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Annual interest rate on loan

  Annual interest rate on loan

QUESTION `1. [6 + 8 = 14 Marks.]

This is a two period certainty model problem.
Assume that William Brown has a sole income from Bobcat Ltd in which he owns 12% of the ordinary share capital.

In its financial year 2016-17 just ended, Bobcat Ltd reported net profits after tax of $600,000, and announced its net profits after tax expectation for the next financial year, 2017-18, to be 25% higher than this year’s figure. The company operates with a dividend payout ratio of 70%, which it plans to continue, and will pay the annual dividend for 2016-17 in mid-August, 2017, and the dividend for 2017-18 in mid-August, 2018.

In mid-August, 2018, Jack wishes to spend $100,000, which will include the cost of a new car.. How much can he consume in mid-August, 2017 if the capital market offers an interest rate of 9% per year

QUESTION 1 continued.

This question relates to the valuation of shares.
Big Ideas Ltd has just paid a dividend of $1.20 a share. Investors require a 12% per annum return on investments such as Big Ideas. What would a share in Big Ideas Ltd be expected to sell for today (August, 2017) if the dividend is expected to increase by 20% in August, 2018, 15% in August, 2019, 10% in August, 2020 and thereafter by 5 per cent a year forever, from August, 2021 onwards

QUESTION 2. [(4 + 6) + (4 + 4 + 4 + 4 + 4) = 30 Marks]

This question relates to the time value of money and deferred perpetuities.
Colin Greenway attended Bunyip High School in the 1970s. After leaving school, Colin became a successful entrepreneur and is now very wealthy. He wishes to establish a perpetual scholarship fund which will provide $10,000 a year, payable to five high performing students at Bunyip High School each year in Year 12, that is, $50,000 a year, starting in early 2020. It is now early 2017. The High School Principal believes that the required funds can be invested at 5 per cent a year in perpetuity.

What is the present value in early 2017 of the whole income stream, and thus the amount which Colin must contribute to establish the fund
The High School Principal, while most appreciative of Colin’s great generosity, mentions that fees at Bunyip High are rising on average by 3 per cent every year because of inflation, and that in several years, $10,000 will not be enough to keep a student in year 12 for a whole year. Colin decides that he will increase the amount to establish the fund so as to provide for increases in the scholarship amount by 3 per cent a year in perpetuity, the first increase occurring in early 2021. How much extra (above the amount calculated in i) above, will Colin need to contribute in early 2017 so as to provide for these inflation increases forever
[HINT: Consider a formula similar to the dividend growth model.]

QUESTION 2 continued.

This question relates to loan repayments and loan terms.
Ron and Robin Reid wish to borrow $540,000 to buy a home. The loan from Biggles Bank requires equal monthly repayments over 20 years, and carries.an interest rate of 7.8% per annum, compounded monthly. The first repayment is due at the end of the first month.

You are required to calculate:

the effective annual interest rate on the above loan.
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 $X, if – instead of the above – Biggles Bank agrees that Ron and Robin will repay the loan by paying the bank $3,300 per month for the first 12 months, then $3,750 a month for the next 12 months, and after that $X per month for the balance of the 20 year term.
QUESTION 2 b) continued.

how long (in years and months) it would take to repay the loan if, alternatively, Ron and Robin decide to repay $2,500 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.
under option iv) above, the amount of the final repayment. [NOTE: Towards the end of the loan repayment period, after the final full monthly instalment of $2,500 is paid, a lesser amount is likely to be outstanding. That amount, plus interest to the end of the following month, is the final loan repayment amount.]
QUESTION 3. [(2 + 3 + 3 + 4 + 3 + 3) + (6 + 2 + 4) = 30 marks]

This question relates to alternative investment choice techniques
Stanley Livingstone is considering the following cash flows for two mutually exclusive projects.

Year Cash Flows, Investment X ($) Cash Flows, Investment Y ($)

0 -40,000 -40,000

1 12,000 18,000

2 18,000 18,000

3 27,000 18,000

You are required to answer the following questions:

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

Would the payback periods then be any different to your answer in i) If so, what would the payback periods be
QUESTION 3 a) continued.

Sketch freehand the net present value (NPV) profiles for each investment on the same graph. Label both axes and the NPV profile for each investment
Calculate the internal rate of return (IRR) for each project and indicate them on the graph. [NOTE: It is satisfactory if the approximate IRR is calculated for Investment X by trial and error, and stated as a percentage correct to the nearer whole number. The IRR for Investment Y should be calculated as a percentage exactly, correct to 1 decimal place.]
QUESTION 3 a) continued.

Calculate the exact crossover point and indicate it on the above graph.
State which of the investments you would prefer, depending on the required rate of return (i.e., depending on the discount rate).
This question relates to the valuation of bonds.
Bradley White, a retired school teacher, has two 6 per cent per annum $100,000 Australian Government bonds that mature on 15 August, 2020 and 15 August, 2023 respectively. At the date of the last half-yearly interest payment, viz., 15 February, 2017, both bonds were selling at par.

Since then, interest yields on bonds have risen by 2% per annum, compounded half-yearly. Bradley now intends to sell the bonds and put a deposit on a suburban townhouse.

Calculate the price he will receive from each bond if he sells on 15 August, 2017 at the new yield, immediately after receiving the interest payments due that day.
QUESTION 3 b) continued.

Explain the relative price movements in the two bonds, as evidenced in your answer to i) above.
Suppose that Bradley defers buying the bonds for 84 days, that is until 7 November, 2017. How much will he pay for each bond on that day [NOTE: Between the bond interest due dates from mid-August to mid-February is 184 days, during which time interest accrues on a compound basis.]
QUESTION 4. [24 + 2 = 26 marks].

This question relates to capital budgeting.

Perth Projects Ltd is considering the purchase of new technology costing $600,000, which it will fully finance with a fixed interest loan of 10% per annum, with the principal repaid at the end of 4 years.

The new technology will permit the company to reduce its to reduce its labour costs by $200,000 a year for 4 years, and the technology may be depreciated for tax purposes by the straight-line method to zero over the 4 years. The company thinks that it can sell the technology at the end of 4 years for $30,000.

The technology will need to be stored in a building, currently being rented out for $40,000 a year under a lease agreement with 4 yearly rental payments to run, the next one being due at the end of one year. Under the lease agreement, Perth Projects Ltd can cancel the lease by paying the tenant (now) compensation equal to one year’s rental payment plus 10%, but this amount is not deductible for income tax purposes.

This is not the first time that the company has considered this purchase. Twelve months ago, the company engaged Marvel Consultants, at a fee of $30,000 paid in advance, to conduct a feasibility study on savings strategies and Marvel made the above recommendations. At the time, Perth P:rojects did not proceed with the recommended strategy, but is now reconsidering the proposal.

Perth Projects further estimates that it will have to spend $20,000 in 2 years’ time overhauling the technology. It will also require additions to current assets of $30,000 at the beginning of the project, which will be fully recoverable at the end of the fourth year.

Perth Projects 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.
[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.]

QUESTION 4 a) continued.

Should the company purchase the technology State clearly why or why not.

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