You decide to buy a Bonda Discord Lx automobile. You have $4,000 in cash. If you purchase the car (at a price of $16,000), you will spend all your cash in making a down payment. You can borrow the remaining at an interest rate of 10.5% on the outstanding balance.

(i) Assume (for simplicity) that loan repayments have to be made annually and you pay $2000 every year. How long will it be before you pay off your loan?

(ii) Suppose Bonda offers you a rate of 2.9% on your outstanding balance. How long would it take for you to repay the loan if you repaid $2000 every year? What is the net present value of the loan to you? As far as possible, try to avoid using a spreadsheet to answer this question - in an exam situation you would need to know how to apply the relevant formulas.

(iii) Bonda offers to lease the Discord at $199 a month with no down payment. The car reverts to Bonda at the end of four years. Its resale value at that point is $9500.
Are you better off leasing or buying the car and financing at 2.9%? How would your answer change if you estimate the resale value to be $7500.

Valuation of stocks:
Palooka is a new cosmetics firm which is about to make an initial public offering. It has no physical assets and no debt. Palooka is coming out with an equity issue to raise
$100 million from the markets. The funds raised will be invested in the commercial production of Stumblebum (a new fragrance for men).
There is a 0.8 probability that Stumblebum will catch on with the 'young and beautiful' set. In that case, earnings will be $1 million immediately (at date 0), will grow
at 50% a year for 15 years, and then be constant (zero growth) thereafter. There is a 0.2 probability that Stumblebum will fail, in which case all the investment will then be
wasted (the company will have no earnings ever). Assume the market discounts cash flows at 10%.
For simplicity, you can assume that the IPO happens on January 1, the investment occurs on January 2, and the earnings (if any) happen on January 3 of that year. In other
words, we're assuming that the IPO, the investment, and the initial earnings (if any) will all occur at date 0.

(i) What is the value of the equity before the issue? Assume that no one knows whether
Stumblebum will succeed. Use the following formula:

Value of Equity = Present value of cashflows from existing assets + Net Present Value of cashflows from future investments - Present Value of debt (if any).
(ii) If there are 1 million Palooka shares before the issue, what is the value of each share? (iii) What is the price investors will pay for shares in the new issue? (Hint: What happens
if it differs from the price of shares before the issue?)

(iv) Assume that the company does the IPO, and Stumblebum succeeds (and everyone knows it). What is the PE ratio for the firm? Is this high or low? What do PE ratios indicate? Explain.
 
Dividends in an MM world:
The Dipthong Corporation has a current stock price of $50 per share. Next year, earnings will be $4 per share, and dividends will be $2 per share. There are currently 100 shares outstanding. There is no uncertainty. Under current policy, earnings per share for the company will grow at 8% per year forever. The appropriate discount rate is 12%. Assume no taxes and that all the other MM assumptions hold. Clearly, all the above numbers are consistent with a Gordon dividend growth model, since 50 = 2 / (.12-.08).

Suppose that Dipthong decides to switch from a 50% to a 100% dividend payout policy. It will keep its investment policy (its assets and real operations) unchanged, and will issue shares as necessary to accomodate the new dividend policy.

Use the Gordon model to show that this policy will result in no change in the stock price. What is r, the discount rate? What is g, the growth rate of dividends per share? Explain why these things change.

Capital Structure with Taxes:
The Botolph Corporation produces botolphinators. Next year, Botolph will have EBIT (earnings before interest and taxes) of $200. This EBIT will be constant forever. The appropriate (all-equity) discount rate is 20% for the botolphinator business. Botolph currently has debt of $500, which is in the form of perpetual bonds (consols). Botolph plans (and the market believes) to keep this level of debt permanently. The debt is riskless, and the (constant) riskless interest rate is 5%. 

There are no personal taxes, and the corporate tax rate is 20%. 

A) What is the current value of the Botolph's equity?

B) Botolph unexpectedly announces that it will be switching to a new, permanent level of $600 worth of debt. The debt is still riskless. Botolph plans to issue the $100 in additional debt, and use the proceeds to repurchase equity. The market believes, again, that this $600 level will never change. What is the percentage change in Botolph's stock price, when the announcement takes place? 

C) After they have issued the debt, what is the value of Botolph's market equity? 

D) What is the expected rate of return on Botolph's equity, after they have issued the new debt? (Hint: Do not make any assumptions about the market risk premium. Do not try to use the CAPM. Use your answer in part C) 

E) Evaluate the following statement, explaining why it is right or wrong. Are the facts correct? Is the reasoning correct? Botolph's stock price rises (in part B) because expected returns on Botolph's stock rise (part D) after the debt is issued. The stock has become more valuable because expected returns have gone up.