In this scenario, we are assuming that the company pays out all of its $889,000 net income after tax as dividends; thus, classified as fully franked dividends. Also, due to the absence of investment allowance (which permits businesses to deduct a specified percentage of certain capital costs from their taxable income) and other investment allowances specified under tax law, the company’s taxable income is the same as its accounting net income. Pearl’s Pty Ltd has a net income after tax of $889,000 that could be paid out as dividends to the shareholders, A (55%) and B (45%); therefore, each shareholder will receive a cheque for the following dividend amounts that are fully franked.
A: $488,950 (i.e. $889,000 x 55%) B: $400,050 (i.e. $889,000 x 45%) Total $889,000 (= company net income after tax)
A: $209,550 (i.e. 55% x $381,000 company income tax) B: $171,450 (i.e. 45% x $381,000 company income tax) Total $381,000 (= income tax paid by the company on its net income of $381,000 Alternatively, Imputation Credit = Fully franked dividend x Company tax rate 1 – Company tax rate A’s imputation credit = $488,950 x 30% 1-0.30 = $209,550 B’s imputation credit = $400,050 x 30% 1-0.30 = $171,450 Shareholder A will receive a dividend payment of $488,950 with an imputation credit of $209,550 whereas Shareholder B will receive a dividend payment of $400,500 with an imputation credit of $171,450. (b) The Australian dividend imputation system eliminates the double taxation of dividends wherein fully taxed company profit distributed as dividends is effectively taxed only once at shareholder’s marginal tax rate, a stark contrast to the classical tax system. When a dividend is paid out of corporate profits that have been taxed at the statutory corporate tax rate, the shareholder receives the cash dividend plus an imputation tax credit which can be used to offset personal income tax obligations. In other words, the shareholder is able to reduce the tax paid on the dividend by an amount equal to the tax imputation credits. Basically, taxation of dividends has been partially paid by the company issuing the dividend. The net effect of the imputation process once dividends are distributed by the company is for income tax to be levied on the net income earned by a company at the shareholder’s marginal personal tax rates. Although the dividend imputation system does lower the overall tax rate, the system describes that the amount of income tax payable by a company on its net income will not change the after-tax wealth of its shareholders. Dividend imputation system may also encourage domestic business investment by reducing the cost of capital for domestically owned companies. Consequently, companies would withhold tax on profits as it levels the cost of financing a business with debt, on which interest is deductible, and equity. Thus, this increases company income tax revenues. Also, imputation brings integrity benefits as the benefit to companies and their shareholders encourages the anti-avoidance of income tax. However, imputation tax credits are of no direct value to non-resident shareholders who have no Australian personal tax obligations. Thus, dividends paid to foreign shareholders will be taxed twice as company income tax and by shareholder’s home country as tax on dividend income and vice versa. From the perspective of Australian companies, the non-creditability of foreign taxes may increase the required return for offshore investment, discouraging such investments and encouraging a domestically-oriented investment focus. Thus, this creates biasness against investment in an internationally orientated Australian company or in a foreign company.
Joanna Pickford has been working with ABC Bank for a year and has just been promoted to junior financial adviser. Her first client wants to set up a savings account to accumulate $30,000 for a new car and the client can deposit $200 each fortnight from his salary into the account. ABC Bank currently pays interest on its savings accounts at a daily compound rate of 4.0% p.a. Joanna worked out that with depositing $5,200 (26 x $200) into the account each year it would take the client 5.29 years (30,000 FV, 5,200 +/- PMT, 4 i COMP n) to reach his target. As there are 26 fortnights in a year this would be equivalent to 137.5 fortnights so she told the client that he would have to make 137 fortnightly deposits of $200 and a final deposit of $100 (0.5 of $200) one fortnight later. Do you agree with Joanna’s calculations? Explain why. If not, how long will it take the client to reach his savings target and how much should the last deposit into the account be?
