Financial Analysis And Home Loan Calculations

Pricing Analysis of Shares

Expected return on each security using CAPM is as follows:

E(r) = R_f + ß (R_m – R_f )

Share A   E (r) = 3% + 1.5 (8% – 3%)

= 10.5%

Share B   E (r) = 3% + 0.6 (8% – 3%)

= 6%

Share C  E (r) = 3% + 1.2 (8% – 3%)

= 9%

Share D  E (r) = 3% + 1.8 (8% – 3%)

= 12%

1.  

Security	Expected return using CAPM	Expected return of investor	Share pricing
A	10.5%	14%	Overvalued
B	6%	8%	Overvalued
C	9%	9%	Correctly priced
D	12%	10%	Undervalued

1. Beta measures the volatility of a stock in comparison to the stock market. A beta of 1 means the stock has same volatility as the market, a beta more than 1 means the stock has higher volatility than the market and a beta of less than 1 means the stock has a lower volatility than the market. Stock portfolios build with low volatility stocks tend to outperform the high beta growth stocks. This is because these stocks have low volatility resulting in gradually increasing dividend income and due to low volatility the price also remains more or less stable (Jim 2011)

In the present case also, share A and B have low beta as compared to share D. Even though share D is undervalued and both shares A and B are overvalued, however a portfolio of low beta stocks will tend to outperform share D as they have low volatility.

1. The NPV of the three projects is presented below According to the NPV the ranking of the projects is:

Rank	NPV	Project
1	1,43,085.5	C
2	1,01,373.8	B
3	23,233.0	A

1. The payback period for the company is as follows:

Year	Cash Flows	Cumulative cash flows
	Project B	Project C	Project B	Project C
–	-40,000	-70,000	-40,000	-70,000
1	5,000	30,000	-35,000	-40,000
2	10,000	30,000	-25,000	-10,000
3	30,000	40,000	5,000	30,000
4	80,000	50,000	85,000	80,000
5	1,00,000	1,80,000	1,85,000	2,60,000
Payback Period	2.83 years	2.25 years

Since the company has a policy of accepting projects with a payback period of less than 2.75 years, hence the company would accept projects A and C. project B has a payback period of 2.8 years which is higher than the acceptable.

1. Profitability index

	Project A	Project B	Project C
PV of future cash flows	43,233.0	1,41,373.8	2,13,085.5
Initial investment	20,000	40,000	70,000
PI	2.2	3.5	3.0

Internal rate of return

	Project A	Project B	Project C
IRR	72%	56%	56%

Price of house = $700,000

Down payment = 10% of $700,000 = $70,000

Home loan to be taken (P) = $700,000 – $70,000 = $63,000

Interest rate (r) = 3.5%

1. Annual repayments for Sam for a 20 years loan period and 25 year loan period

Loan instalment = r (P) / (1-(1+r)^-n)

Loan instalment for 20 years loan period = (0.035*630000) / (1-(1+0.035)^-20)

= $22050 / 0.497

= $44,327.5

Loan instalment for 25 years loan period = (0.035*630000) / (1-(1+0.035)^-25)

= $22050 / 0.576

  = $38,224.6

1. Total interest paid on both loans

Interest paid on 20 year loan = $630000*3.5% * 20

= $441,000

Interest paid on 25 year loan = $630000*3.5% * 25

= $551,250

1. With an increase in the loan term, the annual payment reduces and vice versa. This means loan term and annual payment have an inverse relationship .And with an increase in the loan term; the total interest paid also increases. This means loan term and total interest paid have a direct relationship.
2. Annual loan repayment for 20 year loan from August 2021 = (0.06*630000) / (1-(1+0.06)^-17)

= $60,130.2

Annual loan repayment for 25 years loan from August 2021 = (0.06*630000) / (1-(1+0.06)^-22)

= $52,318.7

1. The yield curve for November 2007, May 2008 and November 2008 is presented below b) The shape of a yield curve under normal circumstances is an upward sloping curve. Yield curve plots the yields on bonds of different maturities ranging from short term to medium term to long term. Long term bond will generally have higher yield as compare to short term bonds. This means with an increase in maturity, the yield on the bonds increase. Thus, the shape of a normal yield curve is upward sloping.

1. c)  The yield curve of November 2007 is almost flat with the yield reducing very slightly with the increasing years to maturity. The yield has remained between the levels of 6-6.75%. There is not much of variation. The yield curve of May 2008 is downward sloping. This may also be called a negative or inverted yield curve. This is because the short term yields are higher than the long term yields. The yield curve of November 2008 is upwards sloping from 1 year to maturity. This shows a normal yield curve.

The slope of the yield curve tells us about the future inflation and the economic activity of an economy. An upward sloping yield curve denotes a rising economy as the interest rates move up and vice versa. For the Australian economy, we see that from November 2007 to November 2008, the yield curve has fallen. The yield was in the range of 6-7% in Nov. 2007, it increased to the range of 7 in May, 2008, however in November 2008, and the yield has come down between 3-4%. This shows the economy had slowed down between 2007 to 2008. However, in Nov, 2008, the yield curve has an upward sloping curve denoting a rising economy. So it can be said that the Australian economy is expected to grow in the future with increasing yields on bonds.

