(Due at 11:59pm EST, Aug 2) 1. Suppose firm A’s stock is current sold at $30 per share in the market 23. After careful analysis, you have determined that a firm’s dividends should grow at 7%, on average, in the foreseeable future. The firm’s last dividend was $3. If your required return is 18%, is firm A’s stock a good investment? 𝑃0 = $3 × 1.07 = $29.18 −0.18 − 0.07 It is not a good investment as the stock is worth less than its current price, $29.18 which is $ 30. 2. Can a person with rational expectations expect the price of a share of Google to rise by 10% in the next month? No, if the person similar information to the rest of the market. An expected price increase by10% over the next month implies over a 100% annual return on Google stock, which certainly exceeds its equilibrium return. This would mean that there is an unexploited profit opportunity in the market, which would have been eliminated in an efficient market. The only time that the person’s expectations could be rational is if the person had information unavailable to the market that allowed him or her to beat the market. 3. Angus Bank holds no excess reserves but complies with the reserve requirement. The required reserves ratio is 9%, and reserves are currently $27 million. Determine the amount of deposits, the reserve shortage created by a deposit outflow of $5 million, and the cost of the reserve shortage if Angus Bank borrows in the federal funds market (assume the federal funds rate is 0.25%). Deposits = 27/0.09 = 300. The reserve shortage is calculated as outstanding reserves after the deposit outflow, minus required reserves after the deposit outflow: 22 ‒ 295 × 0.09 = ‒ 4.55 Angus Bank has to borrow $4.55 million. Borrowing from the Fed will cost Angus Bank: 0.0025 × 4.5 = $11,250 dollars. 4. Suppose you are the manager of a bank whose $100 billion of assets have an average duration of four years and whose $90 billion of liabilities have an average duration of six years. Conduct a duration analysis for the bank and show what will happen to the net worth of the bank if interest rates rise by 2 percentage points. The assets decrease by $8 million = $100 million× –2% ×4 years while liabilities decrease by $10.8 million (= $90 million × –2% × 6 years. Given that the liabilities’ decrease in value is more than the decrease n the value of assets by $2.8 million, the bank’s net worth rises by the same value. 5. If the Fed lends five banks a total of $100 million but depositors withdraw $50 million and hold it as currency, what happens to reserves and the monetary base? Use T-accounts to explain your answer. The initial effect; Banking System (all five banks) Assets Reserves Liabilities +$100 million Loans (borrowings from the Fed) +$100 million Federal Reserve System Assets Liabilities Loans (borrowings from the Fed) million +$100 Reserves +$100 million Public Assets Liabilities No change No change After the public withdraws $50 million in deposits ; Banking System (all five banks) Assets Reserves Liabilities +$50 million Loans (borrowings from the Fed) +$100 million Checkable Deposits –$50 million Federal Reserve System Assets Liabilities Loans (borrowings from the Fed) million +$100 Public Assets Checkable Deposits Liabilities –$50 million Reserves +$50 million Currency +$50 million Currency +$50 million 6. Suppose that currency in circulation is $600 billion, the amount of checkable deposits is $900 billion, and excess reserves are $15 billion. a. Calculate the money supply, the currency deposit ratio, the excess reserve ratio, and the money multiplier. The money supply M = C + D = $600 billion + $900 billion = $1,500 billion; c = C/D = 600/900 = 0.667; e = ER/D = 15/900 = 0.017; m = (1 + c)/(rr + e + c) = (1+0.667)/(0.1+0.017+0.667) = 1.667/0.783 = 2.13. b. Suppose the central bank conducts an unusually large open market purchase of bonds held by banks of $1,400 billion due to a sharp contraction in the economy. Assuming the ratios you calculated in part (a) remain the same, predict the effect on the money supply. The monetary base will decrease to $800 + $80 + $18 - $30 = $868 billion. Based on the money multiplier calculated previously, this implies the money supply should decrease to $868 * 1.94 = $ 1683.92 billion c. Suppose the central bank conducts the same open market purchase as in part (b), except that banks choose to hold all of these proceeds as excess reserves rather than loan them out, due to fear of a financial crisis. Assuming that currency and deposits remain the same, what happens to the amount of excess reserves, the excess reserve ratio, the money supply, and the money multiplier? ER = $1415 billion; e = $1415/$900 = 1.57; m = (1 + 0.667)/(0.1 + 1.57 + 0.667) = 0.71. The money supply is remains at $1,500 billion, since the currency and deposits are the same. 7. Using the supply and demand analysis of the market for reserves, indicate what happens to the federal funds rate, borrowed reserves, and nonborrowed reserves, holding everything else constant, under the following situations. a. The Fed raises the target federal funds rate. To raise the target fed funds rate, the Fed will have to conduct an open market sale of securities, which will shift the supply of nonborrowed reserves to the left. The fed funds rate will increase, and as long as the equilibrium fed funds rate remains below the discount rate, borrowed reserves will remain the same. id Feds Funds Rate RS i2 i1 RD NBR1 R NBR2 b. The Fed reduces reserve requirements and then offsets this action by conducting an open market sale of securities. With the decrease in required reserves, this reduces reserve demand as shown in part (e) above. This will decrease the equilibrium fed funds rate. In order to sterilize the effects and keep the fed funds rate unchanged, the Fed will conduct an open market sale of securities, shifting the reserve supply line to the left. The end result is that the fed funds rate and borrowed reserves will be unchanged, and nonborrowed reserves will decrease. id Feds Funds Rate RS i2 i1 RD NBR1 NBR2 R 8. If the Fed has an interest rate target, why will an increase in the demand for reserves lead to a rise in the money supply? Use a graph of the market for reserves to explain. An increase in the demand for reserves will raise the federal funds rate. In order to maintain the interest rate target, the Fed will buy bonds, thereby increasing the amount of nonborrowed reserves, which shifts the supply curve for reserves to the right, thereby keeping the fed funds rate from rising, as shown below. The open market purchase will then cause the monetary base and the money supply to rise. id Feds Funds Rate RS i2 i1 RD NBR1 NBR2 R 9. What does the Taylor rule imply that policymakers should do to the fed funds rate under the following scenarios? a. Unemployment rises due to a recession. If unemployment rises, this would lower the output gap, and trigger a lower fed funds rate according to the Taylor rule. b. An oil price shock causes the inflation rate to rise by 1% and output to fall by 1%. If inflation rises by 1%, this alone would prompt the fed funds rate to rise by 1.5 percentage points. The decrease in the output gap alone would imply the fed funds rate would fall by 0.5 percentage points. Thus, the two factors together imply a net effect of increasing the fed funds rate by one percentage point according to the Taylor rule. c. The economy experiences prolonged increases in productivity growth while actual output growth is unchanged. Longer increases in productivity growth would increase potential output, and with the same rate of actual output growth this would cause the output gap to decline, resulting in a decline in the fed funds rate according to the Taylor rule.
