**QUESTION `1 [6 + 4 + 6 = 16 Marks.]**

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*a) This is a two period certainty model problem. *

Assume that Bradley Lane has a sole income from Fisher Ltd in which he owns 12% of the ordinary share capital. Currently, Bradley has no savings.

In August, 2018, Fisher Ltd reported net profits after tax of $800,000 for the last financial year, 2017-18 (1 July, 2017 to 30 June, 2018), and announced it expects net profits after tax for the current financial year, 2018-19, to be 20% higher than last financial year’s figure. The company has a dividend payout ratio of 70%, which it plans to continue, and will pay the annual dividend for 2017-18 in late-September, 2018, and the dividend for 2018-19 in late-September, 2019.

In late-September, 2019, Bradley wishes to spend $95,000, which will include the cost of a new car. How much can he consume in late-September, 2018 if the capital market offers an interest rate of 10% per year?

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**QUESTION 1 continued**

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*b) This is an annual equivalent costs (AEC) problem.*

Speedy Delivery Ltd, which operates a courier service, requires a new van. It has received two quotes. Van A will cost $70,000 now, has a three year life and will cost $7,000 a year to operate. Van B will cost $90,000 now, has a four year life and will cost $9,000 a year to operate. The relevant discount rate is 6 per cent per annum. Ignoring depreciation and taxes, calculate the AEC for each. Which van do you recommend that Speedy Delivery Ltd buy, and state why?

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**QUESTION 1 continued**

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*c) This question relates to the valuation of interest-bearing securities.*

Because of the drought, Farmers Bank Ltd has experienced large losses on its rural 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 September, 2023 and bear a yearly interest coupon payment of 13%.

The Bank paid the interest due this month (September, 2018), and following a meeting of creditors, arranged to defer payment of the next two interest coupons due in September, 2019 and September, 2020 respectively. Under the arrangement with creditors, the Bank will pay the remaining interest coupons (due in September, 2021, September, 2022 and September, 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. Farmers Bank Ltd’s notes are now seen as risky, and require a 19% per annum return.

REQUIRED: Calculate the current value of each Farmers Bank unsecured note.

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**QUESTION 2 [(4 + 4) + (2 + 2 + 3 + 3) = 18 Marks]**

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*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 63^{rd} 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 63^{rd} 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 63^{rd} birthday, and ending on her 87^{th} 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 87^{th} birthday?

**QUESTION 2 continued.**

*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.

**QUESTION 2 continued.**

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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 3 [(2 + 2 + 4 + 3 + 3 + 2 = 16 marks]**

*This question relates to alternative investment choice techniques*

William Slater is considering the following cash flows for two mutually exclusive projects.

** Year Cash Flows, Investment P ($) Cash Flows, Investment Q ($)**

** ** 0 -60,000 -60,000

1 20,000 30,000

2 30,000 30,000

3 44,000 30,000

You are required to answer the following questions:

i) If the cash flows after year 0 occur evenly over each year, what is the payback period for each project, and on this basis, which project would you prefer?

*IN THE REMAINING PARTS, ASSUME THAT ALL CASH FLOWS OCCUR AT THE END OF EACH YEAR.*

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ii) Would the payback periods then be any different to your answer in i)? If so, what would the payback periods be?

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**QUESTION 3 continued. **

iii) If the required return is 8% per annum, what are:

– The **net present values** of each project?

– The **present value (or profitability) indexes** of each project?

**QUESTION 3 continued.**

iv) Calculate the **internal rate of return (IRR)** for each project.

[**NOTE:** It is satisfactory if the approximate IRR is calculated for Investment P by trial and error, and stated as a percentage correct to the nearer whole number. The IRR for Investment Y, where the positive cash flows form an ordinary annuity, should be calculated as a percentage exactly, correct to 1 decimal place.]

v) Calculate the exact **crossover point** (an interest rate, expressed as a percentage correct to two places of decimals) of the respective net present values (NPVs) for the above projects.

vi) Having regard to the above calculations, state – with reasons – which of investments P and Q you would prefer.

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**QUESTION 4 [18 + 2 = 20 marks].**

*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.]

**QUESTION 4 continued.**

(b) Should the company purchase the new hydrofoils? State clearly why or why not.

**END OF ASSIGNMENT QUESTIONS**

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