Study Questions 1 Econ 130 F19 Partial Answers PDF

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Study Questions No. 1 (October 3, 2019) Economics 130 Fall 2019 See your text for definitions of key terms. Key terms: Money Market Capital market Consol Perpetuity Duration of bond Coupon Bond Coupon Rate Current Yield Discount Bond Face (Par) Value Fixed Payment Loan PDV Rate of Return (one period) Capital Gain Simple Loan Yield to Maturity Commodity Money Fiat Money Financial intermediary Direct Finance

Indirect Finance Divided Diversification Asymmetric information Moral Hazard Adverse Selection Federal Funds rate Investment bank Commercial bank Money Market Instrument Capital Market Instrument Over the Counter Market (OTC) Primary market Secondary market Underwriting M1 M2 Medium of Exchange Store of Value Unit of Account

1. Applied Problem 24 on pg. 47 in textbook (Mishkin, 12th edition). Suppose you have just inherited $10,000 and are considering the following options for investing the money to maximize your return: Option 1: Put the money in an interest-bearing checking account that earns 2%. The FDIC insures the account against bank failure. Option 2: Invest the money in a corporate bond with a stated return of 5%, although there is a 10% chance the company could go bankrupt. Option 3: Loan the money to one of your friend’s roommates, Mike, at an agreed-upon interest rate of 8%, even though you believe there is a 7% chance that Mike will leave town without repaying you. Option 4: Hold the money in cash and earn zero return. a. If you are risk-neutral (i.e., neither seek out nor shy away from risk), which of the four options should you choose to maximize your expected return? (Hint: To calculate the expected return of an outcome, multiply the probability that an event will occur by the outcome of that event.) b. Suppose Option 3 and Option 4 are your only choices. If you could pay your friend $100

to find out extra information about Mike that would indicate with certainty whether he will leave town without paying, would you pay the $100? What does this say about the value of better information regarding risk? a. With Option 1, since deposits are insured it can be assumed a riskless investment. Thus, the expected total payoff would be $10,000 × 1.02 = $10,200. With Option 2, a bond return of 5% implies a potential payoff of $10,000 × 1.05 = $10,500, and there is a 90% chance that this outcome will occur, thus the expected payoff is $10,500 × 0.9 = $9450. Under Option 3, the expected payoff is $10,000 × 1.08 × 0.93 = $10,044. Option 4 is riskless, so the expected total payoff is $10,000. Given these choices and the assumption that you don’t care about risk, Option 1 is the best investment. b. Option 3 implies the very real possibility of either receiving nothing (if he actually leaves town), or $10,800 (if he indeed pays as promised). If you don’t pay Mike, you have an expected return of $10,044 as shown above. If you paid your friend the $100 and learned that Mike would leave without paying, then obviously you wouldn’t loan Mike the money, and you would be left with $9900. However, if you paid the friend $100 and learned that Mike would pay, you would have $10,700 (= $10,000 × 1.08 $100). After paying your friend Mike, but before knowing the true outcome, your expected return would be $10,644 ($9900 × 0.07 + $10,700 × 0.93). Under Option 3, paying your friend the $100 is definitely worth it because it increases your expected return and in addition dramatically reduces the downside risk that you make a bad loan, and increases the certainty of the payoff amount. That is, with asymmetric information (not paying your roommate), you have a range of payoffs of $0 to $10,800 versus $9900 to $10,700 without asymmetric information. Thus, paying a small amount to improve risk assessment under Option 3 can be very beneficial, a task for which financial intermediaries are well suited. Option 4, is riskless, so the expected total payoff is $10,000. If you are more risk averse, Option 4 is likely the better option. However, if you are more risk neutral then paying your roommate the $100 to have a minimum $9900 payment and possibly as much as $10,700 is the better scenario. 2. Web Exercise 1 on pg. 48 in textbook (Mishkin, 12th edition) L1 page3 See Fed Financial Tables: https://www.federalreserve.gov/apps/fof/FOFTables.aspx a. What percentage of assets do commercial banks hold in loans? page 88 L.111 9570.2/15844.8 = 60.40% What percentage of assets is held in mortgage loans? 4899.9/15844.8 = 30.92% b. What percentage of assets do savings and loans hold in mortgage loans? page 88 L.111 4899.9/(10495.3+540.5) = 44.4% c. What percentage of assets do credit unions hold in mortgage loans and in consumer loans? page 90 L.144 538.7/4785.9 = 11.26% 476.1/4785.9 = 9.95% 11.26%+9.95%=21.21% 3. Question 5, page 60 in textbook. a. Brooke accepts money in exchange for performing her daily tasks at her office, since

