QUESTION 1
a) This question relates to the time value of money and deferred annuities.
Ruth Bray is age 42 today and plans to retire on her 63rd birthday. With future inflation, Ruth estimates that she will require around $1,600,000 at age 63 to ensure that she will have a comfortable life in retirement. She is a single professional and believes that she can contribute $3,700 at the end of each month, starting in one month's time and finishing on her 63rd birthday.
i) If the fund to which she contributes earns 4.8% per annum, compounded monthly (after tax), how much will he have at age 63? Will she have achieved her targeted sum? What is the surplus or the shortfall?
ii) Using the entire fund balance, Ruth then wishes to commence a monthly pension payable by the fund starting one month after her 63rd birthday, and ending on her 87th birthday, after which she expects that the fund will be fully expended. If the fund continues to earn the above return of 4.8% per annum, compounded monthly, how much monthly pension will Ruth receive, if the fund balance reduces to zero as planned after the last pension payment on her 87th birthday?
b) This question relates to loan repayments and loan terms.
James and Mary Hall wish to borrow $750,000 to buy a home. The loan from the Federal Bank requires equal monthly repayments over 25 years, and carries an interest rate of 4.5% 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:
i) The effective annual interest rate on the above loan (show as a percentage, correct to 3 decimal places).
ii) 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 25 year period of the loan.
iii) The amount of $Y, if - instead of the above - the Federal Bank agrees that James and Mary will repay the loan by paying the bank $3,000 per month for the first 12 months, then $3,500 a month for the next 12 months, and after that $Y per month for the balance of the 25 year term.
iv) How long (in years and months) would it take to repay the loan if, alternatively, James and Mary decide to repay $4,400 per month, with the first repayment again being at the end of the first month after taking the loan, and continuing until the loan was repaid. [HINT: The final repayment is likely to be less than $4,400, and will be paid one month after the final full installment of $4,400 is paid.)
QUESTION 2
This question relates to capital budgeting.
Bayside Ferries Ltd is considering the purchase in September, 2018 of two new small hydrofoils costing $480,000 each, which it will fully finance with a fixed interest loan of 9% per annum, with interest paid monthly and the principal repaid at the end of 4 years. The hydrofoils will be used in the company's passenger transport business.
The two new hydrofoils will replace three existing steam ferries and will permit the company to reduce its energy and labour costs by a total of $160,000 a year, over the next 4 years. [Assume these savings are realized at the end of each year.]
The new hydrofoils may be depreciated for tax purposes by the straight-line method to zero over the next 4 years. The company thinks that it can sell the hydrofoils at the end of 4 years for $75,000 each.
The three old ferries being replaced were bought two years ago for $300,000 each, with a then life expectancy of 6 years, and are being depreciated by the straight-line method to zero over 6 years. If the company proceeds with the above purchase, the old ferries will be sold in September, 2018 for $170,000 each.
This is not the first time that the company has considered this purchase and replacement. Twelve months ago, the company engaged Sea Travel Consultants, at a fee of $25,000 paid in advance, to conduct a feasibility study on savings strategies and Sea Travel made the above recommendations. At the time, Bayside Ferries Ltd did not proceed with the recommended strategy, but is now reconsidering the proposal.
Bayside Ferries Ltd further estimates that it will have to spend tax-deductible amounts of $30,000 in 2 years' time and $40,000 in 3 years' time overhauling the hydrofoils.
It will also require additions to current assets of $30,000 at the start of the hydrofoils project, which will be fully recoverable at the end of the fourth year after purchase.
Bayside Ferries Ltd's cost of capital is 11%. The tax rate is 30%. Tax is paid in the year in which earnings are received.
REQUIRED:
(a) Calculate the net present value (NPV), that is, the net benefit or net loss in present value terms of the proposed purchase costs and the resultant incremental cash flows.
[HINT: As shown in the text-book, it is recommended that for each year you calculate the tax effect first, then identify the cash flows, then calculate the overall net present value. Finally, make your recommendation.]
(b) Should the company purchase the new hydrofoils? State clearly why or why not.