Homework #1

1. Suppose you hire a real estate agent and tell him to sell your house to the highest bidder. You pay the real estate agent a flat fee of $50,000 when the house is sold.
You learn that, unfortunately, the agent sells the house to the first bidder at a low price. a. What is this type of problem called?
b. What is one way to change the real estate agent’s incentive so he does sell to the highest bidder, instead of to the first one? a. This type of problem is known as an agency problem b. One way to change the real estate agent’s incentive so that he is motivated to find the highest bidder is instead of paying him a flat fee of $50,000 you offer him a commission that pays him a percentage of the house’s sales price. This way he will try to find the highest bidder so he can maximize the amount of money he gets and you can get the best possible price for your house.

2. Suppose you own one share of stock in ABC Inc. and one share of stock in XYZ
Co. You can sell both shares at $100, but it will take you much longer to find a buyer willing to pay $100 for XYZ compared to ABC.
a. Which stock is more liquid?
b. If you had to sell both stocks today, which one would sell for a higher price? a. The stock for ABC Inc. is more liquid because it can be sold more quickly with limited price impact. b. The stock for ABC Inc. would sell for a higher price because it is the most liquid out of the two.

3. National Bank pays 3% simple interest on its savings account balances, whereas
First City Bank pays 3% simple interest compounded annually. If you made a
$165,000 deposit in each bank, how much more money would you earn from your
First City Bank account at the end of 6 years?
National Bank Simple Interest: 165,000(1+.03(6)) = $194,700
First City Bank Compound Interest: N: 6 Years I/Yr: 3% PV: $165,000= FV: $197,018.63
You would earn $2,318.63 more with the First City Bank account than the National Bank account.

4. Assume you will need $500,000 when your child enters college in 17 years. You presently have $79,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education?
N: 17 Years PV: $79,000 FV: $500,000= I/Yr: 11.46%

5. Why might maximizing revenue today not be best when trying to achieve the goal of financial management?
The underlying goal of a financial manager is to maximize the wealth of the firm’s owners. By maximizing revenue today, the financial manager is not serving the best interests of rational shareholders. The best way to achieve the goal of financial management is by maximizing the share price which reflects current and future perspective of the firm.

6. You want to buy a $190,000 Porsche. If you believe your mutual fund can achieve a 7 percent annual rate of return and you want to buy the car in 9 years on the day you turn 30, how much must you invest today?
N: 9 Years I/Yr: 7% FV: $190,000= PV: 103,347.41

7. The US government offered some securities for sale to the public on February 28,
2008. Under the terms of the deal, the government promised to repay the owner of one of these securities $1,000,000 on February, 2038, but investors would receive nothing until then. Investors paid the California government $443,000 for each of these securities.
a. Based on the $443,000 price, what rate was the US government paying to borrow money?
b. Suppose that, on February 28, 2019, the security’s price is $643,380. If an investor had purchased it for $443,000 at the offering and sold it on this day, what annual rate of return would she have earned?
c. If an investor had purchased the security at market on February 28, 2019, and held it until it matured, what annual rate of return would she have earned? a. N: 30 Years PV: $443,000 FV: $1,000,000= I/Yr: 2.75% b. N: 11 Years PV: $443,000 FV: $643,380= I/Yr: 3.45% c. N: 19 Years PV: $643,380 FV: $1,000,000= I/Yr: 2.35%

8. Mineral Inc. has $14,800,000 in taxable income, and Oil Co. has $347,600,000 in taxable income.
a. What is the tax bill for each firm?
b. Suppose both firms have identified a new project that will increase taxable income by $10,000. How much in additional taxes will each firm pay?
Why is this amount the same?
c. What is the average tax rate for each firm?
d. A CFO for a small firm with $75,000 in taxable income argues that launching a new product that generates $4,000 in taxable income will increase the firm’s average tax rate to 34%. Is the CFO correct? Why or why not? a. Mineral Inc. Tax Bill:
$50,000(.15) + $25,000(.25) + $25,000(.34) + $235,000(.39) + 9,665,000(.34) + $4,800,000(.35) = 7,500+6,250+ 8,500+ 91,650+3,286,100+1,680,000 = $5,080,000

Oil Co. Tax Bill:
$50,000(.15) + $25,000(.25) + $25,000(.34) + $235,000(.39) + 9,665,000(.34) + 5,000,000(.35) + 3,333,333(.38) + 329,266,667(.35) = 7,500+6,250+8,500+91,650+3,286,100+1,750,000+1,266,666.54+115,243,333.45= $121,660,000

b. $10,000(.35)= $3,500
$10,000(.35)= $3,500

Both the numbers are the same because Mineral Inc. and Oil Co. are in a taxable income bracket that charges a tax rate of 35%.

c. Mineral Inc. Average Tax Rate: 5,074,750/14,800,000= 34.32%
Oil Co. Average Tax Rate: 121,654,750/347,600,000= 35%

d. Small Firm Tax Bill:
$50,000(.15) +25,000(.25) +4,000(.34) = 7,500+6,250+1,360=$15,110
Small Firm Average Tax Rate: 15,110/79,000= 19%

The CFO is not correct. The average tax rate for the firm takes the total amount you pay for taxes and divides it by total taxable income which in this case is 19%. The marginal tax rate, the rate on the last taxable dollar, will be 34%.