a) According to Joanna’s calculation: PMT = $200 N = 137 I/Y = 4%/26 = 0.153846154% Additional = $100 Using Financial Calculator: 200 +/- PMT 137 N 0.153846154 I/Y 100 +/- PV 1 N 0.153846154 I/Y COMP FV giving $30,475.57 COMP FV giving $100.1538 FV = $30,475.57 + $100.15 = $30,575.72 Note: The future value of final deposit of $100 should also be calculated with reference to the interest rate and compounding periods. Based on the computation above, Joanna’s calculation is incorrect as the client will accumulate $30,575.72 which is greater than what the client wanted ($30,000). This is due to incorrect calculation of compounding periods (which will be calculated in part (b)). b) i) Every fortnight: PMT = $200 FV = $30,000 I/Y = 4%/26 = 0.153846154% N = ? 30,000 FV 200 +/- PMT 0.153846154 I/Y COMP N giving 135.0693802 periods Based on the computation above, the correct compounding periods would be 135 fortnights. Therefore, her client would need to deposit $200 for 135 fortnights or 5.192 years (135/26). ii) PMT = $200 I/Y = 4%/26 = 0.153846154% N = 135 FV = ? 200 +/- PMT 0.153846154 I/Y 135 N COMP FV giving $29,982.94 Therefore, the 135th fortnightly deposit would bring the future value to $29,982.94 $30,000 – $29,982.94 = $17.06 Based on the computation above, the remaining final deposit into the savings account should be $17.06 one fortnight later to achieve his savings target of $30,000.
Kym Baker had a HECS liability of $12,500 at the end of the year in which he finished his degree. The HECS debt accumulates interest at a rate equal to the inflation rate, which was 1.25% per annum over the first year after he graduated and 0.35% for the following year. At the end of the second year after graduation Kym’s annual taxable income has increased to $29,000 and he is required by the tax office to pay an amount equivalent to 1% of his annual taxable income to reduce his HECS debt. How much HECS does Kym owe at the end of the second year after graduation after making payment for that year to the Tax Office? Draw appropriate time-line(s) to demonstrate your calculations.
I/Y = 1.25% pa PV = $12,500 N = 1 12,500 +/- PV 1.25 I/Y 1 N COMP FV giving $12,656.25
I/Y = 0.35% pa PV = $12,656.25 N = 1 12,656.25 +/- PV 0.35 I/Y 1 N COMP FV giving $12,700.55 Payment = $29,000 x 1% = $290 Balance = $12,700.55 – $290 = $12,410.55 Repayments = $290 Balance = $12,410.55 Interest p.a. = $156.25 Interest p.a. = $44.30 $12,500 $12,656.25 $12,700.55 t=0 t=1 t=2 Year Payment Principal Interest Loan 0 $12,500 1 $156.25 $12,656.25 2 $290 $245.70 $44.30 $12,410.55
Mr. Rupert Temby has borrowed some funds to buy a new Hi-fi system from a reputable electrical retailer. The electrical retailer has an associated finance company, Ezy Credit who has provided Mr. Temby with the following finance options to pay for the Hi-fi system; Option A: A lump sum in 10 years from today, or Option B: $500 in 5 years time with a further $1,000 payable in 15 years time. Mr. Temby believes that he could earn a return of approximately 6% p.a. on any savings he would have by not being required to pay for the Hi-fi system today.
