Determination of Interest Rates - Questions with Answers | FINA 4400, Assignments of Financial Market

Download Determination of Interest Rates - Questions with Answers | FINA 4400 and more Assignments Financial Market in PDF only on Docsity! Chapter 02 - Determination of Interest Rates Answers to Chapter 2 Questions 1. Time value of money specifically assumes that any interest or other return earned on an investment is reinvested and interest is, in turn, earned on the earlier interest payments. That is, interest is compounded. This is in contrast to the earning of simple interest which is a 12-month (nominal or stated) interest rate. Simple interest on an investment assumes you do not reinvest the annual interest earned. 2. a. PV = $5,000 (PVIF 6%/1, 5(1)) = $5,000 (0.747258) = $3,736.29 b. PV = $5,000 (PVIF 8%/1, 5(1)) = $5,000 (0.680583) = $3,402.92 c. PV = $5,000 (PVIF 10%/1, 5(1)) = $5,000 (0.620921) = $3,104.61 d. PV = $5,000 (PVIF 10%/2, 5(2)) = $5,000 (0.613913) = $3,069.57 e. PV = $5,000 (PVIF 10%/4, 5(4)) = $5,000 (0.610271) = $3,051.35 From these answers we see that the present values of a security investment decrease as interest rates increase. As rates rose from 6 percent to 8 percent, the (present) value of the security investment fell $333.37 (from $3,736.29 to $3,402.92). As interest rates rose from 8 percent to 10 percent, the value of the investment fell $298.31 (from $3,402.92 to $3,104.61). This is because as interest rates increase, fewer funds need to be invested at the beginning of an investment horizon to receive a stated amount at the end of the investment horizon. Also as interest rates increase, the present values of the investment decrease at a decreasing rate. The fall in present value is greater when interest rates rise from 6 percent to 8 percent compared to when they rise from 8 percent to 10 percent. The inverse relationship between interest rates and the present value of security investments is neither linear nor proportional. From the above answers, we also see that the greater the number of compounding periods per year, the smaller the present value of a future amount. This is because, the greater the number of compounding periods the more frequently interest is paid and thus, a greater amount of interest that is paid. Thus, to get to a stated amount at the end of an investment horizon, the greater the amount that will come from interest and the less the amount the investor must pay up front. 3. a. FV = $5,000 (FVIF 6%/1, 5(1)) = $5,000 (1.338226) = $6,691.13 b. FV = $5,000 (FVIF 8%/1, 5(1)) = $5,000 (1.469328) = $7,346.64 c. FV = $5,000 (FVIF 10%/1, 5(1)) = $5,000 (1.610510) = $8,052.55 d. FV = $5,000 (FVIF 10%/2, 5(2)) = $5,000 (1.628895) = $8,144.47 e. FV = $5,000 (FVIF 10%/4, 5(4)) = $5,000 (1.638616) = $8,193.08 From these answers we see that the future values of a security investment increase as interest rates increase. As rates rose from 6 percent to 8 percent, the (future) value of the security investment rose $655.51 (from $6,691.13 to $7,346.). As interest rates rose from 8 percent to 10 percent, the value of the investment rose $705.91 (from $7,346.64 to $8,052.55). This is because as interest rates increase, a stated amount of funds invested at the beginning of an investment horizon accumulates to a larger amount at the end of the investment horizon.. Also as interest 2-1 Chapter 02 - Determination of Interest Rates rates increase, the future values of the investment increase at an increasing rate. The rise in present value is greater when interest rates rise from 8 percent to 10 percent compared to when they rise from 