Present Value Calculation, EMI And Future Value Computation In Financial Analysis

Calculating Present Value using Relevant Formula

The amount of money that one should pay for the above investment opportunity should be equal to the present value of the expected cash inflows. The applicable rate of return is 6% p.a.

The relevant formula for present is as follows (Parrino & Kidwell, 2014).

PV = FV/(1+r)ⁿ

FV = Future Value, r= rate of return, n= number of years

Thus, the present value of the given streams = (3000/1.06) + (65000/1.06²) + (280/1.06³) + (1400/1.06⁴) + (3000/1.06⁵) + (10000/1.06⁷) = 2830.19 + 57849.77 + 235.09 + 1108.93 + 2241.78 + 6650.57 = $70,916.33 

1. Total loan amount = $ 1.8 million or $ 1,800,000

Nominal interest rate= 5% p.a or (5/12)% = 0.4167% per month

Repayment Period = 30 years or 30*12 = 360 months

The relevant formula for EMI (Equal Monthly Instalment) is indicated below (Brealey, Myers & Allen, 2014).

EMI = P*R*(1+R)^N/((1+R)^N-1)

In the given case, P = $1,800,000

R = 0.004167 and N = 360

Hence, EMI = 1800000*0.004167*(1.004167³⁶⁰)/(1.004167³⁶⁰ -1)= $9,662.79

Thus, Jarrad would have to pay $ 9,662.79 on a monthly basis to discharge the given loan in 30 years. 

1. (i) The monthly contributions are in the form of annuity and the first payment is being today or at the beginning of the period.

Total monthly payments = 35 *12 = 420

Interest rate applicable = 7% p.a or (7/12) or 0.5833% per month

The relevant formula for computation of future value of the monthly payments of $1,500 beginning from today is as follows (Damodaran, 2015). 

Thus, future value of all monthly payments till retirement = (1.005833)*1500(1.005833⁴²⁰ -1)/(0.005833) = $ 2,717,341.13

With regards to computing the future value of the lump sum payment, the relevant formula is as shown below (Arnold, 2015).

FV = PV (1+r)ⁿ

In the given case, PV = $50,000, r = 0.5833% and n= 420 months

Hence, FV = 50000*1.005833⁴²⁰ = $575, 307.6

Therefore, total FV at the time of retirement = $ 2,717,341.13 + $ 575,307.6 = $ 3,292,648.72 

(ii) The first step is to estimate the present value of the $ 200,000 at the time of retirement using 5% p.a.

PV = FV/(1+r)ⁿ

In the given case, FV = $ 200,000, r = 0.05, n =25 years

Hence, PV = 200000/1.05²⁵ = $ 59060.55

Total amount of amount at retirement = $ 3,292,648.72

Amount of money from which the annuity payment for the next 25 years can be derived = 3,292,648.72 – 59060.55 = $ 3,233,588.17

Let the annuity payment at the end of year after retirement be X

The relevant formula would be related to the present value of annuity payments given below. 

In the given case, P = X, r= 5%, n =25

Hence, 3,233,588.17 = X (1-1.05^-25)/0.05

Solving the above, X = $ 229.431 

1. The requisite time line is indicated below. 

1. The requisite accumulated values of cash flows are shown below.

T₀ – The cumulated cash flows is zero.

T₄ = 2500*1.045³ + 2500*1.045 = $ 5,465.42

T₁₀ = 5,465.42*1.06²*1.07⁴ + 2700*1.06*1.07⁴ – 1500*1.07⁴ + 7000*1.07 + 10000 = $ 27,324.83 

With the drop in US corporate tax rates from 35% to 21% earlier this year, there has been a renewed debate in Australia regarding corporate tax rate cut so as to enhance the competitiveness of Australia as a destination for businesses. The proponents of the corporate tax cut cite facts such as the following graph to support their cause (Smith, 2015). 

Calculating Equal Monthly Installment (EMI)

While quoting the above comparison, the proponents seem to forget the dividend imputation system that is prevalent in Australia which besides New Zealand does not any match in any of the nations listed above.  Hence, a high amount of the tax that is paid by the company is distributed to the shareholders in the form of tax credits owing to franked dividends. Therefore, the higher the tax paid by the company, the lower would be the tax burden for the shareholders. This is in sharp contract with the system prevalent in other nations where there is double taxation of income. Firstly, the corporate profits are taxed at the corporate rate and further when this income is passed on the shareholders, personal income tax is levied on the dividends. As a result, the effective tax rate levied by these nations may well exceed that of Australia even though there corporate tax rates are lower (Smith, 2015).

