1. An investor is in the 33% tax bracket. If corporate bonds offer 5% yields, what yield must municipals offer for the investor to prefer them to corporate bonds?
2. You purchase a share of stock for $60. One year later you receive $3.00 as dividend and sell the share for $63. What was your holding period return? Suppose the rate of inflation over the year was 10%. What was the exact rate of growth of purchasing power?
Suppose the tax rate on dividends is 40% and the tax rate on capital gain is 33%. What is the after-tax real rate of return on your investment?
3. Find prices for 6 bonds and three yield levels for each of the following bonds: 2 and 30 year maturities, coupons 0%, 3%, 6%, and yields 2%, 3%, 4%. Find the percentage change in price both as you go from 3% yield to 2% and from 3% to 4%.
4. Find the rates of return for 3 year and 30 year bonds in a steepening rally. Assume two points on the initial yield curve are: 10% for 3 years and 5% for 30 years. Assume the yield curve 1 year later has these two points: 2% for 2 years and 4% for 29 years. What are the 1 year holding period returns for each of these bonds? Do this both for zero coupon bonds and par bonds.
5. Suppose the price per share of XYZ stock at the beginning of years 2005, 2006, 2007, 2008 is $100, $120, $90 and $99, respectively. The stock pays a $3 dividend per share each year. Suppose you buy 10 shares of XYZ at the beginning of 2005, buy another 5 shares at the beginning of 2006, sell 3 shares at the beginning of 2007, and sell all remaining shares at the beginning of 2008. What are the arithmetic and geometric average time-weighted rates of return? What is the dollar weighted rate of return?
6. Consider Karl, an individual investor. Karl is 30 years old, earns after-tax income of $50,000 per year, expects to retire at age 65, and receive after-tax Social Security payments in retirement of $20,000/year. Karl has a current net worth of $50,000 and the after-tax return on investment is 1% per year. He believes he will continue to earn $50,000 per year in real terms over the next 25 years. Assuming Karl believes he may live as long as 100 years, what is the maximum steady rate of consumption that he can maintain while keeping net worth positive through age 100? How does your answer change if the return on investment is 3% per year instead of 1%? How does your answer change if Karl wishes to leave an estate at death of $1,000,000? For each case, what is the "savings rate" defined as (1-Consumption/Income)?
7. In EXCEL, replicate the five year financial projections for Bill Ackman's lemonade business. Extend the projections out to ten years using the assumption that you invest in as many new lemonade stands you can given the cash balance at the beginning of the year.