Financial Mathematics Assignment: Loan And Investment Problems

Question 1

a.i) Indicating the payment Jayne should choose:

Particulars	Value
New house	$ 500,000.0 Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper
Time	30.0
Weekly pay	30 * 52 = 1,560.0
Fortnight	30 * 26 = 780.0
Weekly pay interest rate	4.55%/12 = 0.00088
Fortnight interest rate	4.75%/12 = 0.00183
Weekly Payments	$           587.7
Fortnight Payments	$       1,203.2

Particulars	Value	Fortnight interest rate	Weekly pay interest rate
New house	$ 500,000.0	4.750%/12 = 0.00183	4.550%/12 = 0.00088
Time	30.0	780.0	1560.0
PMT	1000
Time 1	414.9	8.0 Years
Time 2	355.5	13.7 Years

Particulars	Value
Investment	$ 200,000.0
Time	18.0
Interest rate	2.500%
N	216.0
I	0.0021
Per Month Investment	$           734.1
Jennifer monthly payment	$           220.2

Particulars	Value
Amount in 18 years	$ 200,000.0
Allowable withdrawal	$ 100,000.0
Savings	$ 100,000.0
Interest rate	4.0%
Time	10.0
Deductions per month	1000.0
FV of Total Savings	148024.4
FV of deductions	52254.1
Total Amount received at 28 years	95770.3

Particulars	Value
House	800000.0
Gift amount	95770.3
Term	30.0
Interest	4.500%
Monthly Payment on loan	$       3,568.2

i) Drawing a timeline showing cash flow of the ordinary shares:

ii) Calculating market value of Kai’s investment portfolio:

Particulars	Value
Bond market return (A)	7%
Preference market return (B)	11%
Share market return (C)	20%
Market return of Kai’s Investment [(A+B+C)/3]	13%

i) Identifying the major differences between the classical taxation system and the dividend imputation taxation system:

Classical taxation system is relevantly considered an adequate measure, where the companies are taxed for the profits that has been incurred during the financial year, which relevantly indicates that the overall tax has been conducted on the dividend income (Unda, 2015). On the other hand, the dividend imputation system might eventually help in eliminating the double taxations, which are been conducted by the tax authorities. The imputations system eventually benefits the overall shareholders, who can offset the tax with their taxes or get the relevant refund from the authorities. There is major difference between the classical and dividend imputation calculation system, which are depicted as follows.

• The major difference between the two method are that under the classical method the dividends of the organisation are double taxed, where first the organisation pays the tax at their level s and them after the distribution of the tax the investors pay the tax at their marginal tax rate. However, the imputation system relevantly alters the overall double taxation system, which can be charged for the organisation and shareholder of the organisation.
• Moreover, the shareholders under the classical system needs to be pay the whole tax that falls in their marginal tax rate system. This eventually increases the chance of double taxations system under the classical taxation method. However, under imputations system the investor is only liable to pay taxes for the income, which is excess the marginal tax rate (Scholes, 2015).
• The use of dividend imputation system would eventually help in improving the level of taxation system, which reduces the level of double taxation on investors, which is not conducted in classical taxation system.
• The other difference between the imputation system and classical system, is the preference among the investors, as investors does not want to increase their cash outflow, while raising the level of income from investment.

Imputation Tax system
Particulars	Tax payer 1	Tax payer 2
Marginal Tax rate	35%	15%
Corporate level
NPBT	$4	$4
Corporate [email protected]%	$2.80	$2.80
Shareholders level
Cash Dividends	$2.80	$2.80
Gross-up adjustments	$1.20	$1.20
Grossed up dividends	$4.00	$4.00
Personal tax	$1.40	$0.60
Franking credit	$1.20	$1.20
Tax payable	($0.20)	$0.60
Dividend tax after taxes	$2.60	$3.40

Classical Tax system
Particulars	Tax payer 1	Tax payer 2
Marginal Tax rate	35%	15%
Corporate level
NPBT	$4	$4
Corporate [email protected]%	$2.80	$2.80
Shareholders level
Cash Dividends	$2.80	$2.80
Personal tax	$0.98	$0.42
Dividend tax after taxes	$1.82	$2.38

The above table relevantly indicates the overall example for dividend imputation taxations system and classical taxations system. The above examples would eventually help in detecting the level of income, which can be generated by the investors under both the classical and imputations taxation system. From the evaluation it can be detected that under the classical method the overall dividends that is received by the investors after the marginal taxation system relevantly lower than the imputation taxation system. Ratiu (2015) mentioned that investors would eventually increase the level of income from dividends under the imputation system, where the overall income of the government will reduce, as double taxation system is neglected by the government.

