Savings, Loans, And Bond Analysis

Part a: Christine’s savings plan for a house deposit

Part a

• Christine would be saving the amount in terms of annuity payment which is made at the end of financial year.

Annuity payment (P)
Duration of annuity (N)
Interest res (R )

Future value of annuity is calculated as highlighted below.

• Formula taken into consideration is given below.

Present value of house (PV)
Rate of increase (R)
Time period (N)
At the end of five year, the expected value of house
20% of the expected value of house would be the down payment amount

It can be seen from the above that future value calculated in part (i) is higher than the 20% of the future value calculated in part (ii) which means the deposit amount requirement would easily be met.

• Let x amount needs to borrow by Christine from the bank in order to buy the home at the end of5 year.

At the end of five year, the expected value of house
Total deposit amount
Total amount needs to borrow (x)

Part b

• Monthly instalment amount needs to find here.

Principal loan amount (P)	$749,406.32
Total months of maturity of loan (N)
Interest rate (R)

Therefore,

Monthly salary after getting the promotion
Total monthly saving amount

It can be seen from the above that the monthly saving amount is higher than the EMI and hence, Christine can easily pay the instalment of the loan.

• Total repayment amount over the 30 years and the interest amount need to pay.

Total repayment amount
Interest amount need to pay = Total repayment amount – Total amount needs to borrow

Part c

• Christine’s monthly repayment if she has decided to pay-off the loan in 15 years.

Duration of loan

Total repayment amount over the 15 years and the interest amount need to pay.

Total repayment amount
Interest amount need to pay = Total repayment amount – Total amount needs to borrow

Christine has ready to contribute 40% of the average salary after getting the promotion.

Monthly salary after getting the promotion
Total monthly saving amount

It can be seen from the above that the monthly saving amount is lower than the EMI and hence, Christine cannot pay the instalment of the loan when she agrees to contribute 40% of her average salary.

Part d

• The available cash amount needs to be found here.

Additional monthly cash flow based on tenants
Additional living expenditure payable per month to the parents
Extra cash available (every month)
Monthly saved amount
The available cash amount

It can be seen that EMI amount is higher comes out be higher even in the duration of loan has reduced to 15 years. Therefore, it can be concluded that Christine will not be able to complete the EMI payment.

• It is apparent that Christine will not be able to afford the EMI payment under 15 year mortgage and hence, she should not accept the offer.

Question 2

Part a

Bond A, Bond, Bond C and Bond D would be sold at a premium price to their parity value. The reason behind this underling is that the coupon rate given on these bonds is exceeded the yields. Further, Bond D would be sold at a discount rate to their parity value because the coupon rate given on this bond is significant lower than the yield (Damodaran, 2015).

Part b

It can be said that bond’s current value is same as the present value of all the coupon payment along with the principal.

Bond A
Face value of bond
Total maturity period
Coupon payment amount
Yield
Bond price for A

Bond B
Face value of bond
Total maturity period
Coupon payment amount
Yield
Bond price for B

Bond C
Face value of bond
Total maturity period
Coupon payment amount
Yield
Bond price for B

Bond D
Face value of bond
Total maturity period
Coupon payment amount
Yield
Bond price for B

Part c

Here, the increase of 1% has taken into consideration in the market interest rate.

Bond A
Bond price for A

Bond B
C = $ 1.625, I = (1.19%+ 0.5%)=1.69%, n= 14, M=100
Bond price for B

Bond C
Bond price for C

Bond D
C = $ 1.375, I = (1.44% +0.5%)=1.94%, n= 40, M=100
Bond price for D

Part d

 Here, the reduction of 1% has taken into consideration in the market interest rate.

Bond A
Bond price for A

Bond B
C = $ 1.625, I = (1.19%- 0.5%)=0.69%, n= 14, M=100
Bond price for B

Bond C
Bond price for C

Bond D
C = $ 1.375, I = (1.44% -0.5%)=0.94%, n= 40, M=100
Bond price for D

Part e

There is a decrease of 2% in the expected yield and due to this reduction the interest rate would be different.

Bond A
	$111.99
	$101.97
Return on bond

Bond B
	$119.80
	$105.58
Return on bond

Bond C
	$125.90
	$105.87
Return on bond

Bond D
	$134.225
	$98.03
Return on bond

It can be concluded based on the above tables that bond D has highest return on bond which is 36.91% and hence, it would profitable to buy bond D.

