Financial Markets Homework Solutions for Economics 423 - Spring 2014 - Prof. Michae Aguila, Study notes of Financial Market

Download Financial Markets Homework Solutions for Economics 423 - Spring 2014 - Prof. Michae Aguila and more Study notes Financial Market in PDF only on Docsity! Economics 423 - Spring 2014 Prof. Aguilar Financial Markets UNC at Chapel Hill Student Name: PID: Honor Code Signature: HW #1 Due - 02/06/14 @ beginning of class Instructions: • Students may work together, but each must turn in their own assignment. • Answers should be typed whenever possible and submitted with this page as a cover sheet. • Please submit any computer code used to complete the assignment. If you are using EXCEL, then you can print out formuals by hitting Ctrl+ ∼. Specialzied functions for time value of money, bond valuation, and the like are NOT permitted. • Please explain all answers thoroughly. There may be more than one correct solution. • Point Allocation (1a,1b,1c)=(2,1,2)pts (2a,2b,2c)=(1,2,2)pts 3=5pts (4a,4b)=(2,3)pts 1. You are purchasing a $25, 000 car. The financing officer at the dealership quotes you a 5yr loan with an APR of 5%. Assume payments are made monthly, and that the monthly interest rate is 1/12 of the annual interest rate. (a) What is the fixed payment associated with this loan? Provide an analytical as well as a numerical expression. Solution: We know that the PDV of a fixed payment loan is PDV = FP ∑n i=1 1 (1+i)n . We can solve easily for the fixed payment as FP = PDV (∑n i=1 1 (1+i)n )−1 . In our case, FP = 471.78. (b) What is the interest paid, principal paid, and amount due in month 20? Explain your numerical solution Solution: In any given month, the fixed payment is split between interest and principal. The interest amount is the monthly interest rate times the amount of the loan outstanding. The portion paid to principal is the difference between the fixed payment and the interest paid. For month 20, the interest paid is 73.95, which comes from 17,747 due on the loan times the monthly interest rate. The difference between the fixed payment and the interest paid is 397.83, which is the principal paid. The amount due can then be found as 17,747 - 397.83 = 17349.28. (c) Suppose you had $5, 000 available to put toward the purchase of the car. You could either i) use that money to lower your loan amount and invest the monthly savings in a series of discount bonds all maturing at the end of month 60 (note: the monthly savings are accrued beginning in the first period of the loan, not today), or ii) you could use the $5, 000 to purchase a single asset that compounds at a set interest rate each month (note: the first compounding period occurs in the first month of the loan, not today). In either case, the monthly interest rates are identical to that used for the car loan. Which scenario do you prefer? Provide analytical expressions and numerical justification. State all necessary assumptions. Solution: By putting 5,000 towards a downpayment, the loan amount drops by 5,000, which lowers the monthly payments to 377.42. This is a monthly savings of 94.36 per month. If each month’s savings were invested in an CD maturing at the end of the 60th month, the future value of this stream would be 6416.79. Of course, this assumes that the discount rate remains unchanged for the entire period. Alterna- tively, I could invest the 5,000 in an asset that grows by the monthly APR each period, which would have a future value of 6416.79. Therefore, I should be indif- ferent between these two options, if the earnings described are the only factors in my decision making process. 2. You are a financial engineer tasked with creating a new security called a ”Jobless Bond”. The asset is designed as follows: The owner of this $10, 000 face value coupon bond is gauranteed an annual coupon of no less than $50. In those years where the unemployment rate is greater than 6%, the coupon is adjusted. For each tenth of a percentage point of Page 2