Week 5 finance questions PDF

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Week 5 tutorial questions, including all answers...

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4.3 what is the difference between a perpetuity and an annuity? The primary difference between an annuity and perpetuity is the time period of cash flows. An annuity is a financial contract that consists of equally spaced level cash flows over a finite number of periods. Whereas, perpetuities involve a contract dictating continuing cash flow payments to go on for an infinite period with no end date. 4.6 Present value with multiple cash flows: Biosynthetics Pty Ltd expects the following cash flow stream over the next 5 years. The company discounts all cash flows at a 17.9 per cent discount rate. PV = FV / (1+i)n Year 1 CF: -$1 035 546 / (1.179)1 = - 878325.70 Year 2 CF: -$1 094 678 / (1.179)2 = -787514.90 Year 3 CF: $293 427 / (1.179)3 = 179043.54 Year 4 CF: $822 105 / (1.179)4 = 425473.06 Year 5 CF: $1 873 588 / (1.179)5 = 822441.60 PV = - 878325.70 -787514.90 + 179043.54+ 425473.06 +822441.60 PV = -$238882.40 4.7 Present value of an ordinary annuity: An investment opportunity requires a payment of $592 for 12 years, starting a year from today. If your required rate of return is 8.8 per cent, what is the value of the investment today? PVA = $592 N= 12 I = 8.8% i 1+¿ ¿ n ) ¿ PVA = CF ( ¿ 1 1− ¿ ¿ 1− PVA = 592 (

1 12 ( 1.088 ) ) 0.088

PVA = 592 (7.23) = $4282.19

4.20 Future value with multiple cash flows: Stephanie Holland plans to adopt the following investment pattern beginning next year. She will invest $2719 in each of the next 3 years and

will then make investments of $3650, $3725, $3875 and $4000 over the following 4 years. If the investments are expected to earn 7.3 per cent annually, how much will she have at the end of the 7 years? Year 1 FV1 = 2179(1.073)6 Year 2 FV2 = 2179(1.073)5 Year 3 FV3 = 2719(1.073)4 Year 4 FV4 = 3650(1.073)3 Year 5 FV5 = 3725(1.073)2 Year 6 FV6 = 3825(1.073) Year 7 FV7 = 4000 Total value = 3325.49 + 3099.25 + 2888.39 + 4509.12 + 4288.70 + 4104.23 + 4000 = 26215.18 4.34 You are now 50 years old and plan to retire at age 67. You currently have a share portfolio worth $150 000, a superannuation fund worth $250 000, and a money market account worth $50 000. Your share portfolio is expected to provide you annual returns of 12 per cent, your superannuation will earn you 9.5 per cent annually, and the money market account earns 6.25 per cent, compounded monthly. a If you do not save another cent, what will be the total value of your investments when you retire at age 67? Share portfolio FV = 150 000 (1+0.12)17 = $1029906.13 Superannuation FV = 250000 (1+0.095)17 =$1169445.63 Money Market FV = 50000 (1+0.0625)17 =$140139.95 Total value of investments = $2339491.71 b Assume that your superannuation contribution is $12 000 per year for the next 17 years (starting 1 year from now). How much will your investments be worth when you retire at 67? i 1+¿ ¿ ¿ n ) PVA = CF ( ¿ 1 1− ¿ ¿

0.095 1+¿ ¿ 17 ¿ PVA = 12000 ( ) ¿ 1 1− ¿ ¿ PVA = $99312.44 Total value of superfund = $1169445.63 + $99312.44 = $1268758.07 Total value of all investments = $1268758.07 + $140139.95 + 1029906.13 = $2,438,804.15

c Assume that you expect to live 23 years after you retire (until age 90). Today, at age 50, you take all of your investments and place them in an account that pays 8 per cent (use the scenario from part b in which you continue saving). If you start withdrawing funds starting at age 68, how much can you withdraw every year (e.g. an ordinary annuity) and leave nothing in your account after a 23rd and final withdrawal at age 90? Total value of investments today = $450,000 Savings = 12, 000 a year FVA = CF (

(1 +i )n−1 ) i

= 12 000 (

(1.08 ) 17 −1 ) 0.08

=$405002.71 Interest on 450,000 after 17 years = =450000(1.08)17 =$1665008.12 Total value at age 67 = 405002.71 + 1665008.12 = $2,070,010.83 1. Surprise Party Supply Pty Ltd has made an investment in another company that will guarantee it a cash flow of $512 per week for the next 4 years. If the company uses a

discount rate of 3.5 per cent per annum (compounded weekly) on its investments, what is the present value of this investment? (round to the nearest 2 d.p.) CF=512 n = 208 I = 3.5/52 = 0.0673% = 0.00067 i 1+¿ ¿ PVA = CF ( ¿ n ) ¿ 1 1− ¿ ¿ 208 1.00067 ¿ ¿ ¿ ) = 512( 1 1− ¿ ¿ = $99377.37 (2.d.p) 2. What is the effective annual interest rate of an investment with a return of 4.99% compounded fortnightly? (round to the nearest 2 d.p.) EAR = (1+

= (1+

APR m ) −1 M

0.0 499 26 ) −1 26

= 0.63930 = 6.4% (2.d.p)...