Is ma cro solve with explaination

4. Explain the key distinctions between Solow Model with Technology and Without Technology (emphasize their predictions for what drives economic growth dynamics and long-run growth). (5 points) 5. Why do we call Solow Model an exogenous growth model? How is it different from the endogenous growth model? (5 Points)8. Overhaul of a production line generates the following incremental cash inflows over the line's 5-year remaining life. C1 C2 C3 CA C's Cash inflow ($ million) +1.5 +1.3 +1.05 +0.9 +0.75 (a) What is the PV of the inflows? The cost of capital is 12%. (b) Part (a) used a nominal discount rate and the cash inflows incorporated inflation. Redo Part (a) with real cash flows and a real discount rate. The forecasted inflation rate is 3% per year. 9. You have just inherited an office building. You expect the annual rental income (net of maintenance and other cost) for the building to be $100,000 for the next year and to increase at 5% per year indefinitely. A expanding internet company offers to rent the building at a fixed annual rent for 5 years. After year 5, you could re-negotiate or rent the building to another tenant. What is the minimum acceptable fixed rental payments for this five-year agreement? Use a discount rate of 12%. 10. Two dealers compete to sell you a new Hummer with a list price of $45,000. Dealer C offers to sell it for $40,000 cash. Dealer F offers "(-percent financing:" 48 monthly payments of $937.50. (48x937.50=45,000) (a) You can finance purchase by withdrawals from a money market fund yielding 2% per year. Which deal is better? (b) You always carry unpaid credit card balances charging interest at 15% per year. Which deal is better? 11. Your sales are $10 million this and expected to grow at 5% in real terms for the next three years. The appropriate nominal discount rate is 10%. The inflation is expected to be 2% per year during the same period. What is the present value of your sales revenue for the next three years? Fall 2008 Page 2 of 66 12. Company ABC's after-tax cash flow is $10 million (at the end of ) this year and expected to grow at 5% per year forever. The appropriate discount rate is 9%. What is the value of company ABC? 13. You own three oil wells in Vidalia, Texas. They are expected to produce 7,000 barrels next year in total, but production is declining by 6 percent every year after that. Fortunately, you have a contract fixing the selling price at $15 per barrel for the next 12 years. What is the present value of the revenues from the well during the remaining life of the contract? Assume a discount rate of 8 percent. 14. A geothermal power station produces cash flow at a current rate of $14 million per year, after maintenance, all operating expenses and taxes. All the cash flow is paid out to the power stations owners. The cash flow is expected to grow at the inflation rate, which is forecasted at 2% per year. The opportunity cost of capital is 8%, about 3 percentage points above the long-term Treasury rate. (Assume this is an annually compounded rate.) The power station will operate for a very long time. Assume for simplicity that it will last forever. (a) What is the present value of the power station? Assume the first cash flow is received one year hence (b) Now assume that the power stations cash flow is generated in a continuous stream, starting immediately. What is the present value?1. True or False? Briefly explain (or qualify) your answers. (a) The duration of a coupon bond maturing at date T is always less than the duration of a zero-coupon bond maturing on the same date. (b) When investing in bonds, we should invest in bonds with higher yields to maturity (YTM) because they give higher expected returns. (c) The phrase "On the run" refers to junk bonds that have recently defaulted. 2. True or false? Briefly explain (or qualify) your answers. (a) Investors expect higher returns on long-term bonds than short-term bonds because they are riskier. Thus the term structure of interest rates is always upward sloping. (b) Bonds whose coupon rates fall when the general level of interest rates rise are called reverse floaters. Everything else the same, these bonds have a lower modi- fied duration than their straight bond counterparts. 3. True, false or "it depends" (give a brief explanation): (a) Term structure of interest rates must be always upward sloping because longer maturity bonds are riskier. (b) Bonds with higher coupon rates have more interest rate risk. 4. True, false (give a brief explanation): The term structure of interest rates is always upward sloping because bonds with longer maturities are riskier and earn higher re- turns. 5. True or false (give a brief explanation): A flat term structure (identical spot rates for all maturities) indicates that investors do not expect interest rates to change in the future. 