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Portfolio Theory and Capital Budgeting

Your client, for whom you are writing the report, is a school teacher by profession. She has two children aged under five, with a steady income. Her knowledge of financial theory and financial mathematics is now at an intermediate level. She (and her partner) is in a position to invest into sound investments for both short-term and long-term returns. She has done some research and has found a number of investments that she wishes to have analysed. As such, you do not have to search for viable investments for her.

You also note that she wishes to invest into securities for retirement, with only the viability of the investment being considered in this report.

While we can garner a degree of information to the clients financial position, we still do not know her (and her partner’s) financial position. In the same manner as the previous report you presented to them, it is impossible to know how many of these investments they can purchase / invest. Therefore you are expected to provide advice on each investment in isolation from the other investments, i.e. not as a portfolio of investments.

  • Provide a brief discussion of approximately 300 words detailing the risks inherent in stock returns in a portfolio of shares using the concepts of standard deviation and diversification as a basis for your
  • Under what conditions can a firm’s weighted average cost of capital be used for assessing newprojects?
  • In the context of the net present value (NPV) modeldiscuss:
  • The conditions that must be observed such that a project that has a positive NPV should be chosen. Why, in these circumstances, would a project that has a positive NPV bechosen?
  • Why depreciation does not involve a flow of cash and therefore can be
  • Within the standard present-value model, why tax savings on interest payments are excluded from the cash-flow
  • The effect of sunk costs within the analysis of a project’s
  1. Lloyds Ltd., is a publicly listed Australian company that your client is following closely, however your client does not have the requisite skills to evaluate the company and, as such has provided you with sufficient information. The historical price of Lloyds Ltd. is given below. Lloyds Ltd. is closely integrated with the Australian economy and so the rates of return for the Australian economy as a whole can be used in the evaluation process.

You know that Australian Treasury bills currently pay a return of 4% p.a., the stock market return over the same period averaged 10% p.a., and have calculated the standard deviation of the market returns to be 12% p.a. Lloyds Ltd. beta is estimated at 1.40. Lastly, you have identified the historical returns and dividends (below).
























Using the above information, identify whether it is a good idea, for your client, to invest in Lloyds. Explain your reasoning for your decision.

  1. RunRig Ltd. is an investment company with the following balancesheet:

Long-term debt


Bonds: Par $100, annual coupon 10% p.a., 5 years to maturity



Preference shares


Ordinary shares





The company’s bank has advised that the interest rate on any new debt finance provided for the projects would be 9% p.a. if the debt issue is of similar risk and of the same time to maturity and coupon rate.

There are currently 100,000 preference shares on issue, which pay a dividend of $1.20 per year. The preference shares currently sell for $8.65.

The company’s existing 500,000 ordinary shares currently sell for $2.95 each. You have identified that RunRig has recently paid a $0.25 dividend. Historically, dividends have increased at an annual rate of 4% p.a. and are expected to continue to do so in the future.

The company’s tax rate is 30%.

Your client wishes to understand, with the use of workings, the following aspects of this company and states that their required rate of return for the investment in a company with similar characteristics to RunRig would be 11% p.a.

Advise the client on whether you believe this to be a good or bad investment and the rationale for investment (or not investing).

  1. What are the assumptions underlying the use of a dividend growth model for the estimation of a company’s cost ofequity?
  1. Determine the market value proportions of debt, preference shares and ordinary equity comprising the company’s capital
  1. Calculate the after-tax costs of capital for each source of
  1. Determine the after-tax weighted average cost of capital for the company.
  1. Your client is investigating two start-up companies that operate in the same telecommunications sector in Australia. These two companies are investigating similar projects (not both) in which they will invest. However, your client is not sure which is better and has sent the relevant details to you for advice. The characteristics of the two systems are given below:

Project 1

Project 2

Initial Outlay (IO)



Annual Cash Flows (CF)



Life of system

8 years

5 years

Notes: 1) All cash flows are after tax and depreciation.

2) A flat rate of 14% is estimated as the risk in both of these projects.

Your client wishes you to provide detailed calculations indicating which system you believe to be the best. The client will then decide whether to invest into the company looking to invest in the project.

