wii's common stock after issuing debts?
e) What are the limitations of M&M proposition 2?
Q7. You are given with the following information of a firm "Hunger Game" in food industry. Assume that the firm did not issue preferred stocks while the firm may have some foreign subsidiaries overseas. The firm is making hi-tech instruments for medication. This industry tends to have gross profit margin such as 18% and other set-up costs are also high due to the production and technology. The R&D (Research and Development) costs are entirely reported as operating expenses according to the GAAP.
Balance Sheet (in millions)
2011 2012 2013
Assets
Cash 130 210 70
Marketable securities 51 200 1000
Accounts Receivable 220 350 200
Inventory 1062 1078 450
Plant, Building, and Equipment (net) 1873 2203 1790
Investments in affiliates 0 430 329
Total Assets 3336 4471 3839
Liabilities
Short-term debts 107 130 30
Advances from customers 121 326 534
Accounts payable 585 1092 357
Interest payable 75 298 62
Tax payable 147 120 128
Other Accrued Expenses 20 15 35
Bonds payable 1028 1076 450
Stockholders' Equity
Common stock 1001 1201 1975
Additional paid-in capital 74 154 144
Retained earning 178 59 124
Total liabilities and equities 3336 4471 3839
Income Statement(in millions)
2011 2012 2013
Net Sales 6529 5418 6083
Cost of Goods Sold 2215 3109 3310
Selling and General Expenses 1771 812 1059
Depreciation Expense 213 169 484
Interest Expense 397 109 221
Income Tax Expense 275 237 254
Net Income 1658 982 755
a) Perform the Ratio Analysis for the firm. (Present all ratios you know.) Will the accounting policy on revenue recognition influence the ratios? Why or why not?
b) Show the Common-Size Statements for Company Hunger Game.
c) Given your result in a), what is your opinion on the firm's performance so far? What is the firm's strategy in raising capital? What are the firm's possible business and financial strategies in your opinions?
d) Given the above information, what will be possible dividend per share for 2013 of Company Hunger Game? Suppose the firm has 6 million shares of stock issued in the market, what is the possible required rate of return for their stock if you based on the shareholders' equity of 2013?