Midterm Exam Solutions - Investment, Capital, and Finance | ECON 422, Exams of Economics

Download Midterm Exam Solutions - Investment, Capital, and Finance | ECON 422 and more Exams Economics in PDF only on Docsity! Econ 422 Eric Zivot Fall 2005 Midterm Exam Solutions This is a closed book exam. However, you are allowed one page of notes (double-sided). Answer all questions. For the numerical problems, if you make a computational error you may still receive full credit if you provide the correct formula for the problem. There are 25 questions, and each question is worth 4 points. Total points = 100. You have 1 hour and 50 minutes to complete the exam. Good luck. I. Intertemporal Consumption and Investment Decisions (25 points, 5 points each) In the figure below, the downward sloping straight line connecting the points (0,5) and (4,0) represents the opportunities for investment in the capital market (money market), and the downward sloping curved line connecting the points (0,4) and (2.6,0) represents the opportunities for investment in physical capital (e.g. plant and machinery). The only asset at time 0 is $2.6 million in cash (initial endowment). There is no additional endowment present at time 1. IC 42.61.61 3 4 3.75 5 Dollars, year 0 Dollars, year 1 Please answer the following questions related to the figure: a. What is the interest rate, r , and what is the slope of the capital market line? To determine the interest rate, r, we use the money market line and solve 4(1 + r) = 5 => 1 + r = 5/4 = 1.25 => r = 0.25 or 25% The slope of the capital market line (intertemporal budget constraint) is –(1+r) = -1.25. b. How much should be invested in physical capital (plant and equipment), and how much will this investment be worth next year? Optimal investment occurs where the slope of production function (MRT) = slope of budget constraint = -(1 + r). This tangency point occurs when 2.6 – 1.6 = 1 M is invested. The investment of 1 M returns 3 M next year. c. What is the present value (PV) and net present value (NPV) of this investment? The PV and NPV of the investment project is PV = 3/1.25 = 2.4 M NPV = 2.4 – 1 = 1.4 M d. What is the optimal consumption at times 0 and 1? The optimal allocation of consumption at times 0 and 1 is determined by the tangency point of the IC with the budget constraint. From the figure, we see that optimal consumption at time 0 is 1 M and optimal consumption at time 1 is 3.75 M. e. How much is borrowed or lent at time 0? The owner lends 1.6 – 1 = 0.6 M (at r = 25%) today and receives 0.6*(1.25) = 0.75 M next period. Consumption next period is then consists of the 3M investment return plus the 0.75 M money market return (= 3.75 M). II. Present Value Computations (25 points, 5 points each) 1. You have $1,000 to invest today in a money market account that pays an annual interest rate of r. a. If you invest the $1000 for T years, what is the future value of the investment as a function of r? The FV of the investment is $1,000(1 )TFV r= + III. Bond Pricing and the Term Structure of Interest Rates (25 points, 5 points each) The following is a list of prices for zero coupon bonds (STRIPS) of various maturities (taken from finance.yahoo.com): Maturity (years) Price of zero coupon bond 1 96.56 2 92.48 3 88.42 4 84.65 The bond prices are quoted as a percentage of par (face) value, and the par value is $1,000. Please answer the following questions: a. Calculate the spot rates associated with each bond, and plot the term structure of interest rates. The spot rates are computed using 0,1 1/ 2 0,2 1/ 3 0,3 1/ 4 0,4 1000 1 0.0356 965.6 1000 1 0.0399 924.8 1000 1 0.0419 884.2 1000 1 0.0425 846.5 r r r r  = − =     = − =     = − =     = − =    The term structure is plotted below. Term Structure 0.0350 0.0360 0.0370 0.0380 0.0390 0.0400 0.0410 0.0420 0.0430 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Maturity (years) Sp ot ra te b. Calculate the implied 1-year forward rates, 1,t tf − , for t=2, 3, 4 The implied forward rates are computed using ( ) ( ) 2 0,2 1,2 0,1 3 0,3 2,3 2 0,2 4 0,4 3,4 3 0,1 (1 ) 1 0.0441 1 (1 ) 1 0.0459 1 (1 ) 1 0.0445 1 r f r r f r r f r + = − = + + = − = + + = − = + c. If the expectations hypothesis of the term structure holds, what does the information in the yield curve say about the course of future interest rates? The expectations hypothesis states that the implied forward rates are the best forecasts of the future spot rates. Using the implied forward rates from part b, we see that the expectations hypotheses predicts slightly rising one year spot rates for two years and then a slight decrease. d. What is the price of a 2 year coupon bond making annual coupon payments with a annual coupon rate of 3% and a face value of $1,000? ( ) 1 2 0 2 0,1 0,2 2 1 1 $30 $1,030 $981.51 1.0356 1.0399 C CPV C r r = + + + + = + = Extra credit (5 points). Compute the value of the yield-to-maturity on the 2 year coupon bond from part d above. To find the yield-to-maturity on the bond, solve the following equation: 2 $30 $1030$981.51 0 1 (1 )r r − − = + + This is a quadratic equation. The positive root is given by r = 0.0398.