Portfolio Theory and Capital Budgeting

The objective of the given report is to answer the financial questions with regards to different aspects of NPV coupled with risk and return related discussion. In this regards, reference has been given to the portfolio theory and theoretical underpinnings related to capital budgeting. Additionally, the client investments have also been critically analysed in order to provide advice to the client with regards to the appropriate choice so as to maximise returns on the investments at hand. A key limitation is that the analysis has been based on standard assumptions related to NPV and other valuation models such as dividend discount model which may not be true.

1) The central tenet of portfolio theory is that the risk and return tend to be correlated. It is based on the assumption that investors are risk averse and therefore to invest in a risky asset class, compensation is required in the form of higher returns. The stock market investments need to be viewed in the backdrop of portfolio theory.  The average returns of the stock market tend to exceed the average returns of lower risk class assets such as bonds. This indicates towards higher risk being present which need to be properly managed to reduce exposure (Damodaran, 2015).

With regards to stocks, there are two types of risks namely systematic risk and unsystematic risk. Systematic risk is also called as non-diversifiable risk as it is a general risk associated with market investment and cannot be mitigated using portfolio or diversification. On the other hand, unsystematic risk is the diversifiable risk and therefore can be managed by diversification of the portfolio. In this regards, it is noticeable that the risk associated with the stock is captured by the standard deviation of the stock returns. Through diversification, there tends to some natural hedge and hence the deviations from mean is lowered which enables lowering of risk (Northington, 2015).

In order to maximise the benefits of diversification, it is essential that the portfolio must contain of stocks that are negative correlated since this tends to reduce the diversifiable risk component to almost zero. For example, comprising the portfolio of a company which exports goods and one which imports goods would make the portfolio stable in time of volatile currency. However, through perfect diversification also, risk cannot be made zero since systematic risk would still be present which would be captured using beta. This term represents the underlying risk associated with the portfolio or stock and is used to deriving expected returns (Petty et. al., 2015).

Risk and Return Considerations

2) There are two main conditions which ought to be fulfilled in order to ensure that WACC of the firm is used for assessing new projects. One key requirement is that the new project should have similar risk profile in comparison to the firm as a whole. If the project has higher or lower risk in comparison to the average risk of the firm, then the WACC also needs to be revised upwards or downwards respectively. This is because the underlying returns expected on funding would be dependent on the perceived risk of the project (Parrino and Kidwell, 2014).

Another key aspect is that the capital structure related to funding the project should match the existing capital structure of the firm. IF there is any significant difference in this regards, then the firm WACC cannot be used for the project (Brealey, Myers and Allen, 2014).

3) a) The decision rule for NPV is that the project which has a positive NPV must be selected. However, in case of mutually exclusive projects, even if a project has positive NPV, it may not be selected as the alternative project may have a higher positive NPV. Thus, for a project with positive NPV to be selected, it is imperative that the company should have enough resources particularly finance for implementing the project. In case of shortage of finance, projects having the highest positive NPV are selected and those at the lower end are ignored (Arnold, 2015).

  1. b) Depreciation is essentially an accounting cost which is not actually incurred thereby implying that there is no cash implication as it is not paid in cash by the company. Depreciation essentially captures the wear and tear in the fixed assets which causes a decline in their book value. However, with regards to NPV, depreciation is considered owing to the tax shield that it provides which is relevant considering the fact that NPV considers the post-tax cashflows (Damodaran, 2015).
  2. c) The tax savings on interest payments are excluded as the cost of debt taken into consideration for the computation of WACC is already post tax and hence the tax savings are already reflected in the form of lower cost of debt which essentially leads to lower value of cost of capital (Parrino and Kidwell, 2014).
  3. d) Sunk costs are not taken into consideration for the purpose of NPV analysis as irrespective of the decision made regarding the project, these costs cannot be recovered. Hence, these costs are not incremental costs since they cannot be altered with regards to the decision to go ahead with the project or drop the project. If these are considered, then the NPV would be revised to a lower value and may lead to incurred decision being made (Petty et. al., 2015).

1) The first step is to compute the required return on equity for the Lloyd stock which would require the use of CAPM Model (Arnold, 2015).

Required return on equity = Risk free rate + Beta*Market Risk Premium

Considering the given data, the following computation can be made.

Required return on Lloyd share = 4 + 1.4*(10-4) = 12.4 %

In order to estimate the fair price of the stock in 2017, it is imperative to use the Gordon Dividend approach highlighted below (Brealey, Myers and Allen, 2014).

Intrinsic share price = Next year dividend/( Required return – Perpetual growth of dividend)

Thus, based on the dividend history, the next year dividend and also the dividend growth rate till perpetuity ought to be determined.

