Pacc6003 Business Finance For Equivalent Assessment Answers

.(i)  Your company management has asked you to select only one out of the four projects available, which one would you select? Show your calculation and justification of selection. ?

(ii)  Consider an alternative situation. Your company management has setup a minimum acceptance criteria for any new project selection. Such minimum acceptance criteria or required rate of return is set up at 12.5%. The management has asked you to select all projects generating return higher than the required rate of return (12.5%).

Answers:

Calculation of equivalent annual rate of interest earnings for the available projects: 

Annual interest earnings rate from project A is to be calculated using the following formula:

Assuming the principal amount of investment of $100.00. The Interest earnings over the period of 10 years @ 11.56% per annum compounded annually will be calculated using the following formula:

Year 1 = 100 X 111.56% = 111.56 – 100.00 = 11.56

Accordingly, the total interest earnings from the project A shall be as following:  

Total interest earnings over the 10 years period = 298.60 – 100.00 = 198.60

Average interest earnings per year = 198.60 / 10 years = 19.86

Equivalent Annualized rate of interest earnings = 19.86 X 100 / 100 = 19.86% (Anderson et al. 2015) 

The interest earning rate for the project is 12% per annum to be compounded monthly. Using the following formula let us calculate the annualized rate of interest earnings for the project.

Assuming the principal at $100.00, the annualized interest earning rate would be calculated using the following formula:

Interest earning per month will be:

(100.00 X 12%) X 1/12 = 1.00  

 Accordingly, the annualized interest earning rate would be:

Annualized interest earnings rate would be: (1+1.01+1.0201+1.0303+1.0406+1.0510+1.0615+1.0721+1.0829+1.0937+1.1046+1.1157)) = 12.68% per annum

Assuming the principal amount of investment of $100.00. The Interest earnings over the period of 10 years @ 12.68% per annum compounded annually will be calculated using the following formula:

Year 1 = 100 X 112.68% = 112.68 – 100.00 = 12.68

Accordingly, the total interest earnings from the project B shall be as following:   

Total interest earnings over the 10 years period = 329.97 – 100.00 = 229.97

Average interest earnings per year = 229.97 / 10 years = 22.997

Equivalent Annualized rate of interest earnings = 22.997 X 100 / 100 = 22.99% 

Assuming the principal at $100.00, the annualized interest earning rate would be calculated using the following formula:

Interest earning per month will be:

(100.00 X 5%) X 1/6  = 0.833

The annualized rate of interest earning will be as following:

(Miles 2015)

Annualized interest earnings rate would be: (0.833+0.840+0.847+0.854+0.861+0.868+0.876+0.883+0.890+0.898+0.905+0.913) = 10.47% per annum

Assuming the principal amount of investment of $100.00. The Interest earnings over the period of 10 years @ 10.47% per annum compounded annually will be calculated using the following formula:

Year 1 = 100 X 110.47% = 110.47 – 100.00 = 10.47

Accordingly, the total interest earnings from the project C shall be as following:  

Total interest earnings over the 10 years period = 270.67 – 100.00 = 170.67

Average interest earnings per year = 170.67 / 10 years = 17.067

Equivalent Annualized rate of interest earnings = 17.067 X 100 / 100 = 17.07% 

Annual rate of interest earning from project D is = 3.26 X 4 = 13.04%

Assuming the principal amount of investment of $100.00. The Interest earnings over the period of 10 years @ 13.04% per annum compounded annually will be calculated using the following formula:

Year 1 = 100 X 113.04% = 113.04 – 100.00 = 13.04

Accordingly, the total interest earnings from the project D shall be as following:  

Total interest earnings over the 10 years period = 340.66 – 100.00 = 240.66

Average interest earnings per year = 240.66 / 10 years = 24.066

Equivalent Annualized rate of interest earnings = 24.066 X 100 / 100 = 24.07% (Turner 2016)

Project D should be selected as the interest earnings from the project is highest at equivalent annual rate of interest of 24.07%. Thus, the management if only has the option of making investment in only one of the above four alternative investment proposals then the management shall invest the money on project D as the rate of interest earning from the project is higher than all the other projects (Titman and Martin 2014). 

Let us first have the relevant data of equivalent annual interest earnings rate of all the four projects to assess the projects which have met the organizational criterion of investment:

Since all the projects have a higher rate of interest earnings than 12.50%, i.e. conditional rate of return to be earned by investment proposals for making investment, the management should invest in all the four available projects in front of it. 

Thus, considering the management will invest in the project which will have the shortest repayment duration of loan hence, project G should be selected and invested in by the management as the loan repayment duration for the project is 7 years which is the shortest amongst the four probable investment projects. 

Part (i):

According to normal dividend model the value of a share can be calculated by using the following formula:

Value of a share = Dividend paid / Cost of capital

Value of stock A = $8.56 / 0.12 = $71.33

According to Gordon’s dividend growth model the value of a share is calculated by using the following formula:

Value of a share = Dividend paid / Cost of capital – growth rate

Value of stock B = $6.23 / 0.12 – 0.04 = $77.88 

According to normal dividend model the value of a share can be calculated by using the following formula:

Value of a share = Dividend paid / Cost of capital

Expected dividend at the end of 5^th year:

Value of stock C = $9.23 / 0.12 = $76.92

Since, all the shares have been offered at $80.00 none of the shares are valued above the prices at which they are being offered by the broker at present. However, in case it is essential to acquire one of the stock at any cost then stock B should be purchased as it has the highest value at $77.88 per share. However, the recommendation to the investor should be to not make any investment in any of the stocks as none of the stock have been valued above the cost at which they are being offered by the broker (Arrow and Lind 2014). 

Note: Coefficient of variation is calculated by using the following formula:

= Standard deviation / Expected return

Since, the coefficient of variation is lower for stock D it shall be preferred by the management over stock E. 

Diversification is an important element in maintaining a portfolio by managing the risk and returns effectively. It is often alluring for the investors to invest in a single stock which is providing higher return over the other stocks however, in case any disaster struck with the stock of such company then the whole investment portfolio of an investor would be in jeopardy. Thus, to manage the risk and returns effectively it is essential to use diversification strategy. The reason the investor have invested in both Stock D and E instead of only E which has a higher return compare to stock D is to manage the risk along with the return. Though the expected return of stock D is lower compare to stock E yet the investor has decided to make investment in stock D as it has much lower rate of interest compare to stock E, standard deviation being 16% compare to 24% of stock E. The overall risks associated with the investment portfolio have subsequently reduced due to combining of investment in stock D and E (Peppard and Ward 2016). 

When correlation is – 0.89

 When correlation is 0.15

When correlation is +0.95

The above calculations have made the impact of different correlations on the investment portfolio risks very clear (Hammond et al. 2015). 

References:

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. and Cochran, J.J., 2015. An introduction to management science: quantitative approaches to decision making. Cengage learning.

Arrow, K.J. and Lind, R.C., 2014. Uncertainty and the evaluation of public investment decisions. Journal of Natural Resources Policy Research, 6(1), pp.29-44.

Hammond, J.S., Keeney, R.L. and Raiffa, H., 2015. Smart choices: A practical guide to making better decisions. Harvard Business Review Press.

Miles, L.D., 2015. Techniques of value analysis and engineering. Miles Value Foundation.

Peppard, J. and Ward, J., 2016. The strategic management of information systems: Building a digital strategy. John Wiley & Sons.

Titman, S. and Martin, J.D., 2014. Valuation. Pearson Higher Ed.

Turner, R., 2016. Gower handbook of project management. Routledge.