1. You borrow $500,000 to purchase a house. The mortgage is a 30-year fixed rate mortgage, with monthly payments.
A. Assume that you have good credit, and can borrow money at a 3.75% annual interest rate. What will your monthly payment be?
B. Now, assume that you have lousy credit, and must pay a 6.5% annual interest rate to obtain a mortgage. What will your monthly payment be?
C. Having lousy credit can be costly. How much additional interest will you pay over the 30-year period if you have bad credit, relative to what you would pay if you have good credit? (Hint: Calculate the total interest over the 30-year period on the loan in Part A, and the total interest over the 30-year period for the loan in Part D. What is the difference between the two amounts?).
D. Explain why it is not necessarily unethical for banks to charge people with poor credit histories higher interest rates (within reason, of course)?
2. Fred and Erma will retire in 30 years. They plan to save $4,000 each year in a savings account, earning 6% interest (both before and after retirement).
A. How much money will they have accumulated 30 years from now?
B. Assume that Fred and Erma wish to spend $30,000 a year for 20 years once they retire, and then leave a $150,000 inheritance for their kids. How much do they need in savings when they retire?
C. Will Fred and Erma have enough savings when they retire? (Hint: No!). If not, what additional ANNUAL amount must they save in years 1 to 30?
3. A $1000 face value bond has a 4 percent coupon, with interest paid annually. The bond will mature 10 years from today.
A. What is the bond's price if the required return (i.e., the yield to maturity) is 3%?
B. What is the bond's price if the required return (i.e., the yield to maturity) is 5%?
C. Explain in one or two complete sentences why the bond sells for a premium in part A, and a discount in part B.
4. Calculate the price (today) of the following stocks (A, B, and C are independent cases). The required return is 8%.
A. Stock A is expected to pay a dividend of $4.50 next year (one year from today). The dividend is then expected to grow at a 3% annual rate, forever.
B. Stock B is not expected to pay a dividend for the next five years. Its first dividend is expected to be $4.50, paid six years from today. The dividend is then expected to grow at a 3% annual rate, forever.
C. Stock C is not expected to pay a dividend for the next three years. Its first dividend is expected to be $2.50, to be paid four years from today. The dividend will increase to $3.50 in year five, and $4.50 in year six. The dividend is then expected to grow at a 3% annual rate, forever.
5. A three-year project requires an initial investment of $500,000, and will produce $225,000 in EBIT before depreciation every 12 months (Years 1 and 4 are half years). Interest expense is $0, and the tax rate is 35%. The first cash flow will occur one year from today, and will include OCFs for six months. The cash flows received at n = 2 and 3 will include OCFs for twelve months. The final cash flow will occur 3.5 years from today, and will include OCFs for 6 months.
A. Using straight line depreciation, calculate the NPV of the project using discount rates of 8% and 10%. In addition, calculate the IRR of the project. Over what range of discount rates should the company accept the project?
B. Using MACRS depreciation, calculate the NPV of the project using discount rates of 8% and 10%. In addition, calculate the IRR of the project. Over what range of discount rates should the company accept the project?
C. If the company decides to invest in this project, which depreciation method should it use for tax purposes? Why?
6. On the distant planet of Zurg, the stock market had a return last year of -60%. This year, due to an economic recovery, the stock market had a return of +100%. What was an investor's effective annual return over this two year period? If the investor requires an annual return of 10% to be happy, is the investor happy?
7. A stock currently sells for $20. Over the next three years, the price of this stock is expected to increase to $21.80, $23.76, and $25.90 in years 1 to 3, respectively. The company does not pay dividends. What is the standard deviation of the expected annual return from this stock?
8. Here are the expected returns on two stocks:
Returns
Outcome Probability X Y
1 0.2 15% 7%
2 0.6 10% 12%
3 0.2 5% 17%
A. What is the expected return and the standard deviation of Security X?
B. What is the expected return and the standard deviation of Security Y?
C. What is the expected return and the standard deviation of a portfolio consisting of 50% Security X and 50% Security Y?
D. What is the correlation between Security X and Security Y? (Note: If you do the calculations in Parts A to C correctly, you do not have to do any calculations in Part D).