6 percent to 8 percent. The inverse relationship between interest rates and the present value of security investments is neither linear nor proportional. From the above answers, we also see that the greater the number of compounding periods per year, the greater the future value of a future amount. This is because, the greater the number of compounding periods the more frequently interest is paid and thus, a greater amount of interest that is paid. The greater the amount of interest paid and the greater the future value of a present amount. 4. a. PV = $5,000(PVIFA 6%/1, 5(1)) = $5,000 (4.212364) = $21,061.82 b. PV = $5,000(PVIFA 6%/4, 5(4)) = $5,000 (17.168639) = $85,843.19 c. PV = $5,000(PVIFA 6%/1, 5(1))(1 + .06) = $5,000 (4.212364)(1 + .06) = $22,325.53 d. PV = $5,000(PVIFA 6%/4, 5(4))(1 + .06/4) = $5,000 (17.168639)(1.015) = $87,130.84 5 a. FV = $5,000(FVIFA 6%/1, 5(1)) = $5,000 (5.637092) = $28,185.46 b. FV = $5,000(FVIFA 6%/4, 5(4)) = $5,000 (23.123667) = $115,618.34 c. FV = $5,000(FVIFA 6%/1, 5(1))(1 + .06) = $5,000 (5.637092)(1 + .06) = $29,876.59 d. FV = $5,000(FVIFA 6%/4, 5(4))(1 + .06/4) = $5,000 (23.123667)(1.015) = $117,352.61 6. FV = $2,250(FVIF 18%/1, 4(1)) = $2,250 (1.9387778) = $4,362.25 FV = $9,310(FVIF 6%/1, 9(1)) = $9,310 (1.68947896) = $15,729.05 FV = $76,355(FVIF 12%/1, 15(1)) = $76,355 (5.47356576) = $417,934.11 FV = $183,796(FVIF 8%/1, 21(1)) = $183,796 (5.03383372) = $925,198.50 7. EXCEL Problem: FV = $179,585.63 FV = $201,219.65 FV = $251,817.01 FV = $313,842.84 8. PV = $15,451(PVIF 4%/1, 6(1)) = $15,451 (0.79031453) = $12,211.15 PV = $51,557(PVIF 12%/1, 8(1)) = $51,557 (0.40388323) = $20,823.01 PV = $886,073(PVIF 22%/1, 16(1)) = $886,073 (0.0415186) = $36,788.51 PV = $550,164(PVIF 20%/1, 25(1)) = $550,164 (0.0104826) = $5,767.15 9. EXCEL Problem: PV = $55,683.74 PV = $49,696.94 PV = $39,711.38 PV = $31,863.08 2-2 Chapter 02 - Determination of Interest Rates available to businesses, or the better the overall economic conditions, the greater the demand for loanable funds. Governments also borrow heavily in financial markets. State and local governments often issue debt to finance temporary imbalances between operating revenues (e.g., taxes) and budgeted expenditures (e.g., road improvements, school construction). Higher interest rates cause state and local governments= to postpone such capital expenditures. Similar to households and businesses, state and local governments= demand for funds vary with general economic conditions. In contrast, the federal government=s borrowing is not influenced by the level of interest rates. Expenditures in the federal government=s budget are spent regardless of the interest cost. Finally, foreign participants might also borrow in U.S. financial markets. Foreign borrowers look for the cheapest source of funds globally. Most foreign borrowing in U.S. financial markets comes from the business sector. In addition to interest costs, foreign borrowers consider nonprice terms on loanable funds as well as economic conditions in the home country. 18. Factors that affect the supply of funds include total wealth risk of the financial security, future spending needs, monetary policy objectives, and foreign economic conditions. Wealth. As the total wealth of financial market participants (households, business, etc.) increases the absolute dollar value available for investment purposes increases. Accordingly, at every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the supply of funds due to an increase in the total wealth of market participants results in a decrease in the equilibrium interest rate, and an increase in the equilibrium quantity of funds traded. 