1. The yield on the 2 year bond in January 2007 is 6.18%.

according to the expectations theory, the rate investors would expect for a 1 year bond next year (Jan 2008) is calculated as follows:

Step 1

Add 1 to the January 2007 interest rate = 1.0618

Square the figure = 1.127

Step 2

Divide the above by 1 year interest rate plus 1 = 1.127 / 1.0626 = 1.061

Rate expected for a 1 year bond in January 2008 = 1.061 – 1

= 6.1%

The expected rates on 1- year bonds for all the months of 2008 is calculated below:

Month (2007)	YTM for 2 years bond (2007)	Step 1	YTM for 1 year bond (2007)	Step 2	Expected rate on 1-year bond (2008)
January	0.0618	1.127	0.063	1.061	6.10%
February	0.0608	1.125	0.062	1.059	5.93%
March	0.0612	1.126	0.065	1.058	5.79%
April	0.0625	1.129	0.063	1.062	6.20%
May	0.0619	1.128	0.064	1.060	6.03%
June	0.064	1.132	0.065	1.063	6.30%
July	0.0638	1.132	0.066	1.062	6.19%
August	0.0629	1.130	0.065	1.061	6.06%
September	0.0632	1.130	0.066	1.061	6.09%
October	0.0658	1.136	0.069	1.063	6.30%
November	0.0667	1.138	0.068	1.065	6.51%
December	0.0672	1.139	0.069	1.066	6.58%

1. Comparison of actual interest rates with expected interest rates in 2008:

Month	Expected interest rates (2008 1 year bond)	Actual interest rates (2008 1 year bond)
January	6.10%	6.83%
February	5.93%	7.12%
March	5.79%	7.03%
April	6.20%	7.21%
May	6.03%	7.35%
June	6.30%	7.26%
July	6.19%	6.87%
August	6.06%	6.34%
September	6.09%	5.63%
October	6.30%	4.33%
November	6.51%	3.09%
December	6.58%	2.67%

From the above table we see that the expectation theory does not hold true for the 1 year bonds in 2008. The expected and actual interest rates are different. The theory has underestimated the interest rates from January to August and understated the rates from September to December.

Possible reasons why expectation theory may not hold true include:

1. Change in inflation (Tease 1986)
2. Change in economic growth pattern

1. The average spread between the Australian Government bonds and the NSW Treasury for 3, 5, 10 year bonds is calculated below:

Date	3 year bond	Spread	5 year bond	Spread	10 year bond	Spread
	Australian Federal Gov.	NSW Treasury		Australian Federal Gov.	NSW Treasury		Australian Federal Gov.	NSW Treasury
Jan-2007	6.11	6.33	0.23	6.05	6.28	0.23	5.88	6.17	0.30
Feb-2007	6.02	6.24	0.22	5.97	6.19	0.23	5.81	6.09	0.28
Mar-2007	6.04	6.27	0.23	5.95	6.19	0.24	5.74	6.03	0.30
Apr-2007	6.19	6.42	0.23	6.11	6.35	0.24	5.91	6.19	0.28
May-2007	6.15	6.38	0.23	6.07	6.32	0.25	5.92	6.21	0.29
Jun-2007	6.39	6.66	0.26	6.34	6.66	0.32	6.20	6.56	0.35
Jul-2007	6.38	6.68	0.31	6.30	6.71	0.41	6.15	6.62	0.47
Aug-2007	6.24	6.64	0.41	6.13	6.62	0.48	5.93	6.46	0.54
Sep-2007	6.29	6.73	0.44	6.21	6.70	0.49	5.99	6.52	0.52
Oct-2007	6.56	6.93	0.38	6.45	6.87	0.42	6.17	6.66	0.49
Nov-2007	6.57	7.15	0.58	6.36	7.01	0.65	6.03	6.66	0.63
Dec-2007	6.66	7.18	0.53	6.46	7.09	0.63	6.21	6.76	0.55
Jan-2008	6.58	6.99	0.41	6.34	6.92	0.57	6.08	6.58	0.50
Feb-2008	6.75	7.33	0.59	6.50	7.26	0.76	6.29	6.96	0.67
Mar-2008	6.21	6.94	0.74	6.10	6.90	0.80	6.09	6.82	0.73
Apr-2008	6.25	6.89	0.64	6.19	6.84	0.65	6.17	6.78	0.61
May-2008	6.47	7.02	0.54	6.33	6.91	0.58	6.36	6.89	0.54
Jun-2008	6.84	7.36	0.52	6.69	7.23	0.54	6.59	7.10	0.51
Jul-2008	6.49	7.14	0.65	6.40	7.05	0.65	6.37	7.01	0.64
Aug-2008	5.74	6.35	0.62	5.77	6.38	0.61	5.86	6.49	0.63
Sep-2008	5.48	6.21	0.73	5.54	6.24	0.70	5.65	6.33	0.69
Oct-2008	4.59	5.27	0.68	4.83	5.48	0.65	5.22	5.85	0.63
Nov-2008	3.96	4.75	0.79	4.28	5.14	0.87	4.94	5.69	0.75
Dec-2008	3.43	4.54	1.10	3.72	4.87	1.15	4.22	5.12	0.90
	Average spread		0.50	Average spread		0.55	Average spread		0.53

The average spread is the highest for 5 year bonds. Australian Federal Government bond is a bond issued by the federal government whereas NSW treasury bond is a state government bond. There is likely to be a difference in the yields of the bond because of the monetary policies initiatives of  both the federal and state government.

1. The graph showing the spread between the Australian government bonds and NSW Treasury is presented below:

For all three maturity periods, the bonds follow the same pattern from 2007 to 2008. The spread is the highest for 10 year bond followed by 5 year and then 3 year bonds. This means when there is an increase in the Australian government bonds, there is also an increase in the NSW bonds at all the levels of bonds.

Jim, F 2011, ‘The Greatest Anomaly in Finance: Low-Beta Stocks Outperform’, InvestingDaily, 22 September 2011.