Planning for Buying a House in 4 Years

In order to start a business in Australia a person first needs to select the most suitable business structure. The major forms of business structure from which the investor has to choose are sole proprietorship, partnership and company.

Sole proprietorship is the form of business in which all the risks and rewards belong to one person. This single person is wholly responsible for all the aspects of the business. This is the simplest form of business structure and relatively the most inexpensive one. (Fabozzi & ‎ Mann, 2012)

The partnership form of business is very similar to that of sole proprietorship. The risks and rewards of the business are distributed amongst all the partners in the agreed partnership ratio. Each partner is liable for the actions of any other partner. This is also a simple business form. The benefit of this type of structure over proprietorship is that the risks are divided amongst all the partners.

The company form of business structure is the most complex form of business structure. Under this business structure the corporate veil divides the ownership and management. The company stands as a separate legal entity and can sue and be sued in its name. The owners hold a stake in the company in the form of shares and are responsible for the management. The liability of the shareholders under this business structure is limited to the value of shares held by them. (Berk, Demarzo & Harford, 2012)

Therefore, based on the availability of the capital, scale of operations and risks involved, the best suitable form of business structure is to be opted for.

An investor can invest in bond or equity market or in both. Based on his requirements and ability to deal with risk they can take a decision (Graham & Dodd, 2009). Few factors which can help an investor take a decision are listed below:

• Liquidity:the equity market is more liquid than the bond market. Equity is traded over the counter and can be any time easily converted into cash, as and when required. The bonds usually have a lock in period and cannot be converted into cash. Therefore, a person who is need of high liquid investments should invest in the equity market. 
• Fixed Income:an investor who looks for a stable income should not opt for equity market. In the bond market the investor gets to earn fixed coupon interest at particular intervals. But there is no such fixed income in equity investment. The equity investor may or may not earn dividend. The amount of dividend is based on the profits earned by the company. The management then decides if any dividend is required to be paid or the profits are to be retained for further expansion. Therefore, an investor who wants to earn a stable income should not invest in the equity market. (Graham, Buffett & Zweig, 2013)
• Risk:the equity market involves more risk than the bond market. The prices of the stock are governed by the market forces and the investor may or may not earn any profits. When the investor expects that the market price of a share is expected to rise he would invest in that share. Similarly other investors would also buy that share. In order to fill in the demand supply gap, the share price increases. As soon as the price increases the investors start selling that stock and the price tends to fall. Therefore it is difficult to predict the movement in stock prices. Due to this volatile nature, the equity market involves high risk. An investor not willing to take risks should invest in bond market. (Robert Parrino, 2013)
• Rate of returns:the bonds are also referred to as risk free investments. The coupon in the bond market in very low since it has low risks. Due to high risks involved in the equity market, the return in the equity market includes the risk premium. The coupon provided in the bond market is risk free and hence lower that the returns of the equity market. Therefore a person seeking to earn stable but low returns should invest in the bond market, but the investor who has the ability to take risks and wants to earn high profits should invest in equity market. (Penman, 2013)

Share	02 March 2017	03 November 2017	Difference in Price	Dividend per share	Total Return per share	Total number of shares
BHP.AX	25.7	27.69	1.99	1.52	3.5061	500
CBA.AX	83.86	77.79	-6.07	3.29	-2.7843	500
TLS.AX	4.57	3.5	-1.07	0.22	-0.8486	500

Share	Total Return	Total Investment	Number of Days of Investment	Holding Period Yield
BHP.AX	1753.05	12850	246	20.24
CBA.AX	-1392.15	41930	246	-4.93
TLS.AX	-424.3	2285	246	-27.55

Share	Expected Return	Weights	Portfolio Return
BHP.AX	20.24	0.6	12.14
CBA.AX	4.93	0.2	0.99
TLS.AX	27.55	0.2	5.51
			18.64
Share	Expected Return	Weights	Portfolio Return
BHP.AX	20.24	0.4	8.10
CBA.AX	4.93	0.4	1.97
TLS.AX	27.55	0.2	5.51
			15.58

Share	Beta	Weights	Portfolio Beta
BHP.AX	1.39	0.6	0.834
CBA.AX	1.33	0.2	0.266
TLS.AX	0.79	0.2	0.158
			1.258
Share	Beta	Weights	Portfolio Beta
BHP.AX	1.39	0.4	0.556
CBA.AX	1.33	0.4	0.532
TLS.AX	0.79	0.2	0.158
			1.246

The first portfolio with the ratio of 0.6, 0.2 and 0.2 is much riskier than the other portfolio since the beta of first portfolio is higher than that of the other portfolio.

