Q11.32 Evaluate whether supermarkets operate in perfect markets.
Supermarkets do not operate in a perfect market. The majority of the competition comes from a limited number of players. There are obviously taxes, transaction costs, and differences of opinion as well. Considering that there is nearly an unlimited amount of buyers and sellers and the other violations of perfect market assumptions are slight, supermarkets operate in competitive markets but not perfect markets.
Q11.33 What are the perfect market assumptions?
Q11.34 Your borrowing rate is 15% per year. Your lending rate is 10% per year. The project costs $5,000 and has a rate of return of 12%.
\(1\). Invest \(2,000\) means borrow \(3,000\) at \(.15\); pay back \(3,450\). Thus the return would be \(5,000 \cdot 1.12 - 3,450 = 2,150\). By lending the \(2,000\), the return would be \(2,000 \cdot 1.10 = 2,200\). The lending rate yields a better return than taking this project.
\(2\). The return on investing would be \(5,600 - 2,000 \cdot 1.15 = 3,300\). The return from lending would be \(3,000 \cdot 1.1 = 3,300\). Either strategy suffices.
\(3\). Lending yields \(4,400\). Taking the project earns \(5,600-1,150 = 4,450\). Do the project.
Q11.35 An entrepreneur is quoted a loan rate of 12% at the local bank, while the bank pays depositors 6% per annum.
\(1\). If the bank has an expected return of \(6\%\) to cover their cost to pay depositors, then \[ 6\% = p12\% + (1-p)0\% \implies p = 0.5\] \(2\). \(6\%\)
\(3\). \(6\%(1-p) + 6\%(p) = 6\%\)
Q11.36 “If the world is risk neutral, then the promised and expected rates of return may be different but the expected rates of return on all loans should be equal.” Evaluate.
The promised rate of return can be different than the expected rate of return because the promised rate contains a default premium. However, in a risk neutral world, the default premium on loans would be zero.
Q11.37 Go to the Edgar page on the SEC’s website. Look up the El Torito company (also Real Mex Restaurants, Inc) S-4 filing on 2004-06-09. Describe the covenants and requirements to which El Torito is obligated. (Note: This may take a while, but reading this S-4 will introduce you to how these agreements look in the real world.)
Real Mex Restaurants, Inc. is offering $105 million in new notes in exchange for old notes. The will pay 10% interest semi-annually and mature April 1, 2010.
Q11.38 The bid quote on a corporate bond is $212; the ask is $215. You expect this bond to return its promised 15% per annum for sure. In contrast, T-bonds offer only 6% per annum but have no spread. If you have to liquidate your position in 1 month, what would a $1 million investment be worth in either instrument? Which instrument should you purchase?
A $1 million dollar investment in the corporate bond would yield $1.0125 million if you liquidated it in one month minus the bid-ask spread. If you paid $212 per bond, with $1 million dollars you would buy 4716.981 bonds. Thus the price of the spread is $13,953.49. Therefore the return from the corporate bond is $998,546.50, yielding a loss. The T-bond offering a return of $1.005 in one month would be the better instrument to purchase.
Q11.39 Look up on a financial website what the cost of a round-trip transaction on $10,000 worth of shares in Exxon Mobil Corp would cost you today.
Currently, the bid and ask price on XON shares are $83.29 and $83.40 respectively. Further, assume a $5 transaction cost per transaction. Then the cost of the round-trip transaction is \[10,000(83.4-83.29)+10 = 1,110 \]
Q11.40 You have discovered an investment strategy that can beat the market by 300 basis points per year. Assume that the stock market is expected to return 9% per annum. Unfortunately, to implement your strategy, you will have to turn over your portfolio three times a year. Think of this as rebalancing (selling and purchasing) 25% of your portfolio every month. You have very good traders, who can execute trades at a cost of only 7.5 cents per transaction (15 cents round-trip) on a $30 stock. Does this strategy make sense?
This strategy would yield a return of 12% per year. If every month, 25% of the portfolio had to be rebalanced, then this strategy makes sense depending on the size of the portfolio. Say the portfolio is worth $1 million, then trading $250,000 worth of stocks would cost \[ 250,000 \cdot \frac{7.5}{30} = 62,500 \text{ cents} = \$625\] Thus, the entire cost would be $1,250 a month, or equivently $15,000 a year. Therefore the annual return on the $1 million dollar investment would be $1,000,000 1.12 - 15,000 = 1,105,000$. So the rate of return for this strategy turns out to be 10.5%, meaning it beats the market return. This strategy makes sense up to a certain amount of monthly transactions.
Q11.41 A day trader has $10 million in assets. She buys and sells 30% of her portfolio every day. Assume that this day trader is very good and incurs single round-trip transaction costs of only 10 cents on a $30 stock. Roughly, by how much does this day trader’s strategy have to beat the benchmark in order to make this a profitable activity? Assume that the trader could earn $200,000 in an equivalent alternative employment and that there are 252 trading days per year.
Buying and selling $10 million is stocks a day yields $6,666.67 per day in transaction costs, or $1,680,000 a year. To cover the transaction costs, the trader would at least have to earn 16.8% in returns a year. Therefore, to validate this strategy rather than taking a $200,000 a year job, the trader would have to earn the 16.8% return plus an extra 2%. Thus the benchmark for this being a good strategy is 18.8%.
Q11.42 Search online for the current federal income tax rates on the four different types of income for individual taxpayers and corporate taxpayers.
What are these rates?
