Midterm_1_2021

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Boston College *

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MFIN

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Finance

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Apr 3, 2024

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Fundamentals of Finance: Midterm 1 Spring 2021 PLEASE READ: You have 1 hour and 10 minutes to complete the midterm exam. There are five questions, and in total the midterm is worth 115 points. Note the number of points next to each question and use those points to allocate your time. Please note that you must justify all of your calculations! State the formula you are using, then plug in values and solve. If you just write down an answer, you will not get much credit. NAME: Section: 9:00 AM 1:30 PM 3:00 PM (Circle one) 1
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1. Time Value of Money (15 points) (a) (5 points) Would you rather borrow money at an APR of 12% compounded semi- annually or an APR of 11.5% compounded weekly? Justify your answer. (b) (5 points) How long will it take for an investment to triple in value if the investment has an APR of 2% and pays interest once per year? (c) (5 points) How much money will you have in 2.5 years if you put $ 1000 into a savings account paying an APR of 5% and continuous compounding. 3
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2. Present Value of Annuities (20 points). Your firm, Tall Towers Construction, has just signed a contract to help renovate Burj Dubai, a skyscraper expected to stand 2,691 feet tall. Before you can begin construction, you need to purchase a very tall crane and have it delivered to Dubai. The crane costs $ 10 million to purchase and transport. You have two financing options for the crane. 6.0% APR with monthly financing for 120 months but with a $ 2 million discount on the price of the crane 3.0% APR with monthly financing for 72 months but no discount on the price of the crane. In both cases, assume that you make the first payment next month and that your firm’s discount rate is 1.0% per month. (a) (10 points). What are the monthly payments under the two financing options? 4
(b) (10 points). Which financing option should you choose? Please justify your choice with the appropriate calculations. 5
3. Perpetuities, Annuities, and Inflation (30 points). Please assume that you can invest at an APR of 6%, compounded monthly. The monthly inflation rate is 0.25%. (a) (10 points) Congratulations, you won a perpetuity that will pay $ 200 every three months. However, the payments won’t begin for 5 months. What is the value of this perpetuity? (b) (10 points) How much do you need to save each month for the next 35 years if your goal is to have $ 2 million in your bank account in 35 years? 6
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(c) (10 points) You want to convert the $ 2 million into an annuity that provides you with the same purchasing power for each of the next 20 years. What is the real value of each annuity payment? What is the nominal value of the annuity payment in year 20? 7
4. Bond Valuation (30 points). In each of the questions below, assume that the one-year spot rate is 2.0%, the two-year spot rate is 2.4%, the three-year spot rate is 3.0%, and the four-year spot rate is 3.6%. (a) (10 points) What is the appropriate price for a four-year U.S. treasury note with a face value of $ 1,000 and a 5% coupon rate? (b) (10 points) If you buy the bond in part (a) and sell it three years from today (immedi- ately after the year-three coupon payment is made), what effective annual rate of return do you expect to earn between years 2 and 3? 8
(c) (10 points) Yesterday, Google had no debt and $ 20 billion in cash. Today, it just issued a four-year corporate bond with a face value of $ 1 million. The bond will make no coupon payments. Assume that the probability of default is only 0.1%, but that Google will pay $ 0 if it defaults on its bond. Further assume that the appropriate discount rate is the risk-free rate. What is the value of Google’s bond? 9
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5. Bond Valuation and Forward Rates (20 points). The one-year spot rate ( r 1 ) is 4.00%, the two-year spot rate ( r 2 ) is 4.25%, the three-year spot rate ( r 3 ) is 4.50%, the four-year spot rate ( r 4 ) is 4.75%, and the fifth-year spot rate ( r 5 ) is 5.25%. (a) (10 points) What is the two-year forward rate between years 3 and 5? (b) (10 points) Consider a five-year bond with a coupon rate of 8% in the first 3 years and a coupon rate of 5% in the forth and fifth year, a par value of $ 1000, and a price of $ 1045. Please write down (but do not attempt to solve) the equation that implicitly defines the yield to maturity of this bond. 10
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