6. True or false (give a brief explanation): To reduce interest rate risk, an over-funded pension fund, i.e., a fund with more assets than liabilities, should invest in assets with longer duration than its liabilities. 7. Which security has a higher effective annual interest rate? (a) A three-month T-bill selling at $97, 645 with face value of $100, 000. (b) A coupon bond selling at par and paying a 10% coupon semi-annually. 8. The Wall Street Journal quotes 6.00% for the Treasury bill with a par value of $100,000 due two months from now. What is the effective annual yield on the bill? 9. Which security has a higher effective annual interest rate? Fall 2008 Page 9 of 66 (a) A six-month T-bill selling at $98,058 with face value of $100,000. (b) A coupon bond selling at par and paying a 4.2% coupon (2.1% every six months). 10. Spot rates. You are given the following prices of US Treasury Strips (discount or zero coupon bonds): Maturity Price (per 100 FV) 96.2 91.6 86.1 (a) Compute the spot rates for years 1, 2 and 3. (b) Now, suppose you are offered a project which returns the following cashflows: $300m at the end of year 1 $210m at the end of year 2 $400m at the end of year 3 The project costs $600m today. Calculate the NPV of the project using the spot rates computed above.11. Assume that spot interest rates are as follows: Maturity (year) | Spot Rate (%) 3.0 N 3.5 4.0 4.5 Compute the prices and YTMs of the following bonds: (a) A zero-coupon bond with 3 years to maturity. (b) A bond with coupon rate 5% and 2 years to maturity. (c) A bond with coupon rate 6% and 4 years to maturity. Assume that spot rates and YTMs are with annual compounding, coupon payments are annual, and par values are $100. 12. Treasury bonds paying an 8% coupon rate with semiannual payments currently sell at par value. What coupon rate would they have to pay in order to sell at par if they paid their coupons annually? 13. Yields on three Treasury notes are given as follows: Fall 2008 Page 10 of 66 Bonds and Notes Coupon Rate Maturity Bid Asked Asked yield 7.250 Aug. 04 110:00 110:00 2.07% 10.750 Aug. 05 123:12 123:13 2.55% 5.750 Aug. 10 112:00 112:01 3.97% 5.00 Aug. 11 106:24 106:25 4.09% 8.750 Aug. 20 143:26 143:27 5.02% 6.125 Aug. 29 114:11 114:12 5.13% Strips Maturity Bid Asked Asked yield Aug. 04 96:03 96:04 2.00% Aug. 05 92:19 92:21 2.58% Aug. 10 71:13 71:17 4.24% Aug. 11 67:06 67:08 4.47% Table 1: Treasury Prices and Yields, August 20, 2002 Maturity (yrs) Coupon rate (%) Yield to maturity (%) 5.25 5.50 6.00 Coupons are paid annually. (a) What are the prices of the 1-year, 2-year, and 3-year notes? (b) What are the spot interest rates for years 1, 2 and 3? (c) What is the implied forward rate for year 2 to year 3? 14. Using the following data given in Table 1, answer these questions: (a) What were the 2-, 3- and 8-year spot interest rates? (b) What is the forward interest rate from August 2004 to August 2005? From August 2010 to August 2011? (c) What does the slope of the term structure imply about future interest rates? Explain briefly. Express your answers to (a) and (b) as effective annual interest rates.19. The Wall Street Journal gives the following prices for the STRIPS: Maturity (years) 1 2 3 Price (% of par value) 97.56 95.18 92.86 Suppose that you have a short term liability of $10 million every year for the next three years. (a) Calculate the present value of the liability. (b) Calculate the duration of your liability. (c) Suppose that you want to set aside $20 million to pay part of the liability and the fund will be invested in STRIPS. In order to avoid interest rate risk, what maturity for the STRIPS should you pick? (d) If the interest rates increase by 0.10%, how much will be the remaining short fall for your liability? 20. The Wall Street Journal gives the following prices for the STRIPS: Maturity (years) 2 3 Price (% of par value) 96.1538 92.4556 88.8996 You are holding an asset which yields a sure income of $20 million every year for the next two years. (a) Calculate the present value of the asset. (b) Calculate the modified duration of the asset. (c) If the interest rates increase by 0.10%, how much will the asset's value change in dollars? (d) Suppose that you want to use an interest rate futures to hedge the interest rate risk. The futures has a contract value of $100,000 and a modified duration of 5. Assume a flat term structure of interest rates. What will be your hedging strategy? Fall 2008 Page 13 of 66 (e) Show that with the hedging position in the futures, the value of your total position (the asset plus the futures position) is insensitive to the change in interest rate. 21. The term structure of spot interest rates is given in the table below: Maturity (years) 2 3 5 Interest rate (%) |3.5 4.0 4.0 4.0 4.0 You have just signed a lease on an office building with a rental payment of $1 million per year forever. The first payment is due one year from now. (a) What is the present value of the lease? (b) New inflation figures imply that expected inflation will be 0.5% percent higher. As a result, interest rates for all maturities now increase by 0.5%. What is the PV of the lease under the new market conditions? 