Value of Invested $50000 at the end of year four
FV=PV*(1+i/m)^(m*n)
Here
PV	25000
I	4%
M	12
N	4
FV	=	25000*(1+4/12)^(12*4)
	=	29,329.97
Value of $1000 Invested monthly at the end of year four
FV	=	c*{(1+i)^n-1}
Here
C	1000
I	0.0033333
N	48
FV	=	1000*{(1+.003)^48-1}
		0.003
	=	51,545.06
Total Funds available at the end of year 4	80,875.00

Amount of Loan To be taken
Total Funds required	2,50,000
Total Funds available	80,875
Loan to be taken	1,69,125

Assuming Equal annual payments for 20 years are required to be made
PV of Annuity	=	FV
	PVIAF(i,n)
Here
FV	169125
i (0.065/12)	0.01
N	20
PVIAF(I,n)	18.05
PV of Annuity	=	1,69,125.00
	18.05
	=	9,372.12

Therefore, $9372 will have to be paid annually for 20 years including the interest due amount.

Working: Calculation of PVIAF

1	0.990099
2	0.980296
3	0.97059
4	0.96098
5	0.951466
6	0.942045
7	0.932718
8	0.923483
9	0.91434
10	0.905287
11	0.896324
12	0.887449
13	0.878663
14	0.869963
15	0.861349
16	0.852821
17	0.844377
18	0.836017
19	0.82774
20	0.819544
	18.04555

In order to calculate the future value the formula is:
FV	=	PV*(1+i)^n
Here,
FV	3500
I	2.50%
N	4
Therefore,
3500	=	PV*(1+.025)^4
PV	=	3,500
		(1+.025)^4
	=	3,171

Therefore, the investor needs to invest $3171 today in order to receive $3500 after 4 years with interest 2.5% compounded annually.

In order to calculate the future value the formula is:
FV	=	PV*(1+i/4)^(n*4)
Here
FV	2500
PV	1000
I	4%
Therefore,
2500	=	1000*(1+0.01)^(4n)
2.5	=	1.01^4n
N	=	22.75 years

Therefore, an investor needs to invest $1000 today for a period of 22.75 years to get $ 2500 with interest 44% compounded quarterly.

As per CAPM
Re	=	Rf+(Rm-Rf)*Beta
Here
Rf	5%
Rm-Rf	7%
Beta	1.8
Therefore
Rf	=	5+(7*1.8)
	=	17.60%

In order to calculate the bond value
P0	=	PV of Future cash Flows
	=	Face Value + Coupon Value *PVIAF(i,n)
Here
Face Value	1,000
Coupon Value	25
I	3.50%
N	20
Therefore
P0	=	1000+25*PVIAF(3.5%,20)
	=	1000+(25*14.21)
	=	1,355

The Bond is trading at premium.

Calculation of Share Price using Dividend Discount Model
Year	Dividend	PV Factor @ 17%	PV of Dividend
1	4.38	0.8547009	3.74
2	5.47	0.7305136	3.99
3	6.84	0.6243706	4.27
Dividend for year 4	7.182
Price of the share at the end of year 3	=	7.182
17.5-.5
	=	42.25
PV of this Price	=	42.25/(1.175^4)
	=	22.17
Therefore Price of the share today	=	12+22.17
	=	34.17

Since the share is currently trading at $35 and the theoretical price of the share is $34.17 we can say that the share is trading rich and the investor should go short.

References

Berk, J., Demarzo, P., & Harford, J. (2012). Fundamentals of corporate finance. Boston, MA: Prentice Hall.

Fabozzi, F. J., & ‎ Mann, S. V. (2012). The Handbook of Fixed Income Securities. New York: McGraw-Hill Education.

Graham, B., & Dodd, D. (2009). Security analysis. New York: McGraw-Hill.

Graham, B., Buffett, W., & Zweig, J. (2013). The intelligent investor. New York: Harper Collins.

Penman, S. (2013). Financial statement analysis and security valuation. New York: McGraw-Hill Irwin.

Robert Parrino, D. S.-K. (2013). Fundamentals of Corporate Finance, 2nd Edition. Milton: John Wiley & Sons