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QUESTION `1. [6 + 4 + 6 = 16 Marks.]
This is a two period certainty model problem.
Assume that Daisy Brown has a sole income from Fantasy Ltd in which she owns 15% of the ordinary share capital. Currently, she has no savings.
In February, 2018, Fantasy Ltd reported net profits after tax of $600,000, and announced it expects net profits after tax for the current calendar year, 2018, to be 30% higher than last year’s figure. The company operates with a dividend payout ratio of 75%, which it plans to continue, and will pay the annual dividend for 2017 in late-May, 2018, and the dividend for 2018 in late-May, 2019.
In late-May, 2019, Daisy wishes to spend $100,000, which will include the cost of an overseas trip. How much can she consume in late-May, 2018 if the capital market offers an interest rate of 10% per year?
This is an annual equivalent costs problem.
Y Ltd has received two offers for a new computer system. System P will cost $200,000 now, has a three year life and costs $10,000 a year to operate. System Q costs $240,000 now, has a four year life and costs $12,000 a year to operate. The relevant discount rate is 6 per cent per annum. Ignoring depreciation and taxes, calculate the AEC for each. Which do you prefer, and why?
QUESTION 1 continued.
This question relates to the valuation of interest-bearing securities.
Wildcat Bank Ltd has experienced large losses on its commercial loan portfolio and is unable to meet its next two annual interest payments on its recent issue of unsecured notes. The notes are of $1,000 face value each, mature in May, 2023 and bear a yearly interest coupon payment of 14% per annum.
The Bank paid the interest due this month (May, 2018), and following a meeting of creditors, arranged to defer payment of the next two interest coupons due in May, 2019 and May, 2020 respectively. Under the arrangement with creditors, the Bank will pay the remaining interest coupons (due in May, 2021, May, 2022 and May, 2023) on their due dates, and pay the two deferred coupons (without interest) along with the normal final interest payment and face value of the notes on the maturity date.
Wildcat Bank Ltd’s notes are now seen as risky, and require an 18% per annum return.
REQUIRED: Calculate the current value of each Wildcat Bank unsecured note.
QUESTION 2. [(4 + 4) + (2 + 2 + 3 + 3) = 18 Marks]
This question relates to the time value of money and deferred annuities.
Joan Daly is age 38 today and plane to retire on her 600h birthday. With future inflation, Joan estimates that she will require around $1,800,000 at age 60 to ensure that he will have a comfortable life in retirement. She is a single professional and believes that she can contribute $3,600 at the end of each month, starting in one months’ time and finishing on her 60th birthday.
If the fund to which she contributes earns 5.4% per annum, compounded monthly (after tax), how much will he have at age 60? Will she have achieved her targeted sum? What is the surplus or the shortfall?
Using the entire fund balance, Joan then wishes to commence a monthly pension payable by the fund starting one month after her 60th birthday, and ending on her 85th birthday, after which she expects that the fund will be fully expended. If the fund continues to earn the above return of 5.4% per annum, compounded monthly, how much monthly pension will Joan receive, if the fund balance reduces to zero as planned after the last pension payment on her 85th birthday?
QUESTION 2 continued.
This question relates to loan repayments and loan terms.
Jack and Jill Jacobs wish to borrow $700,000 to buy a home. The loan from the Highway Bank requires equal monthly repayments over 20 years, and carries.an interest rate of 4.2% per annum, compounded monthly. The first repayment is due at the end of one month after the loan proceeds are received.
You are required to calculate:
the effective annual interest rate on the above loan (show as a percentage, correct to 3 decimal places).
the amount of the monthly repayment (consisting of interest and principal repayment components) if the same amount is to be paid every month over the 20 year period of the loan.
QUESTION 2 continued.
the amount of $X, if – instead of the above – the Highway Bank agrees that Jack and Jill will repay the loan by paying the bank $3,500 per month for the first 12 months, then $3,800 a month for the next 12 months, and after that $X per month for the balance of the 20 year term.
How long (in years and months) would it take to repay the loan if, alternatively, Jack and Jill decide to repay $4,500 per month, with the first repayment again bein…
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