Tutorial 1 HW questions

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School

University of Technology Sydney *

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25300

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Finance

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May 1, 2024

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docx

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Tutorial 1 questions -HW 1. B 2. C 3. A 4. B 5. B 6. B 7. False 8. Yes 9. Investment decision 10. FB book is the amount of money shareholders would receive. The market value is the value of a FB on stock price and no of outstanding shares. 11. Company has made sales on credit. 12. When managers’ and shareholders’ incentives are not aligned. 13. Takeover should serve the best interest if owners of both bidding and target firms. Tutorial 2 1. You invest $100,000 today in an online savings account for 5 years. If the interest rate is 4% p.a., calculate the future value under each of the following scenarios: (a) interest rates are compounded annually FV= 100000(1+0.04) 5 =121665.29 (b) interest rates are compounded monthly FV= 100000(1+(0.04/12)) 60(5 x 12) = 122099.66 2. You expect to receive $50,000 from your superannuation in 3 years from today. If the interest rate is 8% p.a., calculate the present value under each of the following scenarios: (a) interest rates are compounded annually PV = 50000(1+0.08) -3 =39691.61 (b) interest rates are compounded quarterly PV = 50000(1+(0.08/4)) -12(-3x12) = 39424.66 3. $10,000 is invested for 10 years at an interest rate of 3.75% p.a. with annual compounding. How much interest is earned in: (a) the first year? I1= 10000 x 0.0375 = $375 (b) the tenth year? I10 = FV= (10000(1+0.0375) 10 )= 14450.44 I9 = FV =(10000(1+0.0375) 9 )= 13928.13 I10-19= 522.31 4. You have a student loan of $2,000. How much will be required on 14 December 2026 to repay the loan if it was made on 14 December 2022 at 8% p.a. compounding half-yearly? PV= $2000 Half yearly = 2 I = 8%
FV= 2000(1 +0.08/2) 8(4x2) = 2737.138 5. On your 21st birthday you receive $10,000 as a result of a deposit that your grandparents made on the day you were born. How large was that deposit if it earned interest at 6% p.a.? PV = 10000(1+0.06) -21 = 2921.554 6. A one-bedroom unit in Darwin can be purchased now for $160,000 cash, or an $80,000 cash deposit today and $110,000 cash payable in five years. If interest rates are 9% p.a. compounding monthly, which method of payment is better? Explain. O1 $160000 O2 $80000 PV of O2 80000+110000(1+0.09/12) -60(5x12) = 150256.97 Option 2 is cheaper. 7. To repay a $50,000 debt that accrues interest at 12% p.a., you agree to make two equal-sized payments in one year and two years’ time, respectively. What is the size of each payment? PV of x1 + PV of x2 =50000 x/(1+0.12) 1 + x/(1.0.12) 2 = 50000 x(1/(1+0.12) 1 + 1/(1+0.12) 2 )= 50000 x = 50000/(1+0.12) 1 + (1+0.12) 2 )= 29584.91 8. You have $30,000 that you want to invest in an online account for the next 10 years. You are offered an investment plan that will pay you 3% p.a. for the first 5 years and then 6% p.a. for the remaining 5 years. What will be the balance in your online account at the end of the 10 years? Assume that the interest rate is compounded semi-annually. PV= 30000 FV5= 30000(1+0.03/2) 10 (5x2) = 34816.22 FV10= 34816.22(1+0.06/2) 10 (5x2) = 46790.09 Tutorial 3 1. How much would you have accumulated after 10 years if you save $2,400 each year in a savings account with an interest rate of 4.8% p.a.? FV (10) = 2400( (1+0.048) 10 -1)/0.048 = 29906.63 2. You borrow $18,713.49 today. If the loan repayments are made annually over ten years and the interest rate is 4.8% p.a., then what is the dollar value of each annual repayment? 18713= PMT x ((1 – (1.048) -10 )/0.048 PMT =2400 3. You are an elite sportsperson and are about to sign a contract with a rugby league team reportedly, “worth $10 million over eight years”. The contract reveals you will receive $24,038.46 each week for eight years. A competing team is prepared to offer you $8.5 million cash today for an eight-year playing contract. If interest rates are 4% p.a. compounded weekly, which team’s offer should you accept?
Offer 1: PV (0)= 24038.16 x (1-(1+(0.04/52)) -8 x 52 /0.09/52) = 8.55 million Offer 2: PV = 8.5 million Therefore, Offer 1 Is better. 4. Your eccentric wealthy uncle wants to donate money to you so that you can pursue your hobbies without fulltime employment. If given a choice between the following four income streams, which would you prefer assuming an interest rate of 5% p.a.? a) PV = 400k b) PV = 15k/0.05 =500k c) PV = 30k x (1-(1.005) -20 /0.005) d) PV = 600k x (1 +0.05) -10 5. You invest $800 cash each year with the first deposit made in 2024 and the final deposit made in 2031. What is the future value of your investment? Assume interest rates are 5% p.a. In what year is the future value determined? In what year is the present value determined? PV(2023) = 800 x (1-(1.05) -8 )/0.05 PAF FV (2031) = 800 x ((1.05) 8 -1/0.05 FAF 6. With an 8% p.a. rate, how much would you pay for a business that produces $1,200 per year forever, with the first cash flow occurring in one year’s time? PV = 1200/ 0.08 = 15k 7. Your budget shows you can afford to service a loan with a maximum repayment of $400 per month over a five-year loan term. If interest rates are 6% p.a. compounded monthly, can you afford to borrow $20,000 for a new car? Explain. PV = 20k PV = 400 x (1-(1+(0.06/12)) -5 x 12 / 0.06/12 = 20.6k 20k = PMT (1-(1+(0.06/12)) -5 x 12 /0.06/12 PMT < 400
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