Outline. Not assigned problems Chapter 11. Q10 Go Chapter 11. Q14 Go Chapter 11. Q20 Go Chapter 11. Q22 Go Chapter 11. Q26 Go

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1 Outline Not assigned problems Chapter 11. Q10 Go Chapter 11. Q14 Go Chapter 11. Q20 Go Chapter 11. Q22 Go Chapter 11. Q26 Go Assignment problems: Chapter 11. Q4 Go Chapter 11. Q8 Go Chapter 11. Q12 Go Chapter 11. Q16 Go Chapter 11. Q18 Go Chapter 11. Q24 Go Chapter 11. Q28 Go Chapter 11. Q34 Go

Q26 Go Assignment problems: Chapter 11. Q4 Go Chapter 11.

2 Chapter 11. Q10 A piece of land is expected to sell for $100,000 in ve years, and currently sells for $30,000. The current interest rate is 2%. What is expected to happen to the interest rate over the next ve years? The present value of the land is ( ) If the price is only $30000, then we should expect interest rate to increase dramatically.

3 Chapter 11. Q14 People in a certain nation are anticipating having a war in the future. The economists there, who don't have too much concern about human suerings, are only interested in what will happen to the interest rate. a. suppose people gure that they don't have a great chance of surviving the war. Will the interest rate increase or decrease? Increase if they don't have much future, might as well bring their future consumption to the present. b. If it is expected that goods and property will be destroyed during the war but no people will be killed, how will this aect the interest rate? This will increase the marginal return on investment in capital goods. This will decrease the supply of funds and raise the interest rate.

Will the interest rate increase or decrease? Increase if they don't have much future, might as well br

4 Chapter 11. Q20 In 1975 the BC government passed a law allowing farmers to pay considerably less property tax than other land owners. This law is still in eect today. A real estate person was heard stating The great thing about buying acreage in BC, is that you don't have to pay property tax on small farms. Although this is technically true, in what sense do purchasers in 2002 have costs similar to those who pay the full tax? If you can buy a property without paying property tax, you'd expect that property to sell for a higher price The property tax savings are capitalized into the price of the land.

A real estate person was heard stating The great thing about buying acreage in BC, is that you don't have to pay property tax on small farms.

5 Chapter 11. Q20 Save it, somebody says. Don't sell it. It's not worth much now, but in 20 years it will probably be worth ve times as much. Should you save it or sell it? Depends on the interest rate. Fivefold growth in 20 years is pretty high though.

worth ve times as much. Should you save it or sell it?

6 Chapter 11. Q26 Suppose your wealth level today is $191,633, and the interest rate is 3.97%. If you consume all of your income for the next ve years, after ve years what will be your wealth level? Your wealth level will still be $191,633 Suppose you have $191,633 today, call it W. Invest it, and next year your total income = interest payment + labor income, all of which you consume. So by the end of the year, all you're left with is still W Invest it again, and consume all investment and labor income Again, your wealth level is still W Do this for ve years, you'll nd that wealth is still W This gets at the idea of permanent income: the amount of income you consume every period without changing your wealth level.

Your wealth level will still be $191,633 Suppose you have $191,633 today, call it W.

7 Chapter 11. Q4a The following was in the Wall Street Journal. Indoor sprinklers can save on insurance rates by providing added protection. By one estimate the savings over 30 years would pay for the system, but high-rise buildings are often built by speculators who plan to sell them far sooner than that. a. Why is the fact that builders soon sell the buildings irrelevant? The value of the sprinkler would be capitalized into the value of the building. Therefore, if they were worth putting in, the builder would do so.

By one estimate the savings over 30 years would pay for the system, but high-rise buildings are often built by speculators who

8 Chapter 11. Q4b b. Suppose a sprinkler system costs $30,000 to install and produces savings in insurance premiums of $1000 per year. How many years of such savings would be required to justify the expenditure? The choice is between saving $30,000 right now, versus saving $1000 for n years We want to nd n such that the owner is indierent between the two } {{ } PV of saving 30K today = 1000 (1 + r) (1 + r) } {{ n } PV of saving 1K for n years So the answer depends on the interest rate r If r = 0, then n = 30 years If r > 0, then n > 30 years

The choice is between saving $30,000 right now, versus saving $1000 for n years We want to nd n such that the owner is indierent between

9 Chapter 11. Q8 Your dad has $100,000 to invest and is considering a stock that is expected to yield about $10,000 per year in dividends. If you advise purchase of stocks that pay out no earnings as dividends, your dad complains there will be no income. How would you explain that there still is an income of $10,000 per year? This is basically asking you to explain the puzzle why some stocks pay dividends while others don't People who buy stocks that don't pay dividends can expect a capital gain of an equivalent amount

If you advise purchase of stocks that pay out no earnings as dividends, your dad complains there will be no income.

