(a) This is a two period certainty model problem.
Assume that Dorothy Pix has a sole income from Oz Electronics Ltd in which she owns 15% of the ordinary share capital. Currently, she has no savings.
In early December, 2018, Oz Electronics Ltd reported net profits after tax of $600,000 for the last accounting year, 2017-18 (1 October, 2017 to 30 September, 2018), and announced it expects net profits after tax for the current accounting year, 2018-19, to be 25% higher than last financial year’s figure. The company has a dividend payout ratio of 60%, which it plans to continue, and will pay the annual dividend for 2017-18 in late-January, 2019, and the dividend for 2018-19 in late-January, 2020.
In late-January, 2020, Dorothy wishes to spend $84,000, which will include the cost of a new car. How much can she consume in late-January, 2019 if the capital market offers an interest rate of 8% per year?
(b) This is an annual equivalent benefits problem.
Fast Track Ltd, which operates a delivery service, requires a new van. It has received two quotes. Van M will cost $60,000 now, has a three year life and will cost $6,000 a year to operate. Van N will cost $90,000 now, has a four year life and will cost $8,000 a year to operate. Sales in the first year under both vans are expected to be $50,000, and will increase by 10% a year over the following 2 years with Van M and 15% a year over the following 3 years with Van N. The relevant discount rate is 7% per annum. Ignoring depreciation and taxes, calculate the AEB for each. Which van should the company purchase and why?
(c) This question relates to the valuation of interest-bearing securities.
Because of the drought, Country Bank Ltd has experienced large losses on its rural loan portfolio and is unable to pay its next three annual interest payments on its recent issue of unsecured notes. The notes are of $10,000 face value each, mature in January, 2024 and bear a yearly interest coupon payment of 9%.
The Bank paid the interest due this month (January, 2019), and following a meeting of creditors, arranged to defer payment of the next three interest coupons due in January 2020, January, 2021 and January, 2022 respectively. Under the arrangement with creditors, the bank will pay the remaining interest coupons (due in January, 2023 and January, 2024) on their due dates, and pay the three deferred coupons (without interest) along with the normal final interest payment and face value of the notes on the maturity date. Country Bank Ltd’s notes are now seen as risky, and require an 18% per annum return.
REQUIRED: Calculate the current value of each unsecured note issued by Country Bank Ltd.
a) This question relates to the time value of money and deferred annuities.
Lisa Li is 36 years old today and plans to retire on her 60th birthday. With future inflation, Lisa estimates that she will require around $1,900,000 at age 60 to ensure that she will have a comfortable life in retirement. She is a single professional and believes that she can save $4,000 at the end of each month, starting in one month’s time and finishing on her 60th birthday.
- If the fund to which she contributes her monthly saving of $4,000 earns 3.9% per annum, compounded monthly (after tax), how much will she have at age 60? Will she have achieved her targeted sum? What is the surplus or the shortfall?
- When she reaches age 60, Lisa plans to travel extensively, and wishes to draw from her accumulated fund a monthly pension of $12,000, starting one month after her 60th birthday, and ending on her 65th She then wishes to draw a monthly pension starting one month after her 65th birthday, and ending on her 90th birthday, after which she expects that the fund will be fully expended.
If, after she reaches age 60, the fund continues to earn the above return of 3.9% per annum, compounded monthly, calculate the monthly pension Lisa will be able to draw from the fund, starting one month after her 65th birthday. Assume that the fund balance reduces to zero as planned after the last pension payment is drawn on her 90th birthday.
b) This question relates to loan repayments and loan terms.
Samuel and Sandra Sharp wish to borrow $600,000 to buy a home. The loan from the Highway Bank requires equal monthly repayments over 20 years, and carries an interest rate of 5.1% 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 following. :
- 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 repaid every month over the 20 year period of the loan.
- The amount of $K, if – instead of the above – the Highway Bank agrees that Samuel and Sandra will repay the loan by paying the bank $3,200 per month for the first 12 months, then $3,600 a month for the next 12 months, and after that $K per month for the balance of the 20 year term.
- How long (in years and months) from inception will it take to repay the loan if, alternatively, Samuel and Sandra decide to repay $4,500 per month, with the first repayment now being at the end of the thirteenth month after taking the loan, and continuing until the loan is repaid?
- The final repayment is likely to be less than $4,500 and will be paid one month after the final full instalment of $4,500 is paid.
- While no repayments will be made during the first 12 months, interest will be charged by Highway Bank at the stipulated rate.]
This question relates to alternative investment choice techniques
William Slater is considering the following cash flows for two mutually exclusive projects.
Year Cash Flows, Investment W ($) Cash Flows, Investment Y ($)
0 -90,000 -90,000
1 30,000 45,000
2 45,000 45,000
3 66,000 45,000
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.
ii) Would the payback periods then be any different to your answer in i)? If so, what would the payback periods be?
iii) If the required return is 8% per annum, what are:
– the net present values of each project?
– the net present value indexes of each project?
iii) Calculate the internal rate of return (IRR) for each project. [Express answers as percentages, correct to 1 decimal place.]
iv) Calculate the exact crossover point (an interest rate, expressed as a percentage correct to 2 places of decimals) of the respective net present values of the above projects.
v) Having regard to the calculations in part v), state – with reasons – which of the investments W and Y you would prefer.
This question relates to capital budgeting.
Farming Services Ltd is considering the purchase in January, 2019 of three new tractors costing $300,000 each, which it will fully finance with a fixed interest loan of 8% per annum, with interest paid monthly and the principal repaid at the end of 4 years. The tractors will be used in the company’s rural services business.
The three new tractors will replace four existing smaller tractors enabling the company to increase sales and to reduce its labour, etc. costs by a net total of $175,000 each year, over the next 4 years. [Assume these benefits are realized at the end of each year.]
The new tractors 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 tractors at the end of 4 years for $50,000 each.
The four old tractors being replaced were bought three years ago for $210,000 each, with a then life expectancy of 7 years, and are being depreciated by the straight line method to zero over 7 years. If the company proceeds with the above purchase, the old tractors will be sold in January, 2019 for $100,000 each.
This is not the first time that the company has considered this purchase. Twelve months ago, the company engaged Agrarian Consultants, at a fee of $20,000 paid in advance, to conduct a feasibility study on savings strategies and Agrarian made the above recommendations. At the time, Farming Services Ltd did not proceed with the recommended strategy, but is now reconsidering the proposal.
If the changeover proceeds, Farming Services Ltd further estimates that it will have to spend $20,000 in 2 years’ time and $30,000 in 3 years’ time overhauling the tractors.
It will also require additions to current assets of $20,000 at the start of the new tractors project, which will be fully recoverable at the end of the fourth year after purchase.
Farming Services Ltd’s cost of capital is 10%. The tax rate is 30%. Tax is paid in the year in which earnings are received.
- 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.
- Should the company purchase the new tractors? State clearly why or why not.
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