Quiz 2020, questions and answers PDF

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ADM 2350R Winter 2020 Quiz #2 solutions

Name:_______________________ Student #:_______________________

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Problem 1: Find the PV (at t=0) of a growing perpetuity that starts at year t=5 with the first payment of $3000 and has a growth rate of 5% if the annual interest rate is 8%. Round you answer to the nearest cent. Ans:___$73508.99_________ (3000/(0.08-0.05))/1.08^4=$73508.99

Problem 2: Find the PV (at t=0) of a bi-annual perpetuity that pays $1000 each other year starting at year t=3 (i.e., it pays at years t=3, 5, 7, 9, 11, …) if the annual interest rate is 10%. Round you answer to the nearest cent.

Ans:___$ 4329.00_________ r=1.1^2-1=21%, PV at t=3 is 1000/0.21=$4761.90 (give 0.5 if students give this answer or have 1000/0.21 anywhere in the solution), hence, PV at t=0 is 4761.90/1.1=4329.00

Problem 3: Find the PV of a growing annuity that pays $1000 next year; makes a total of 15 annual payments, the payments are growing at a rate of 3% per year; and there risk-free interest rate is 9%. Round you answer to the nearest cent. Ans: $9537.98 1000*(1-(1.03/1.09)^15)/(0.09-0.03)=$9537.98 Problem 4: You plan to retire in 40 years and you plan to save for your retirement by making 40 annual contributions to your retirement saving plan starting next year. Your first contribution will be $1000 and the size of your annual contribution will grow at a rate of 7% per year. How much money will be on your saving account right after you made your last contribution if the annual interest rate is 5%. Round you answer to the nearest cent. Ans: 396,723.46 PV of growing annuity is 1000*(1-(1.07/1.05)^40)/(0.05-0.07)=56352.85 Hence, FV=56352.85*1.05^40=$396,723.46

Problems 5-7 are based on the following information 2

Assume you’ve just took a 20-year $418,742.315 mortgage with APR=6% compounded monthly (i.e., your monthly interest rate is 0.5%). Based on this information, you were able to compute that your monthly payments will be $3,000.

Problem 5: How much of you SECOND monthly payment will go toward interest? Round you answer to the nearest cent. Ans: (418742.315*1.005-3000)*0.005=$2089.18

Problem 6: What will be your balance 5 years from now (right after you make your 60th payment)? Round you answer to the nearest cent. Ans: 355,510.54 PMT=3000; N=180; I/Y=0.5; CPT PV

Problem 7: Assume that, in addition to your regular $3000 payment, you were able to make an extra $36,000 exactly 3 years from now (with your 36th payment). By how many month will it reduce the length of your mortgage (i.e., by how many monthly payments less you will need to make in total to repay your mortgage)? Round your answer to the nearest month. Ans: 30.79 (accept both 30 and 31) month reduction or 209.21 (accept both 209 and 210) total mortgage lenght. PV of this extra repayment is 36000/1.005^36=30083.22. Hence original balance is reduced to 418,742.315-30083.22=388659.10. Now, set up question as PV=-388659.10; I/Y=0.5; PMT=3000; CPT N. Find N=209.21. Hence, length reduction is 240209.21=30.79

Problem 8-10 are based on the following information: Consider a bond that has 20 years to maturity, face value of $1000; pays annual coupons with annual coupon rate of 6% and has YTM=8%. Round your answer to the nearest cent Problem 8: Find the price of the bond. Round your answer to the nearest cent Ans: 803.64 FV=1000; PMT=60; I/Y=8; N=6; CPT PV 3

Problem 9: Find the current yield on the bond during the first year. Round your answer to 1/100th of a percent. Ans: 60/803.64=7.47% If students have incorrectly found price of the bond in the previses question, but computed current yield as 60/price (using the price they found0 – give full credit Problem 10: Find the capital gain yield on the bond during the first year. Round your answer to 1/100th of a percent. Ans: 8-7.47=0.53% If students made mistakes in the previous questions, give full credit as long as the answers to Question 11 and 12 sum up to 8%

Problem 11: A 20 year bond with face value of $1000 and annual coupon rate of 9% (paid annually) is selling at $1200. This pond is callable 12 years from now and has YTC=8%. Find the call price of this bond (i.e., how much bondholder will receive, in addition to the regular coupon, at the time when the bod will be called). Round your answer to the nearest cent

Ans: $1313.86 N=12; PV=-1200; I/Y=8; PMT=90; CPT FV

Problems 12-13 are based on the following information: You have invested 60% of you money in ABC equity with expected return of 12% standard deviation of 20%, and beta of 0.9; and you have invested 40% of your money in CBA equity with expected return of 15%, standard deviation of 25%, and beta of 1.3. The correlation between the stocks returns is 0.3 Problem 12: Find your portfolio’s standard deviation. Round your answer to 1/100th of a percent. Ans: Sd.dev=sqrt(0.6^2*0.2^2+0.4^2*0.25^2+2*0.6*0.4*0.2*0.25*0.3)=17.78% Problem 13: Find beta of your portfolio. Round your answer to 2 decimal digits. 4

Ans: 0.6*0.9+0.4*1.3=1.06 Problem 14: Find the risk-free interest rate if the expected return on a stock with =0.8 is equal to 12% while expected return on a stock with =1.5 is equal to 20% Ans: (20-x)/1.5=(12-x)/0.8. Hence, x=(12*1.5-20*0.8)/(1.5-0.8)=2.86% Problem 15: A long-term non-callable dividend-paying risk-free bond is currently selling below its par value. Assuming its YTM will not change, what can you say about its current yield during the first and the second year? A) The current yield during the first year must be higher than during the second year B) The current yield during the first year must be lower than during the second year C) The current yield during the first year must be equal to the current yields during the second year D) The provided information is not sufficient to compare current yields during the first and the second year Ans: A (bond price will increase, hence, current yield will decrease) Problem 16: Consider stock AAA with beta = 1.2 and standard deviation of return = 20% and stock BBB with beta =0.9 and standard deviation of return 15%. Which of the folloeing statement is correct. A) The expected return on stock A must be higher than on stock B because the return on stock A has higher standard deviation B) The expected return on stock A must be lower than on stock B because the return on stock A has higher standard deviation C) The expected return on stock A must be higher than on stock B because stock A has higher beta D) The expected return on stock A must be lower than on stock B because stock A has higher beta E) The expected returns on stock A and B must be the same since the ratio of standard deviation to beta is the same for both stocks (20/1.2=15/0.9) Ans: C

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