Determine and justify to Mr. Temby the maximum amount that he should pay for Option A. (7 marks) Mr. Temby has now received further advice from Ezy Credit that instead of the lump sum in 10 years time (Option A) or the instalment payments after 5 and 15 years as previously indicated (Option B), they would be willing to accept a payment today of $850. Should Mr. Temby accept this offer? Justify your response. (8 marks) What important assumptions are you making in your answers to a) and b) above which should be discussed with Mr. Temby to ensure that you have given him appropriate advice so that he can readily understand the consequences of any decisions made based on your calculations? (5 marks)
a) At 10th year, PV = $ At 10th year, FV = $ $500 $1000 t=0 t=5 t=10 t=15 From Option B ($500 in 5 years with a further $1,000 payable in 15 years), the future value of this option would be the same as the maximum future value of the lump sum of Option A at 10th year in accordance to the timeline described above. PV = 500 N = 5 I/Y = 6% 500 +/- PV 5 N 6 I/Y COMP FV giving $ 669.11 FV = 1000 N = 5 I/Y 6% 1000 FV 5 N 6 I/Y COMP PV giving $ 747.26 $669.11 + $747.26 = $ 1,416.37 Therefore, the Option A’s maximum amount Mr. Temby should pay in 10 years is $ 1,416.37. b) The third option’s present value is found, as at ‘today’ which is also known as time period 0. In other words, PV0 = $850. Therefore, to be comparable with third option, Option A and B’s present value must also be expressed at time ‘zero’. Option A (A lump sum in 10 years from today): The present value is calculated as below: FV = 1,416.67 I/Y = 6% N = 10 1,416.67 FV 6 I/Y 10 N COMP PV giving $ 791.06 Therefore, the present value of the lump sum of Option A is $791.06. Option B ($500 in 5 years time with a further $1,000 payable in 15 years time): The present value is calculated as below: 1st 5 years: Next 10 years: FV = 500 FV = 1000 I/Y = 6% I/Y = 6% N = 5 N = 15 500 FV 6 I/Y 5 N 1000 FV 6 I/Y 15 N COMP PV giving $373.63 COMP PV giving $417.27 $373.63 + $417.27 = $790.90 The present value of the instalment payment of Option B is $790.90. No, Mr. Temby should not accept the third option wherein he is allowed to pay $850 now to clear his debt. This is unacceptable because the present value from Option B of $790.90 is a cheaper option as compared to the present value of $850 for the third option. c) Assumptions: Individuals have time preference for money due to: Risk Preference for consumption Investment Opportunities
You have just won the Golden Basket lottery which gives you the choice of your prize being either a house and land package with a current market value of $500,000 or receiving cash totalling $600,000 paid in three instalments of $200,000, $150,000, $250,000 respectively. If you choose the cash alternative the first of amount will be paid to you at the end of two years from today’s date and the next and subsequent amount will be paid at the end of 3 years from the date of the previous instalment. If you use the nominal rate of 6.5 percent per annum that currently applies for a monthly repayment housing loan as your time value of money, use appropriate calculations to determine whether you should accept the house and land package or the cash instalment alternative. Draw appropriate timeline(s) to demonstrate your calculations.
Time Lines: House and Loan Package $500,000 t=0 t=2 t=5 t=8 Cash Instalments: The first instalment will be paid in year 2. The next one will be after 3 years and so in year 5 and the last one after another 3 years. So, in year 8, the time line would be: $200,000 $150,000 $250,000 t=0 t=2 t=5 t=8 In order to make the decision, we would need to compare the present value of the two options – the land and house package is given now at present value of $500,000. For the instalments, we would need to discount the cash flows to get the present value. The interest rate is given as 6.5%. This is with monthly compounding as it is applicable to monthly repayments. We would need to calculate the effective annual rate as the cash flows are on yearly basis. Effective annual rate = (1 +j/m)m – 1 = (1+6.5%/12)12 – 1 = 6.6972% 0 ENT 0 ENT 200,000 ENT 0 (x,y) 2 ENT 150,000 ENT 0 (x,y) 2 ENT 250,000 ENT 2ndF CASH 6.6972 ENT ? COMP giving $432,993.47 Therefore, we should accept the house and land package as it has a higher present value ($500,000) as compared to the cash instalments present value at $432,993.47
You have some money to invest for 12 months and are considering purchasing shares in the retail sector. After reviewing the historical performance and future prospects for Elite Jewellery Ltd. and So Lo Supermarkets Ltd, you have prepared the following information that you will use for your investment decision:
Elite Jewellery Ltd
So Lo Supermarkets Ltd
Current share price $9.00 $11.60 Current EPS $1.20 0.90 Current Beta 0.85 0.60
Elite Jewellery Ltd So Lo Supermarkets Ltd
Probability of Return Likely Return over next 12 mths Probability of Return Likely Return over next 12 mths 0.15 -1% 0.10 1% 0.60 12% 0.40 7% 0.25 18% 0.30 10% 0.20 14% Other relevant information: Current risk free rate of return: 5% p.a. Long run average return on market portfolio: 12% p.a.
