problem set 2

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University of Michigan, Dearborn *

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ECON 390

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Finance

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Feb 20, 2024

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pdf

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3

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Ed Cho Financial Markets Problem Set 1 due 02/02 Friday at end of day (11:59pm) You may type or hand write your answers, as long as they are legible. Psets are required to be in PDF format, and submitted as one file (instead of multiple files). Each person must hand in a copy of their own problem set. However, you are encouraged to discuss problem sets with other students. 1. Calculate the present value of $5000 received five years from today if the interest rate is a. 8% compounded annually b. 10% compounded annually c. APR = 10% compounded semiannually 2. You are considering buying a new house worth $250,000. You then decide to put 20% down, and consequently you search for a $200,000, 30 year fixed-rate mortgage, with payments that are made monthly. After your search, the best available offer you find is a mortgage with an APR of 6% compounded monthly. a. What is your monthly mortgage payment? b. Assume instead that the APR is 5% compounded monthly, and calculate the new monthly mortgage payment. Relative to part (a), the APR decreased by 1%. Calculate the percentage change in your monthly payment as a result of this 1% lower interest rate. c. You then decide you want to pay off your mortgage in half the time, so you find a 15 year fixed-rate mortgage, with an APR of 6% compounded monthly. Calculate the new monthly mortgage payment. Does your monthly payment exactly double, more than double, or less than double? Explain intuitively.
3. Your firm’s geologists have discovered a small oil field in New York's Westchester County. The field is forecasted to produce cash flow of C = $2 million/yr, forever. The cost of developing this new oil field is $16.67 million. a. Determine the internal rate of return on this project. b. Suppose that instead of developing the new oilfield, you discover a large underground shale rock deposit, that has the same upfront development cost of $16.67 million to extract the shale gas, and has an internal rate of return of 10%. Assuming you only have $16.67 million to invest, which project would you invest in? c. Redo part (a), except the oilfield is forecasted to produce a cash flow of $2 million for 20 years. Set up the equation that sells for the internal rate of return, but do not solve for it. Is the internal rate of return greater than, less than, or equal to 12%? 4. A General Motors's bond makes the following cash flow payments in the next 10 years. You receive $80 per year starting in t = 1 until t = 10, and you also receive $1000 in t = 10. a. If the interest rate is 9%, what is the current market price of these bonds? b. If the interest rate is 7%, what is the current market price of these bonds? c. What do your answers to the previous two parts say about the relationship between interest rates and the price of bonds? 5. You've just graduated college, and you want to save for a dream vacation that takes you around the world, but that means some serious savings. You estimate that once you start work, you could save 5000 a year out of your income at the end of every year and earn an interest rate of 5% on the savings. How much will you be able to spend after 6 years? (Hint: There's more than one way to solve this question. A quick way is to first find the present value, PV, of these payments using the annuity formula, and then find the future value of the PV.) 6. To buy a house, you borrow a large sum of money from your local savings and loans bank at a nominal interest rate of 15%. Your expectation of inflation is 2%. a. What do you expect to earn in real terms, i.e., the real interest rate? b. After you enter the loan agreement, inflation increases to 7%. Who gains and who loses, i.e., is wealth being redistributed from the borrower (you) to the lender (savings and loans bank), or vice versa? Explain intuitively.
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