Assume that a corporation has just earned $2 million in ordinary income, $1 million in interest income, and $3 million in realized long-term capital gains (net). Focusing only on the basics and ignoring deductions, what is its tax obligation? What are its marginal tax rates? What is its average tax rate?
Assume that you (an individual) have just earned $2 million in ordinary income, $1 million in interest income, and $3 million in realized long-term capital gains (net). Focusing only on the basics and ignoring deductions, what is your income tax obligation? What is your marginal tax rate? What is your average tax rate?
How much would your state income tax, Social Security, and Medicare add to your tax bill? Is your state income tax payment a before-tax or an after-tax expense?
\(1\) For individual tax payers, ordinary income tax varies depending on tax bracket. For this problem lets assume that the individual earns over $1 million. The income tax for this person currently is 33.1%. Interest income tax is roughly the same as ordinary income. Dividend and Capital Gain income is about half, lets say 16%. Corporate tax rates also varies by income earned, going from 15% to 38%. Taxes for dividends and long term capital gains tax is about 15% for corporations.
\(2\). Ordinary income tax \(= 335,000(.39) + 2,665,000(.35) = 1,063,400\). Interest tax \(= 335,000(.39) + 1,665,000(.35) = 713,400\). Capital gains tax \(= 3,000,000(.15) = 450,000\). Therefore the total tax obligation and average tax rate is $2,226,800 and 37.11% respectively. The marginal tax rate is 35%.
\(3\). Ordinary income tax \(= 9,325(.1) + 28,625(.15) + 53,950(.25) + 99,750(.29) + 225,050(.33) + 1,700(.35) + 1,581,600(.391) = 740,908.3\). Interest tax \(= 9,325(.1) + 28,625(.15) + 53,950(.25) + 99,750(.29) + 225,050(.33) + 1,700(.35) + 581,600(.391) = 349,908.3\). Capital gains tax \(= 3,000,000(.15) = 450,000\). Therefore the total tax obligation and average tax rate is $1,090,817.6 and 18.18% respectively. The marginal tax rate is 39.1%.
\(4\). State income is an after tax expense. State income tax would add on about 8% to the total income and interest tax bill, or about $180,000.
Q11.43 If your tax rate is 40%, what interest rate do you earn in after-tax terms if the before-tax interest rate is 6%?
The after tax cost of debt is \(.6(.06) = 3.6\%\).
Q11.44 On September 28, 2007, tax-exempt AAA rated 10-year muni bonds traded at a yield of 3.99%. Corporate 10-year AAA bonds traded at 5.70%. What was the marginal investor’s tax rate?
Since the interest on muni bonds is free of taxes, the marginal investor’s tax rate is 1 - 3.99/5.7 = 30%.
Q11.45 Go to the Vanguard website and look up VWITX and VBIIX. 1. What is the current yield from the tax-exempt Vanguard bond fund? 2. What is your state income tax treatment? 3. How does it compare to the most similar Vanguard taxable bond fund? 4. What tax rate would an investor have to suffer in order to be indifferent between the two bond funds?
\(1\). VWITX currend yield is 2.06%.
\(2\). Tax free for muni bonds.
\(3\). The yield on VBIIX is 2.68% and is a low cost bond.
\(4\). If an investor with a $1 million portfolio invested in VBIIX, he would yield 1,026,800. Thus for this return to be the same as the return for VWITX, the tax rate would have to be 17.45%.
Q11.46 Consider a real estate project that costs $1,000,000. Thereafter, it will produce $60,000 in taxable ordinary income before depreciation every year. Favorable tax treatment means that the project will produce $100,000 in tax depreciation write-offs each year for 10 years (nothing thereafter). For example, if you had $500,000 in ordinary income in year 2 without this project, you would now only have $400,000 in ordinary income instead. At the end of 10 years, you can sell this project for $800,000. All of this $800,000 will be fully taxable as write-up at your capital gains tax rate of 20%. If your ordinary income tax is 33% per annum, if taxable bonds offer a rate of return of 8% per annum, and tax-exempt munis offer a rate of 6% per annum, what would be the NPV of this project?
Ordinary Income: 60,000(10) = 600,000
OI Tax: (198,000)
OI NPV: 379,245.3
Capital Gains: 800,000
CG Tax: (160,000)
CG NPV: 603,773.6
Depr. write offs NPV: 188,679.2
NPV = 1,171,698
Q11.47 You are in the 25% tax bracket. A project will return $20,000 next year for a $17,000 investment-a $3,000 net return. The equivalent tax-exempt bond yields 14%, and the equivalent taxable bond yields 20%. What is the NPV of this project?
The opportunity cost of capital will be the greater of the tax-exempt bonds and (1-.25)(.2) = .15. Thus, the better investment is in taking the project and the NPV will be 2,608.69.
Q11.48 The lottery gives you a 1 in 14 million chance of winning the jackpot. It promises $20 million to the lucky winner. A ticket costs $1. Alas, the lottery forgot to mention that winnings are paid over 20 years (with the first $1 million payment occurring immediately), that inflation is 2% per year, and that winnings are taxable. Is the lottery a good investment? (Assume that you are in a 40% marginal income tax bracket and that the appropriate nominal discount rate is 10% per year.)
The real interest rate is approximately 8%. Therefore the NPV of this jackpot is \[ 1,000,000(0.6)/1.08^{20} = 128,728.9 \] Thus the expected return of the $1 investment is \[ \frac{1}{14,000,000}128,728.9 + \frac{13,999,999}{14,000,000}(-1) = -0.990805 \]. So this is not a good investment (not considering utility function of losing a dollar versus winning over $100,000.)