2-5 Chapter 02 - Determination of Interest Rates Conversely, as the total wealth of financial market participants decreases the absolute dollar value available for investment purposes decreases. Accordingly, at every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve again creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the supply of funds due to a decrease in the total wealth of market participants results in an increase in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. Risk. As the risk of a financial security decreases, it becomes less attractive to supplier of funds. Accordingly, at every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the supply of funds due to an increase in the financial security=s risk results in an increase in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. Conversely, as the risk of a financial security increases, it becomes more attractive to supplier of funds. At every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the supply of funds due to a decrease in the risk of the financial security results in a decrease in the equilibrium interest rate, and an increase in the equilibrium quantity of funds traded. Future Spending Needs. When financial market participants have few near-term spending needs, the absolute dollar value of funds available to invest increases. Accordingly, at every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The financial market, holding all other factors constant, reacts to this increased supply of funds by decreasing the equilibrium interest rate, and increasing the equilibrium quantity of funds traded. Conversely, when financial market participants have near-term spending needs, the absolute dollar value of funds available to invest decreases. At every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in this financial market that, when corrected results in an increase in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. Monetary Expansion. One method used by the Federal Reserve to implement monetary policy is to alter the availability of credit and thus, the growth in the money supply. When monetary policy objectives are to enhance growth in the economy, the Federal Reserve increases the supply of funds available in the financial markets. At every interest rate the supply of loanable funds increases, the supply curve shifts down and to the right, and the equilibrium interest rate falls, while the equilibrium quantity of funds traded increases. Conversely, when monetary policy objectives are to contract economic growth, the Federal Reserve decreases the supply of funds available in the financial markets. At every interest rate the supply of loanable funds decreases, the supply curve shifts up and to the left, and the equilibrium interest rate rises, while the equilibrium quantity of funds traded decreases. Foreign Economic Conditions. Finally, as economic conditions improve in a country relative to other countries, the flow of funds to that country increases. The inflow of foreign funds to U.S. 2-6 Chapter 02 - Determination of Interest Rates financial markets increases the supply of loanable funds at every interest rate and the supply curve shifts down and to the right. Accordingly, the equilibrium interest rate falls, and the equilibrium quantity of funds traded increases. 19. Factors that affect the demand for funds utility derived from the asset purchased with borrowed funds, restrictiveness of nonprice conditions of borrowing, domestic economic conditions, and foreign economic conditions. 