(f) Risk free means that the underlying default risk associated is zero. Typically risk free status is associated with governments of the developed world having AAA credit rating since these governments have the least chance of defaulting and thereby is considered to be risk free. Usually, in various financial computations risk free rate is the yield on the government security since government has ample resources to ensure that there is no sovereign debt default (Parrino and Kidwell, 2014).

Part b: Christine’s loan options to purchase the house

Question 3

(a) The relevant computations have been performed in excel and a screenshot of the same is available as follows.

(b) The extent of linear relationship between the two variables is referred to as correlation. The extent of correlation between the asset returns has sizable influence on the risk associated with the portfolio. The correlation coefficient has a value which varies between -1 and +1. A negative correlation suggests that the stock returns of the two stocks would move in opposite direction which would provide a natural hedge against volatility and risk. On the contrary, a positive correlation between stock returns would imply that the movements would be similar and hence risk would not be diminished to that extent as in negative correlation coefficient (Arnold, 2015).

The above concept of correlation has implications for the given portfolios as well. The correlation between gold and stock returns is the most negative which would imply the highest reduction in risk. On the other hand, the correlation coefficient between property and stocks return in positive which is indicative of lowest risk reduction on account of reasons outlined in the above paragraph (Berk et. al., 2013).

 (c) Diversification is an investment strategy where the underlying portfolio comprises of various asset classes which tend to act as hedge to each other and hence lead to minimisation of unsystematic risk. The unsystematic risk essentially refers to the risk that may be associated with a given asset class. The total risk associated with investing comprises of both systematic risk as well as unsystematic risk (Petty et. al., 2015). While the systematic risk cannot be eliminated, the minimisation of unsystematic risk achieved though portfolio diversification implies that there is reduction in risk and associated volatility. An example could be taken as a portfolio comprising of stocks of exporting companies as well as importing companies. Such a portfolio would not be exposed to currency risk as there would be a natural hedge in place (Northington, 2015).

For the portfolios formed in the given case, it is apparent that by inserting a 30% weight of other asset classes, the risk associated has decreased when compared to stock as the asset class. Further, the reduction in risk is the highest for gold owing to the highest negative correlation between gold and stocks (Brealey, Myers and Allen, 2014).

 (d) The basic concept of risk aversion is that when investors are faced with uncertainty, then there are actions or steps taken by them in order to enhance the certainty. This is typically done by making choices towards shifting to risk free asset classes. An important implication of this concept is that if one has to invest in a risky asset, hence he/she would seek compensation in the form of higher expected returns on the asset If two investment options with same risk are presented, the investors would equivocally choose the one with lower risk profile (Damodaran, 2015).

This concept is the basis of modern portfolio theory where the expected returns on various assets are derived considering the risk free rate and then making compensation for the additional risk assumed by the investor. An apt illustration of this is indicated in the difference of the cost of debt and equity. Since equity has a higher risk than debt, hence the expected returns on equity tend to exceed those on debt (Petty et. al, 2014).

 (e) Three portfolios have been formed and the most superior portfolio would be one which would have the highest return for a unit risk assumed.  This computation has been performed as follows.

The above computations clearly suggest A as the most optimal choices amongst the options presented. This is in line with the modern portfolio theory where the objective is not the maximise returns or minimise risk but rather the key objective is to choose an investment which tends to offer maximum returns per unit risk. Hence, it is essential that risk and returns must not be viewed in isolation (Brealey, Myers and Allen, 2014).

References

Arnold, G. (2015) Corporate Financial Management. 3^rd ed. Sydney: Financial Times Management.  

Berk, J., DeMarzo, P., Harford, J., Ford, G., Mollica, V., and Finch, N. (2013) Fundamentals of corporate finance, London: Pearson Higher Education

Brealey, R. A., Myers, S. C., and Allen, F. (2014) Principles of corporate finance, 2nd ed. New York: McGraw-Hill Inc.

Damodaran, A. (2015). Applied corporate finance: A user’s manual 3rd ed. New York: Wiley, John & Sons.

Northington, S. (2015) Finance, 4^th ed. New York: Ferguson

Parrino, R. and Kidwell, D. (2014) Fundamentals of Corporate Finance, 3rd ed. London: Wiley Publications

Petty, J.W., Titman, S., Keown, A., Martin, J.D., Martin, P., Burrow, M., and Nguyen, H. (2015). Financial Management, Principles and Applications, 6^th ed..  NSW: Pearson Education, French Forest Australia