For instance, if the prevalent system of double taxation was applicable in Australia, then $ 100 worth of corporate profits would be charged $ 30 as corporate tax and if the remaining $ 70 is given as dividends and tax at 30% marginal rate, then another $ 21 would be drawn as tax making the cumulative taxation at 51%. As a result, if there is a decrease in the corporate tax rate, then the company would be able to provide a higher dividend but the franking credits attached would be lower owing to lower tax paid.  Thus, the lower corporate tax could essentially be recouped in the form of personal tax from the shareholders since the corporate tax cut would be akin to a shift to tax burden from the corporate to shareholders.  However, the government would be at a loss with regards to foreign companies that would tend to pay lower tax in Australia and the higher profits would not be given to Australia taxpayers but rather repatriated back to their country of origin thus causing a loss to the exchequer.

Also another key aspect to consider is the generous deductions that are allowed in Australia which tend to lower the effective tax significantly. Typically it has been observed that nations that tend to have a higher statutory tax rate also tend to be generous with exemptions thus bringing down the effective tax rate to comparable values. This is evident in the form of generous R&D concessions coupled with transfer pricing legislations that are permissible in Australia Montgomery, 2018).  Further, it is critical to consider that besides tax, there are other factors also that foreign investors typically consider. With regards to Australia, its limited population along with geographical isolation and high labour costs are also factors that may discourage a number of industries particularly based in manufacturing sector even despite the corporate tax cut. In other economic sectors such as agriculture, animal husbandry along with services, the country already has the competitive edge. Additionally, the fiscal and budgetary constraints also need to be taken into consideration which also does not favour reduction in the corporate tax rate (Taylor, 2018).

Based on the above discussion, it would be fair to conclude that reducing corporate tax in Australia would not bring any significant gains in the form of increased investment from foreign companies since there are other economic issues besides tax. Also, for domestic companies, tax reduction would not offer much advantage since there would be a shift in the tax burden from them to their shareholders. Thus, the corporate tax cut is not a recommended course of action for Australia. 

• The requisite monthly prices for Wesfarmers, Woolworths and All ordinaries index are highlighted below. 

The requisite monthly returns for the stocks and market are summarised below. 

Monthly Returns = (Monthly closing price – Monthly opening price)/Monthly opening price

The requisite graphical representation of the above information is shown below.  

• The average monthly returns can be computed by taking the average of the monthly returns that have been computed for the two stocks and the market. Average can be taken by adding all the monthly returns and dividing the same by 12. The end result is indicated as follows. 

• Annual Holding Returns (Wesfarmers) = (49.36-40.06)/40.06= 23.22%

Annual Holding Returns (Woolworths) = (30.52-25.37)/25.37= 20.3%

Annual Holding Returns (Market) = (6289.7-5764)/5764 = 9.12% 

• The standard deviation of the monthly returns on Wesfarmers can be computed using the table shown below.  

Standard deviation for Wesfarmers monthly returns = √(0.017063/(12-1)) = 0.0394 or 3.94%

The standard deviation of the monthly returns on Woolworths can be computed using the table shown below. 

Standard deviation for Woolworths monthly returns = √(0.016036/(12-1)) = 0.0382 or 3.82%

The standard deviation of the monthly returns on Market can be computed using the table shown below. 

Standard deviation for market monthly returns = √(0.005177/(12-1)) = 0.0217 or 2.17% 

• The relevant scatterplot is shown below. 

• In accordance with the Capital Asset Pricing Model (Arnold, 2015)

Expected Returns = Risk Free Rate + Beta * Market Risk Premium

Expected Returns (WOW) = 2 + 0.77*(5.75-2) = 4.89% p.a.

Expected Returns (WES) = 2+ 0.81*(5.75-2) = 5.04% p.a. 

• The requisite SML is indicated below.  

• Weight of WOW = 0.3 and weight of WES = 0.7

Beta for the portfolio = 0.3*WOW beta + 0.7*WES beta = 0.3*0.77 + 0.7*0.81 = 0.80

Returns for the portfolio = 0.3* WOW returns + 0.7*WES Returns = 0.3*1.62 + 0.7*1.83 = 1.76% per month

• The requisite choice needs to be made considering the underlying risk and return.

Return per unit risk (WOW) = 1.62/3.82 = 0.424

Return per unit risk (WES) = 1.83/3.94 = 0.464

Return per unit risk (MARKET) = 0.75/2.17 =0.35

It is apparent that highest return per unit risk is delivered by WES. However, owing to diversification benefit, the return per unit risk would be even higher for the portfolio formed by 30% WOW and 70% WES which would be the preferable investment choice (Damodaran, 2015).  

References

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

Brealey, R. A., Myers, S. C., & 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.

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

Montgomery, R. (2018, February, 19).Should Australia cut the corporate tax rate ? Retrieved from https://rogermontgomery.com/should-australia-cut-the-corporate-tax-rate/

Smith , W. (2015, February 10). FactCheck: is Australia’s corporate tax rate not competitive with the rest of the region. Retrieved from https://theconversation.com/factcheck-is-australias-corporate-tax-rate-not-competitive-with-the-rest-of-the-region-37226

Taylor, D. (2018, March 29). Corporate tax cuts: What are the key issues in the debate? Retrieved from https://www.abc.net.au/news/2018-03-29/corporate-tax-cuts-explained/9600004