Question 1 Malusi Zondo has been offered four investment opportunities, cunently all equally priced at R45 000. Because the opportunities differ in tenns of risk, Malusi's required retums are not the same for each opportunity. The cash flows and required retums for each opportunity are summarized below: Opportunity A Cashflow R80 000 at the end of 5 years Required Return 12% Compounded monthly Explanation FV = PV (1 + r/m)mn 80k = PV (1 + 0.12/12)12 x 5 PV = R44 035.96 B R 5 000 at year-end for the next 30 years 10% Compounded quarterly C R 8 000 at year-end in perpetuity 18 % ππ = πΆππ β πΉπππ€ π ππ‘π ππ = 8 000 0.18 π·π½ = πΉππ πππ. ππ Opportunity C offers a perpetual cash flow of R8,000 at the end of each year. This is a perpetuity because it continues indefinitely. D End of Year Amount 15% ππ = πΆππ β πΉπππ€ (1 + π) π PVD = R8,695.65 + R9,356.24 + R12,580.57 + R7,394.45 + R8,101.16 + R5,486.91 PV = R51,614.98 1 2 3 4 5 6 10 000 12 000 18 000 10 000 13 000 9 000 (a) Calculate which, if any, of the investment opportunities would be acceptable to Malusi? (b) State which investment opportunity Malusi should choose? a) See above b) Option B Question 2 Earl E. Bird has decided to start saving for his retirement. Beginning on his 21st birthday, which is a year from today, Earl plans to invest R2 000 each birthday into an investment account. He will continue this savings program for 10 years and then stop making payments. His savings will continue to compound for a further 35 years until Earl retires at age 65. Ivana Waite is Earl's twin sister. She also plans to invest R2 000 per annum on each birthday, however she will begin her savings program on her 31 st birthday, and continue the payments until her retirement at 65 years of age (35 years later). The twins will use the First Conselvative Bank to invest their savings. The bank has quoted an annual savings rate of 6.882%, compounded semi-annually. Required: Calculate which twin will be financially better-off upon retirement. Earl will be financially better upon retirement. Earl πΉππΈπππ = π π₯ (1 + π ππ₯π‘ ) π πΉππΈπππ = 2000 π₯ (1 + 0.06882 2 π₯ 45 ) 2 πΉππΈπππ = π 42 012, 055 Ivana πΉππΌπ£πππ = 2000 π₯ (1 + πΉππΌπ£πππ = π 21 355, 990 0.06882 2 π₯ 35 ) 2 Simone Palthab has shopped around for the best interest rates for investing her lump-sum pension payout for the coming year. She has nanowed her search down to the following rates quoted by three different banks: Bank Crooked Dubious Squeeze Rate 6.10% 5.90% 5.85% Compounding annaual Semi annual monthly (a) Calculate which bank Simone should select. (b) Now assume that she will be investing qualterly, and calculate the applicable quarterly rate she would be eaming at each of the above three banks. Question In January 2016, Lukas Dhlomo, one of South Africa's best-known rugby players, signed a contract to play, and later coach, for Pirahna Rugby Club. In terms of his contract, he was guaranteed eamings of R6 075 000 over a 20-year period, broken down as follows: (a) Calculate the contract value when Lukas signed it on the first of January of this year. If the relevant rate of interest is per annum, and earnings are received at the end of each year. (b) If Lukas would prefer to receive an equal annual salary at the end of each year for the period 2016 — 2035, as opposed to the uneven earnings listed above, calculate the equal annual salary he should ask for. Question You have just graduated and started working at a commercial bank. Your first day of work coincides with your 25th birthday. The bank has a mandatory retirement age of 65 years. On your first day of work you decide to supplement the bank's pension scheme by signmg up for a retirement annuity requn•mg you to invest R2 000 per annum, commencing on your 26 birthday and continuing until you reach the age of 65. Your retum will be 9% per annum, compounded monthly, for the duration of the investment. Required (a) Calculate the value ofthe retirement annuity when you retire. (b) Assume the same quoted return of 9% per annum compounded monthly. If you decide to wait until your 35th birthday to begin making annual payments towards the investment, calculate the size of the annual payment you will have to make to achieve the same retirement value as calculated in (a) above. Note: you make the first payment upfront on your 35th bilthday, and the last payment upon retirement.