The above example mentioned in the above table directly indicates that under the classical taxation method the tax payer would only earn $1.82, while under imputation system the overall dividend income is $2.38. The taxpayer 2 also incur lower income of dividend under the classical method, which is valued at $2.38, while imputation taxation yielded $3.40. Hence, from the valuation it can be detected that under the classical method the investors were charged double for the taxes. Loughran & McDonald (2016) argued that use of imputation system relevantly alters the overall dividend policy of the company, as investors gain higher income from their investment.

The imputation taxation system relevantly has positive impact on the overall domestic and international investors as the overall double taxation system, as the double tax is lifted by the regulators. The dividend imputation system has relevant impact on the investors, which are depicted as follows.

• The positive attributes of the imputation system would eventually benefit the investor, as it will reduce the level of cash outflow and increase net dividends of the investors.
• The dividend imputation system will also motivate the investors both domestic and international to increase their investment in the country due to the non-presence of double taxations system, as it will raise their level of income, while reducing the cash flows.
• There is relevant positive attribute for the investor, as the dividends will grow and they can charge reduction on the excess tax that is imposed on their income from investment.
• The investors with the help of imputation taxation system are able to increase the level of yield that is generated from an investment in terms of dividends. Hence, the investors will relevantly increase the level investment in such countries who use imputation system, as it will increase returns, while reducing the level of tax outflow (Dalla & Perego, 2014).

1) Plotting return of WBC, CBA and Market:

Particulars	CBA.AX	WBC.AX	AORD
Holding period return	-12.00%	-3.97%	9.12%

Particulars	CBA.AX	WBC.AX	AORD
Average Holding period return	-0.98%	-0.28%	0.75%

Particulars	CBA.AX	WBC.AX	AORD
Annual Holding period return	-11.81%	-3.32%	9.02%

Particulars	CBA.AX	WBC.AX	AORD
Standard deviation	4.02%	3.60%	2.17%

Particulars	CBA.AX	WBC.AX
10-year government bond	2.78%	2.78%
ASX return	5.85%	5.85%
Beta	1.23	1.26
Expected return	2.78%+1.23*(5.85%-2.78%)	2.78%+1.26*(5.85%-2.78%)
Expected return	6.56%	6.65%

Particulars	CBA.AX	WBC.AX
Weight	60%	40%
Beta	1.23	1.26
Expected return	6.56%	6.65%
Portfolio Beta	(60%*1.23) + (40%*1.26)
Portfolio Beta	1.24
Portfolio Return	(60%*6.56%) + (40%*6.65%)
Portfolio Return	6.59%

From the overall evaluation of the above portfolio it can be detected that investment in the created portfolio would be more beneficial, as the risk attributes is low and returns is higher. Therefore, the investment in the overall portfolio can eventually help in minimising the risk involved in the investment and maximise the level of income generated from operations. Beaumont (2015) mentioned that use of portfolio allows the investment to curb the risky assets by using adequate weights and maximise the level of income generated from investment.

Reference:

Au.finance.yahoo.com. (2018). Au.finance.yahoo.com. Retrieved 16 December 2018, from https://au.finance.yahoo.com/

Beaumont, S. J. (2015). An investigation of the short?and long?run relations between executive cash bonus payments and firm financial performance: a pitch. Accounting & Finance, 55(2), 337-343.

Dalla Via, N., & Perego, P. (2014). Sticky cost behaviour: evidence from small and medium sized companies. Accounting & Finance, 54(3), 753-778.

Loughran, T., & McDonald, B. (2016). Textual analysis in accounting and finance: A survey. Journal of Accounting Research, 54(4), 1187-1230.

Ratiu, R. V. (2015). Financial reporting of European banks during the GFC: a pitch. Accounting & Finance, 55(2), 345-352.

Scholes, M. S. (2015). Taxes and business strategy. Prentice Hall.

Unda, L. A. (2015). Board of directors characteristics and credit union financial performance: a pitch. Accounting & Finance, 55(2), 353-360.

Yohn, T. L. (2015). Research on the use of financial statement information for forecasting profitability. Accounting & Finance.