2-7 20. The fair interest rate on a financial security is calculated as i* = IP + RIR + DRP + LRP + SCP + MRP 8% = 1.75% + 3.5% + DRP + .25% + 0% + .85% Thus, DRP = 8% - 1.75% - 3.5% - .25% - 0% - .85% = 1.65% 21. According to the pure expectations theory, the one year rate one year from now is expected to be less than the one year rate today. 22. 1R2 = [(1 + .052)(1 + .058)]2 - 1 = 5.50% 23. 1R1 = 6% 1R2 = [(1 + .06)(1 + .07)]1/2 - 1 = 6.499% 1R3 = [(1 + .06)(1 + .07)(1 + .075)]1/3 - 1 = 6.832% 1R4 = [(1 + .06)(1 + .07)(1 + .075)(1 + .0785)]1/4 - 1 = 7.085% yield to maturity 7.085% 6.832% 6.499% 6.00% _____________________________ term to maturity (in years) 0 1 2 3 4 24. 1 + 1R2 = {(1 + 1R1)(1+E(2r1))}1/2 1.10 = {1.08(1+E(2r1))}1/2 1.21= 1.08 (1+E(2r1)) 1.21/1.08 = 1+E(2r1) 1+E(2r1) = 1.12 E(2r1) = .12 25. 1.12 = {(1+1R1)(1+E(2r1))(1+E(3r1))}1/3 1.12 = {(1+1R1)*1.08*1.10}1/3 1.4049 = (1+1R1 )*1.08*1.1 1+1R1 = 1.4049/(1.08*1.10) 1R1 = .1826 26. 1 + 1R4 = {(1 + 1R3)(1+E(4r1))}1/4 1.026 = {(1.0225)3(1+E(4r1))}1/4 (1.026) 4 = (1.0225)3(1+E(4r1)) (1.026) 4/(1.0225)3 = 1+E(4r1) 1+E(4r1) = 1.03657 E(4r1) = 3.657% 1 + 1R5 = {(1 + 1R4)4(1+E(5r1))}1/5 1.0298 = {(1.026)4(1+E(5r1))}1/5 (1.0298) 5 = (1.026)4 (1+E(5r1)) (1.0298) 5/(1.026)4 = 1+E(5r1) 1+E(5r1) = 1.04514 E(5r1) = 4.514% 1 + 1R6 = {(1 + 1R5)5(1+E(6r1))}1/6 1.0325 = {(1.0298)5(1+E(6r1))}1/6 (1.0325) 6 = (1.0298)5(1+E(6r1)) (1.0325) 6/(1.0298)5 = 1+E(6r1) 1+E(6r1) = 1.04611 E(6r1) = 4.611% 27. The liquidity premium hypothesis is an extension of the unbiased expectations hypothesis. It based on the idea that investors will hold long-term maturities only if they are offered at a premium to compensate for future uncertainty in a security=s value, which increases with an asset=s maturity. Specifically, in a world of uncertainty, investors prefer to hold shorter term securities because they can be converted into cash with little risk of a loss of capital, i.e., short-term securities are more liquid. thus, investors must be offered a liquidity premium to get them to but longer term securities. The liquidity premium theory states that long-term rates are equal to geometric averages of current and expected short-term rates (as under the unbiased expectations theory), plus liquidity risk premiums that increase with the maturity of the security. For example, according to the liquidity premium theory, an upward-sloping yield curve may reflect investors= expectations that future short-term rates will be flat, but because liquidity premiums increase with maturity, the yield curve will nevertheless be upward sloping. 28. 1R1 = 5.65% 1R2 = [(1 + .0565)(1 + .0675 + .0005)]1/2 - 1 = 6.223% 1R3 = [(1 + .0565)(1 + .0675 + .0005)(1 + .0685 + .0010)]1/3 - 1 = 6.465% 1R4 = [(1 + .0565)(1 + .0675 + .0005)(1 + .0685 + .0010)(1 + .0715 + .0012)]1/4 - 1 = 6.666% yield to maturity 6.666% 6.465% 6.223% 5.65% _____________________________ term to maturity (in years) 0 1 2 3 4 29. (1+1R2) = {(1+1R1)(1+E(2r1) + L2)}1/2 1.14 = {1.10*(1+.10 + L2)}1/2 1.2996 = 1.10*(1+.10 + L2) 1.2996/1.1 = 1+.10+L2 1.18145 = 1+.10+L2 L2 = .08145 30. 1R2 = .065 = [(1 + .055)(1 + E(2r1))]1/2 - 1  [(1.065)2 /(1.055)] - 1 = E(2r1) = 7.51% 1R3 = .09 = [(1 + .055)(1 + .0751)(1 + E(3r1))]1/3 - 1  [(1.09)3 /(1.055)(1.0751)] - 1 = E(3r1) = 14.18% 31. 4f1 = [(1 + 1R4)4/(1 + 1R3)3] - 1 = [(1 + .0635)4/(1 + .06)3] - 1 = 7.41% 5f1 = [(1 + 1R5)5/(1 + 1R4)4] - 1 = [(1 + .0665)5/(1 + .0635)4] - 1 = 7.86% 6f1 = [(1 + 1R6)6/(1 + 1R5)5] - 1 = [(1 + .0675)6/(1 + .0665)5] - 1 = 7.25% 32. 1R1 = 4.5% 1R2 = 5.25% = [(1 + .045)(1 + E(r2))]1/2 - 1  E(r2) = 6.01% 1R3 = 6.50% = [(1 + .045)(1 + .0601)(1 + E(r3))]1/3 - 1  E(r3) = 9.04%