Question 2: Time Value of Money (18 Marks) a. Bill Petty, age 56 has just retired after 31 years of teaching. He is a husband and father of two children who are still dependent. Bill received a $150,000 lump-sum retirement bonus and will also receive $2,800 per month from a retirement annuity for the rest of his life. He has saved $150,000 in a superannuation fund and another $100,000 in other accounts. His superannuation fund is invested in the share market, but most of his other investments are in bank accounts earning 2% or 3% interest annually. Bill has asked your advice in deciding where to invest his lump-sum bonus and other accounts now that he has retired. He also wants to know how much he can withdraw per month, considering he has two children and a non-working spouse. Because he has children, his current monthly expenses total $5,800. (Ignore tax) Required: i. Bill has an emergency fund already set aside, so he can use his $400,000 of savings for retirement. How much can he withdraw on a monthly basis if his investments return 5% annually and he expects to live 30 more years? (2 Marks) ii. Is the amount determined in question 1 sufficient to meet Bills current monthly expenses (keep in mind that he will receive a monthly payment of $2,800)? If not, how long will his retirement last if his current expenses remain the same? What if his expenses were reduced to $4,500 per month? (3 Marks) iii. If the inflation rate averages 3.5% during Bills retirement, how old will he be when prices have doubled from current levels? How much will a can of soft drink cost when Bill dies, if he lives the full 30 years and the soft drink costs $1 today? (3 Marks) b. You deposited $160,000 into an education savings plan, hoping to have $ 420,000 available 12 years later when your first child starts university. However, you did not invest very well, and two years later, the accounts balance has dropped to $140,000. You approached a financial advisor and he agreed to work with you to get the investment value back on track. i. What was the original annual rate of return needed to reach your goal when you started the fun two years ago? (2 Marks) ii. With only $140,000 in the fund and 10 years remaining until your child starts university, what annual rate of return would the fund have to make for you to reach your $420,000 goal if you add nothing to the account? (2 Marks) iii. Shocked by your experience of the past two years, you feel the education savings fund has invested too much in shares, and you want low-risk fund in order to ensure you have the necessary $420,000 in 10 years. You are willing to make end-of-the-month deposits to the fund as well. You find you can get a fund that promises to pay a guaranteed annual return of 6% that is compounded monthly. You decide to transfer the $140,000 to this new fund and make the necessary monthly deposits. How large a monthly deposit must you make into the new fund each month to obtain the $420,000 required at the end of 10years? (4 Marks) iv. After seeing how large the monthly deposit would be in part (biii) above, you decide to invest the $140,000 today and $500 at the end of each month for the next 10 years into a fund comprising 50% shares and 50% bonds and hope for the best. What APR would the fund have to earn in order to reach your $420,000 goal? (2 Marks)