she knows she can use that money to buy goods and services. This situation illustrates the medium-of-exchange function of money. We often do not think why we accept money in exchange for hours spent working, as we are so accustomed to using money. The medium-of-exchange function of money refers to its ability to facilitate trades (hours worked for money and then money for groceries) in a society. b. Tim wants to calculate the relative value of oranges and apples, and therefore checks the price per pound of each of these goods as quoted in currency units. In this case, we observe money performing its unit-of-account function. If modern societies did not use money as a unit of account, then the price of apples would have to be quoted in terms of all the other items in the market. This quickly becomes an impossible task. Suppose that a pound of apples sells for 0.80 pounds of oranges, half a gallon of milk, one-third of a pound of meat, 2 razor blades, 1.5 pound of potatoes, etc. c. Maria is currently pregnant. She expects her expenditures to increase in the future and decides to increase the balance in her savings account. Maria is contemplating the store-of-value function of money. As a medium of exchange and unit of account, measures of money known as M1 or M2 have no important rivals. With respect to the store-of-value function, however, there are many assets that can preserve value better than a checking account. Maria’s choice to preserve the purchasing power of her income by increasing her savings account balance is fine for a small period of time. For a period of 20 years, however, you might choose to buy a U.S. Treasury bond that matures in 20 years (as many grandparents have done as a way to pay for their grandchildren’s educations). 4. Question 13, page 14 of textbook. Because the Federal Reserve affects interest rates, inflation, and business cycles, all of which have an important impact on the profitability of financial institutions. 5. Rank the following assets from least liquid a. Checking account deposits 2 b. Houses 6 c. Currency 1 d. Washing machines 5 e. Savings deposits f. Common stock 4 6. What is a “consol” debt instrument? Why is the yield to maturity on a consol the same as the current yield? Consols = perpetuities; pay a payment Z forever (in principle): price of consol = Z/i 7. Why do corporate bonds with the same years to maturity (e.g. n = 10 years), the same coupon payment (C) and the same face value (F) as a U.S. Treasury Note trade at a lower price? They have greater default risk. What does this imply about the yield to maturity? Comparable maturity corporate bonds have a higher interest rate. 8. What is “indirect” finance? What is “direct” finance? Give examples of different forms of indirect and direct finance? Indirect works through financial intermediaries (e.g. banks); direct links savers and borrowers directly.

9. Would a dollar received in one-year be worth more to you today when the interest rate is 20% or when it is 10%? (Calculate manually). Use PV formula. Which has higher PV? 1/(1.20) < 1/1.10. See Excel Spread Sheet. 10. You have just won $10 million in the state lottery, which promises to pay you $1 million (tax free) every year for the next ten years. Have you really won $10 million? No. Use PV formula to calculate (using a calculator) PV of series of $1 million payments for 10 years. See Excel Spread Sheet. 11. If the interest rate is 10%, what is the present value of a security that pays you $1,000 next year, $1,210 the year after, and $1,331 the year after that? (Use a calculator or computer program: look for “present value formulas”). Use PV formula (using a calculator). See Excel Spread Sheet. 12. Write down the formula that is used to calculate the yield to maturity (YTM) on a twentyyear 10% coupon bond with $1,000 face value that sells for $2,000. Use the Excel computer program to compute the YTM. Standard asset pricing formula to calculate YTM. See Excel Spread Sheet. 13. What is the yield to maturity on a $1,000-face-value discount bond maturing in one year that sells for $800? (Calculate manually). Discount bond formula: YTM = (F – P)/P. See Excel Spread Sheet. 14. Which $1,000 bond has the higher yield to maturity, a twenty-year bond selling for $800 with a current yield of 15% or a one-year bond selling for $800 with a current yield of 5%? Use PDV formulas with financial program or calculator for an exact YTM. Excel Spread sheet. 15. You are offered two bonds, a one-year U.S. Treasury bond with a yield to maturity of 9% and a one-year U.S. Treasury bill with a yield on a discount basis of 8.9%. Which would you rather own? The bond…higher YTM. 16. If mortgage rates rise from 5% to 10% but the expected rate of increase in housing prices rises from 2% to 9%, are people more or less likely to buy houses? The jump in housing appreciation is 7% and borrowing costs 5%, so more people would borrow. 17. Interest rates were lower in the mid-1980s than they were in the late 1970s, yet many economists have commented that real interest rates were actually much higher in the mid1980s than in the late 1970s. Does this make sense? Do you think that these economists are right? Inflation was much lower in mid-1980s, pushing up real interest rates.

Excel Spreadsheet Answers Question No. 9 =1/(1+i) 0.833333333 $1 at 20% 0.909090909 $1 at 10% Question No. 10 Using NPV Function of Excel 10000000 PV of $10,000,000 now and for following 9 years (total of 10 years) 10000000 $ 10,000,000.00 PV of $10million immediately 10000000 $77,861,089.22 PV of $10million received one year hence and each year following (total of 9 future years) 10000000 Total PV 87,861,089.22 $ 10000000 Total Payments 10,000,000.00 $ 10000000 10000000 Question No. 11 NPV Using Excel Spreadsheet 10000000 Amount End of Year 10000000 1000 1 1210 2 1331 3 3541 Total Amounts $2,909.09 NPV Question 12 Using IRR (internal rate of return formula in Excel) ‐2000 0 price of bond 100 1 10% coupon bond= .10 of face value 100 2 100 3 100 100 100 100 100 100 100 100 100 100

100 100 100 100 100 100 19 1100 20 coupon plus face value 3.17% Using Excel IRR formula

Question 13 1+i=FV/P i=(FV/P)‐1 25% Question 14 Note: coupon rate is C/FV, while current yield is C/P (where C=coupon payment, FV is face value of bond, and P is price of bo One year bond: if C/P = 0.05 implies C = (800 * .05) = 40 C YTM = IRR = 1+i=(FV+C)/P 30% YTM 20‐year bond Use IRR formula Current yield = C/P = C/800=0.15 120 C ‐800 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120

120 1120 IRR 15.24% YTM On the basis of a one‐year return prefer the one‐year bond (30%), but longer term bond return (if held to maturity=15%) covers 20 years Question 15 If we were to do the same calculation interpreting the question as "coupon rate" rather than "current yield" we would have: One year bond: C/FV=0.05 implies C=1000*0.05 50 C YTM = IRR = 1+i=(FV+C)/P 31% YTM 20‐year bond Use IRR formula Current yield = C/P = C/800=0.15 120 C ‐800 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150...