Question 1
Karine and Arlo are trying to establish a University Fund for their daughter Amelia, who turns 3 today. They plan for Amelia to withdraw $10,000 on her 18th birthday and $11,000, $12,000 and $15,000 on her subsequent birthdays (19th, 20th and 21st). They wish to fund these withdrawals with a 10-year annuity, and they intend to make their first deposit one year from today, and expect to earn an average return of 6.5%pa.
i. How much will Karine and Arlo have to contribute each year to achieve their goal?
ii. Create a schedule showing the cash inflows (including interest) and outflows of this fund. How much will be in the fund on Amelia's 16th birthday?
Question 2
Stanley has just been advised of a bequest of a lump sum of 111,500 from his Aunt's will, but it is not due to be available for him for sixteen years (at t = 16 he will receive 111500). Stanley wants to receive some cash earlier than this. He is investigating the purchase of a deferred annuity with the first annual cash flow of the annuity is to be paid at the beginning of year 2 (fifteen cash flows). Assume that the annuity and the lump sum are of equivalent risk and that j12 = 6.24% pa is the appropriate interest rate (opportunity cost of funds for Stanley). How much is the annual cash flow associated with the annuity?
Question 3
The required rate of return on the shares in the companies identified below is 12% pa. Calculate the current share price in each case.
(a) The current earnings per share of Alpha Ltd are $3.40. The company does not reinvest any of its earnings. Earnings are expected to remain constant.
(b) Beta Ltd's current dividend is $2.35 and dividends are expected to grow at 3% pa indefinitely.
(c) Gamma Ltd is not expecting to pay dividends for four years, at the end of year five a dividend of $2.39 is planned and dividends are expected to grow at 3.5% pa forever after that.
(d) Delta limited plans to pay dividends of 1.55, 2.75, and 3.50 at the end of years 3, 4, 5 respectively followed by a dividend of 4.20 pa in perpetuity after that.
Question 4
You wish to insure your Ferrari. Mooncorp Insurance has quoted you an annual premium to insure your car of $12915. You are offered a 10% discount if you pay the lump sum immediately. They also offer an alternative payment method. You can pay the account in full by making 11 equal end-of-the month payments of $1160, rather than the lump sum, with no payment in the first month (ie the first payment is at the end of the second month followed by ten further monthly payments). What is the effective annual opportunity cost of paying monthly?
You must provide one complete manual trial calculation of the IRR to demonstrate that you understand the process. Also provide an explanation of this opportunity cost. Failure to follow this instruction will attract a mark of zero.