It is apparent from the dividend history of the company that the dividend in 2010 was $ 0.3 while the corresponding value in 2016 stands at $ 0.5.

Hence, dividend growth rate = [(0.5-0.3)/0.3]*100 = 66.67%

Investment Analysis: Lloyds Ltd.

However, the above growth has been achieved over a period of 6 years, hence annual growth rate = 66.67/6 = 11.11%

Expected dividend in 2018 = 0.5*1.1111 = $ 0.5556

Expected stock price at the end of 2017 = 0.5556/(0.124 -0.111) = $ 43.06

Expected stock price at the end of 2016 = 43.06/1.124 = $ 38.3

It is apparent that at the existing price the stock is strongly undervalued and hence it makes sense to invest in the given stock (Northington, 2015).

2) a) The various assumptions related to dividend growth model are indicated as follows (Petty et. al., 2015).

  • The growth rate of dividend would remain constant and would not alter in the future.
  • The company would continue to pay the requisite dividend in every year and would skip any year.
  • The cost of equity for the future years would continue to remain the same.
  1. b) Current price of preference shares = $ 8.65

Total preference shares = 100,000

Hence, market value of preference shares = 8.65*100000 = $ 865,000

Current price of common share = $ 2.95

Total common shares = 500,000

Hence, market value of common shares = 2.95*500000 = $1,475,000

The market debt of debt can be computed as indicated below.

Total capital = Sum of market value of debt, preference shares and common shares = $ 5,456,689.54

Weight of preferences shares = 865000/5,456,689.54 = 0.1585

Weight of ordinary shares = 1475000/5,456,689.54 = 0.2703

Weight of debt = 3116689.54/5,456,689.54 = $ 5712

  1. c) The tax rate is given as 30%. New debt would be issued at 9% interest rate.

Hence, after tax debt cost = 9% (1-0.3) = 6.3%

Cost of preference shares = (Dividend/Market Price) = (1.20/8.65) = 13.87%

Cost of equity can be computed using the Gordon dividend approach.

Cost of equity = (0.25*1.04/2.95) + 0.04 = 12.81%

  1. d) The WACC computation is indicated below.

WACC = 12.81% * 0.2703 + 13.87% * 0.1585 + 6.3%* 0.5712 = 9.26%

3) In the given case, since the life of the two projects is different, hence the NPV of the projects would be used to compute the equivalent annual annuity using the formula indicated as follows (Damodaran, 2015).

Project 1 Equivalent Annual Cash Flow

Initial outlay = $ 13 million

Annual cash flows = $ 3.5 million

System life = 8 years

It is assumed that the annual cash flows tend to take place at the end of the year.

The present value of annuity can be found using the following formula (Parrino and Kidwell, 2014).

For the given case, P = $ 3.5 million, r=14%, n= 8 years

NPV = [3.5 *(1-1.14-8)/0.14] – 13 = $ 3.24 million

Equivalent annual cash flow = 0.14*3.24/(1-1.14-8) = $ 0.697 million

Project 2 Equivalent Annual Cash Flow

Initial outlay = $ 18 million

Annual cash flows = $ 6 million

System life = 5 years

It is assumed that the annual cash flows tend to take place at the end of the year.

The present value of annuity can be found using the following formula.

For the given case, P = $ 6 million, r=14%, n= 5 years

NPV = [6 *(1-1.14-5)/0.14] – 18 = $ 2.60 million

Equivalent annual cash flow = 0.14*2.60/(1-1.14-5) = $ 0.700 million

Based on the above analysis, it is apparent that the preferred project would be Project 2 as it has a higher equivalent annual cash flow. Hence, the company must invest in this project.

Conclusion & Recommendation

From the above discussion, it can be concluded that diversification tends to reduce the stock risk by eliminating the unsystematic risk. The client is recommended to invest in Lloyds Ltd stock as currently the stock is highly undervalued. Also, with regards to RunRig Ltd, the WACC has been computed as 9.26% by considering the individuals weights and costs of individual sources of financing. In relation to the telecommunication sector start-up company, it would be preferable to invest in Project 2 as the equivalent annual cash flows would be greater in this case.


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

Brealey, R. A., Myers, S. C. and Allen, F. (2014) Principles of corporate finance, 6th ed. New York: McGraw-Hill Publications

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

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

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

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

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