Tutorial Week6

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University of Wollongong *

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Finance

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Jan 9, 2024

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Tutorial Week6 Critical thinking question 4.3 What is the difference between a perpetuity and an annuity? Perpetuity is a series of level cash flows that continue forever. Annuity is a series of equally spaced and level cash flows extending over a finite number of periods. Questions and Problems 4.5 Present value with multiple cash flows: Akram Motavalli borrowed a certain amount from his friend and promised to repay him the amounts of $2079, $1933, $2107, $1396 and $1578 over the next 5 years. If the friend normally discounts investments at 6.2 per cent annually, how much did Akram borrow? PV 5 = (2079/1.062) + (1933/1.062 ^2) + (2107/1.062 ^3) + (1396/1.062 ^4) + (1578/1.062 ^5) = 1957.63 + 1713.89 + 1759.10 + 1097.46 + 1168.11 = $7696.19 4.8 Present value of an ordinary annuity: Dynamic Teleconference Pty Ltd has made an investment in another company that will guarantee it a cash flow of $ 21,846 each year for the next 5 years. If the company uses a discount rate of 10 per cent on its investments, what is the present value of this investment? CF=$21846 n= 5 i= 0.10 PVA= 21846 * [1-((1/1+0.1) ^5/0.10)] = $82813.53 4.9 Future value of an ordinary annuity: Cecilia Fortuna plans to invest $ 23,004 a year at the end of each year for the next 7 years in an investment that will pay her a rate of return of 12.5 per cent per annum. How much money will Cecilia have at the end of 7 years? FVA = 23004 * [(1+0.125) ^ (7) – 1/ 0.125] = $235689.29
4.12 Calculating annuity payment: Anthony Whitlam is saving for a European holiday in 3 years. He estimates that he will need $4229 to cover his airfare and all other expenses for a week-long holiday. If he can invest his money in an S&P/ASX 500 equity index fund that is expected to earn an average return of 11.4 per cent over the next 3 years, how much will he have to save every year if he starts saving at the end of this year? $4229 = CF * ((1+0.114) ^3) – 1/ 0.114) CF = $1260.51 Therefore, Anthony has to save $1281.37 every year for the next three years. 4.15 Perpetuity: Your grandfather is retiring at the end of next year. He would like to ensure that he and, after he dies, his heirs receive payments of $ 11,309 a year forever, starting when he retires. If he can invest at 9.9 per cent per annum, how much does your grandfather need to invest to receive the desired cash flow? PVP = 11309 / 0.099 = $114232.32 4.15 (assuming payment with a 5% growth rate) PVA = 11039 / 0.099-0.05 = $230795.92 ? 4.22 Calculating annuity payment: Marco Boncordo is a Year 9 student. He currently has $7500 in a savings account that pays 5.65 per cent annually. Marco plans to use his current savings plus what he can save over the next 4 years to buy a car. He estimates that the car will cost $ 12,000 in 4 years. How much money should Marco save each year if he wants to buy the car? FV4 = 7500 * (1 + 0.0565) ^4 = $9344.14 FVA = 12000 – 9344.14= $2655.86 2655.86 = CF * {(1 + 0.0565) ^4 -1} / 0.0565 CF = 2655.86 * 0.565/(1.0565) ^4 – 1 = 610.27 4.27 Perpetuity: Calculate the present value of the following perpetuities: a $1250 discounted to the present at 7 per cent. 1250/0.07 = $17857.14 b $7250 discounted to the present at 6.33 per cent. 7250/0.0633 = $114533.97 c $850 discounted to the present at 20 per cent. 850/0.2 = $4250
4.36 The Hardings are buying a new 4-bedroom house in Albury–Wodonga and will borrow $337 000 from Westpac at a rate of 8.375 per cent per annum for 25 years. What is their monthly loan repayment? Prepare an amortisation schedule using Excel. Assume interesting compounds monthly. Therefore, the monthly loan repayment is $ 2685.29. Additional questions 1. CF = $50000 n = 20 i = 0.05% PVA = $623,110.52
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