10 Chapter 11. Q12 You purchase for $900 a $1000 government bond maturing one year from the date of purchase. a. Will you make a prot if you hold the bond to maturity? That depends on what the interest rate is. You'll make zero prot if 900 = r r = 11% If r < 11%, then you'll make a prot. b. Will you make a prot if there is a sharp, general increase in prevailing interest rates a week after your purchase? Again, it depends on the interest rate. If the new interest rate is above 11%, then the bond suers a capital loss.

Will you make a prot if there is a sharp, general increase in prevailing interest rates a week after your purchase?

11 Chapter 11. Q16 Two refrigerators are available for purchase. One costs more to buy but less to operate. Price Oper. Cost / year A B At what interest rate would you be indierent between the two machines if they last three years? If the fridge lasts for three years, then choice is between B, which saves $60 (= ) today, versus A, which saves $20 (= ) each year for three years Equating the two 60 }{{} PV of saving 60 today If r > 0, then option B is better. = r + 20 (1 + r) } {{ 2 } PV of saving 20 forever r = 0

If the fridge lasts for three years, then choice is between B, which saves $60 (= 400 340) today, versus A, which saves $20 (= 120 100)

12 Chapter 11. Q18 Currently in the US, interest on a home mortgage is deducted from income when calculating federal income taxes. How would the removal of this provision aect the wealth of a. current home owners? Current home owners are worse o. They paid a price based on the deduction being there for their purchase, and this price is higher than if there is no deduction. With tax deduction removed, the value of their homes drops b. prospective home owners? At the margin, they are no better or worse o. They don't get the deduction, but the price of housing falls Here, house price falls because there is a decrease in demand c. people in the construction business? Since the demand for houses decreases, so they are worse o.

They paid a price based on the deduction being there for their purchase, and this price is higher than if there is no deduction.

13 Chapter 11. Q24a-b The government borrows money by selling at auction $1,000 bonds, payable in two years, with no interest payments. The market interest rate is 10 percent. a. How much will the bonds sell for? You must provide a formula for the calculation. It'll sell for its present value: PV = 1000 ( ) b. Even though the bonds do not pay interest (the buyer receives $1,000 when the bonds mature and nothing before that), buyers still end up receiving interest on their investment. Explain. A buyer invests $826 and gets $1000 in two years. So the dierence ($174) is the interest payment on her investment.

It'll sell for its present value: PV = 1000 (1 + 0.1) 2 826 b.

14 Chapter 11. Q24c-d c. What interest rate are buyers of the bonds actually receiving on their investment? Explain. They receive 10% per year: FV = PV (1 + r) = 826 (1 + r) 2 r = 10% d. What will happen to the wealth level of bond holders if, immediately after the bonds are sold, the market interest rate unexpectedly falls to 5 percent? Remember that wealth is inversely related to the interest rate. So a fall in interest rate will result in an increase in wealth In particular, the increase will be in the form of a higher bond price, so that the bond holders experience a capital gain

What will happen to the wealth level of bond holders if, immediately after the bonds are sold, the market interest rate unexpectedly falls to 5

15 Chapter 11. Q28 Documents from a 13th century English estate reveal that the value of its ock of sheep was $56. The prot from wool, cheese, and lambs produced in a year were $23. Suppose the expectation was that this yearly stream of prots would continue forever. a. What estimate of the interest rate would you make for the 13th century? (Be explicit about the formula you're using.) We'd use the perpetuity formula 56 = 23 r = 23 r 56 41% b. Using our simple model of interest rate determination, speculate on why the interest rate was likely so high? [hint: do you think there was a lot of borrowing or not so much in 13th century England?] The middle ages were a time of relatively little borrowing. Interest rates were high because the supply of funds was low, not because the demand was high. This reected the huge costs of enforcing loans at the time.

(Be explicit about the formula you're using.) We'd use the perpetuity formula 56 = 23 r = 23 r 56 41% b.

16 Chapter 11. Q34a-c Suppose an asset (say a bond) currently sells for $700 will sell for $900 one year from now. The $900 is xed and known with certainty. a. What is the rate of return on that asset? R = p 1 p = 28.6% p b. Suppose that you know that by the end of the day market interest rates will be 15%, what will be the price of this asset by the end of the day? PV = c. If you buy this asset at $700, and the market interest rate does move to 15%, how much of a capital gain will you have made by the end of the day. Price PV = 83

Suppose that you know that by the end of the day market interest rates will be 15%, what will be the price of this asset by the end of the

17 Chapter 11. Q34d-e d. If someone else buys the asset at the end of the day at the price you found in (b), and then sells the asset for $900 one year from now, what rate of return will have been earned? Note that now we have an equilibrium condition: Price = PV Therefore, rate of interest must equal rate of return at 15% We can also verify: % e. Was the bond a good investment for the person who bought at the price found in (b), compared to what could have been earned elsewhere? Again, since the price in (b) is the equilibrium price, there are no gains or losses at the margin. The investment returns its opportunity cost.

3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.

3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction. Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the