(a) Calculate the expected return (R*) and standard deviation (s) for each share. (9 marks) (b) Briefly explain the meaning of expected return and standard deviation and outline what your calculations indicate about a relationship between risk and return. (4.5 marks) Briefly outline in words that an average person in the street can understand the difference between standard deviation and beta as measures of risk. (3 marks) Calculate the return investors with a diversified portfolio should require from each share. (2 marks) With reasons based on your computations, in (a) and (d) above, provide a recommendation of which share (if any) you should purchase/not purchase. (3 marks) On the basis of your analysis in (e) above detail what you would expect to happen to the price of each share in the market. (2 marks) Briefly explain what is likely to occur, in relation to the risk exposure of your investment portfolio, as you increase the number of diversified investments in your investment portfolio. (2.5 marks)
E(R) = [P(R1) x R1] + [P(R2) x R2] + [P(R3) x R3] = (0.15 x -1%) + (0.60 x 12%) + (0.25 x 18%) = 0.1155 = 11.55% Standard deviation, s = – å (R R )2 x P(R) = – (11.55% – -1%)2 x 0.15 + (11.55% – 12%)2 x 0.60 + (11.55% – 18%)2 x 0.25 = 5.84% Investing in Elite Jewellery Ltd is expected to provide a return of 11.55% with a riskiness of 5.84%
E(R) = [P(R1) x R1] + [P(R2) x R2] + [P(R3) x R3] + [P(R4) x R4] = (0.10 x 1%) + (0.40 x 7%) + (0.30 x 10%) + (0.20 x 14%) = 0.087 = 8.7% Standard deviation, s = – å (R R )2 x P(R) = – (8.7% – 1%)2 x 0.1 + (8.7% – 7%)2 x 0.4 + (8.7% – 10%)2 x 0.3 + (8.7% – 14%)2 x 0.2 = 3.63% Investing in So Lo Supermarkets Ltd is expected to provide a return of 3.63% with a riskiness of 3.63% b) The expected return indicates the average return that we may expect to earn over the next 12 months where all possible outcomes are weighted by the probability that each will occur. The standard deviation serves as an indicator of risk and measures the weighted average of the deviations of the returns from the average (expected) value. Using a normal distribution we can assign probabilities. There would be 68% probability that the returns would be between +/- 1 standard deviation (the return may be 11.55% + 5.84% or 11.55% – 5.84% for Elite Jewellery), 95.5% possibility that returns would be between +/- 2 standard deviation and 99.7% probability that returns would be between +/- 3 standard deviation. The risk is denoted by the standard deviation. The higher the standard deviation, the higher the risk since variability in return is higher. So we would expect to have a higher expected return where the standard deviation is higher. c) The difference is that standard deviation is a measure of the risk if a particular stock is the only stock in the investment portfolio. What this implies is that if we have only one stock in our investment, the standard deviation of the return is the measure of risk since it indicates the variability in return, that is how much more or less the actual return can be from the expected return. On the other hand, Beta is measure of risk in the portfolio context. If we have more than one stock in our investment portfolio, we should not look at standard deviation but the beta of the stocks. The reason is that the portfolio return will be influenced by the expected return of individual stocks in the portfolio and also by the correlation between the returns. It may be possible that one stock has a higher return, whilst another stock has a lower return. The portfolio return would be close to zero and the variability would be less, hence reducing risk. d) As mentioned in point 3, for a diversified portfolio, the measure of risk is the beta, thus the expected return would be dependent on beta. We will use the Capital Asset Pricing Model equation to calculate the expected return. Rf = 5% Rm = 12% b EJ = 0.85 b SL = 0.60
E(R) = Rf + bEJ (Rm – Rf) = 5% + 0.85 (12% – 5%) = 10.95%
E(R) = Rf + b SL (Rm – Rf) = 5% + 0.60 (12% – 5%) = 9.20% Therefore, the expected return for the diversified portfolio on Elite Jewellery Ltd and So Lo Supermarkets Lts is 10.95% and 9.20% respectively. (e) Based on the computation above, it is recommended that Elite Jewellery Ltd shares should be bought as it generates a higher expected return as compared to So Lo Supermarkets Ltd and the risk-free investment. Although higher returns are accompanied with a higher risk, it is assumed that we are interested in shares with the highest return. (f) (g)
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