22. The following is a list of prices for zero-coupon bonds of various maturities. Calculate the yields to maturity of each bond and the implied sequence of forward rates. Maturity (Years) | Price of Bond ($) 943.40 898.47 847.62 792.1623. You have accounts receivable of $10 million due in one year. You plan to invest this amount in the Treasury market for one year after receiving it. You would like to lock into an interest rate today for this future investment. Current yields on Treasury STRIPS are as follows: Maturity Yield (%) 5.25 5.50 5.75 (a) Your bank quotes you a forward rate of 5.50%. Is this in line with the forward rate implied by market interest rates? (b) Suppose that you can buy or sell short the STRIPS at the above yields without additional costs and the STRIPS have face value of $1,000. How can you use the STRIPS to structure the forward investment you wanted? 24. Refer to Table 1, use the quoted yields to calculate the present value for the cash payments on the (a) August 2011 strip. Fall 2008 Page 14 of 66 (b) August 2011 note. Assume that the first note coupon comes exactly six months after August 20, 2002, and that principal is repaid after exactly 9 years. (This timing assumption is not exactly right. Also, the quoted yields are rounded. Your PV will not match the Asked Price exactly.) 25. Spot Rates and Forward Transactions. Suppose you have the following bonds, which pay coupons at the end of each year: Maturity (yrs) YTM (%) Coupon (6) 4% 1% 4.2% 5% 4.8% 5% (a) Determine the price of each bond per $100 face value. (b) What are the spot rates for years 1, 2 and 3? 26. Which of the following statements are correct? With today's Yield Curve, you can compute exactly: (a) The price at which a 5-year T-Strip with $1, 000 face value trades today. (b) The spot rates that will prevail in two years. (c) The price at which a 5-year T-bond with 7% coupon and $1, 000 face value will trade in one year. (d) The forward rates that prevail today. (e) The forward rates that will prevail in two years. 27. Suppose you are given the following prices for two U.S. Treasury strips. Maturity date Price Yield to maturity November 2012 41:25 6.83% November 2013 38:27 6.87% Assume for simplicity that the maturity dates are exactly 13 and 14 years from now (November). Calculate the forward rate of interest between November 2012 and November 2013.28. Here are closing quotes for 4 Treasury securities on October 11, 2002. Fall 2008 Page 15 of 66 Coupon Maturity Asked Price Asked Yield (Note) 6.5 Feb. 2010 119:08 3.50% (Note) 5.0 Feb. 2011 109:20 3.65% (Strip) Feb. 2010 76:22 3.65% (Strip) Feb. 2011 73:08 3.77% (a) Suppose you buy the Feb. 2011 note and hold it to maturity. How much would you have to pay (approximately)? What cash flows would you receive, on what dates? (b) What are the spot interest rates for February 2010 and February 2011? (c) What is the forward rate of interest between February 2010 and February 2011? (d) Which of these securities has the shortest duration? Explain. 29. Yankee Inc. has sold the Super Coupon Absolute Marvel (SCAM) security to raise new funds. Unlike ordinary bonds, it pays no par value/face value at the end of its life. It only pays coupons every year as follows: $100(1 + 0.05) at the end of year one, $100(1 + 0.05)? at the end of year two, and so on. This security lasts for 4 years (i.e., makes 4 payments). The current interest rate is 5% for all maturities. (a) What is the price today of SCAM? (b) What is the duration today of SCAM? (c) Yankee Inc. sold $10 million worth of SCAM. It plans to invest the proceeds in two assets, Al and A2, for the short run. Al is a 12-month T-Bill, whereas A2 is a 4-year STRIPS. How much should Yankee Inc. invest in Al and A2 to avoid interest rate risks? 30. You manage a pension fund, and your liabilities consist of two payments as follows: Time Payment 10 years $20 million 30 years | $30 million Your assets are $18 million. The term structure is currently flat at 5%. (a) Compute the present value of your liabilities. (b) Compute modified duration of your liabilities. (c) Compute an approximate change in the present value of your liabilities, using duration, when interest rates fall by 0.25%. (d) Suppose that you invest the $18 million in 1-year Treasury bills (i.e., 1-year zero- coupon bond) and in a Treasury bond with modified duration of 20. How would you allocate your assets to avoid interest rate risk of your portfolio, which includes both assets and liabilities