finc2011 assignment 2012

Faculty of Economics and Business

The University of Sydney

Individual Assessment Cover Sheet Electronic submission

Last name: Barkley

First Name: Robert

ID Number: 312115245

Email: [email protected]

Unit code: ___FINC2011___ Unit name: ___________Corporate Finance 1________________

Tutor’s name (if applicable):_____Vycke Wu________ Tutorial day/time: ____Tuesday 3 pm____

Full assessment title: _________________Cicero mines Assignment______________________

Word count of assessment:___________________2403__________________________________

Due date:__24__/__10____/___12__ Time & date submitted:___11___ _24__/__10_/_12___

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Cicero Mines Investment Analysis

Part 1: Project Evaluation

When making capital budgeting decisions, there are various techniques that can be utilised. Ross et al. (2008)

describes that the predominant capital budgeting methods used as being the Net Present value (NPV)

method, the Internal Rate of Return (IRR) method, the Payback method, and the Accounting Rate of Return

(ARR) method. Conversely, Brealey, Myers and Allen (2011) proposes that the NPV and IRR methods are

considered prestige compared to the ARR and the Payback Methods, as they take into account the time value

of money. Thus, the following project evaluation will focus on using the NPV and IRR methods.

NPV Method:

The Net Present Value method discounts future cash flows of a project in attempt to discover the value of a

project in present terms, considering the time value of money. Multiplying the tax rate by the incremental

taxable profit, where incremental taxable profit is found by misusing expenses and depreciation from annual

revenues, provides the NPV.

NPV of Machine A:

The tax paid is calculated as the tax rate x the incremental taxable profit as follows:

Year 1-5 6

Annual Revenues 300,000 300,000

Salvage Value 10,000

Less Annual Depreciation (35,000) (35,000)

Less Annual Operating expenses (152,000) (152,000)

Incremental Taxable Profit 113,000 123,000

Annual Tax at 30% 33,900 36,900

Net Profit after Tax 79,100 86,100

Cash flows for the following years are calculated as follows:

Year 0 1-5 6

Machine Cost (200,000)

Installation cost (10,000)

Working Capital (80,000) 80,000



Plus Depreciation 35,000 35,000

Free Cash Flow before Tax (290,000) 148,000 158,000

Less Tax 33,900 36,900

Free Cash Flow (290,000) 114,100 121,100

Analysis and explanation:

• Initially, the machine and installation costs and working capital symbolise the negative cash flows in

year 0

• Working capital is then assumed to be recovered as a positive cash flow in year 6, recognising the

completion of the project

• Sunk costs such as the cost of market analysis are ignored

• Taxation reduces the free cash flow generated by either machine

• Since depreciation is not a cash flow, it is required to be added back to the incremental taxable profit

due to it being initially subtracted from revenue when calculating annual tax

• It should be noted that the 10% loan offered by a salesman for Machine A is not significant in

determining the value generated by the chosen machine.

Discount Rate Calculation

In order to calculate the ‘Discount Rate’, the cash flows are required to be discounted to derive their present

value. Since Cicero Mines is 100% equity financed, the discount rate is the shareholders required rate of

return. Megginson (2005) explains that investments of a 100% equity financed firm must be sufficient to satisfy

the shareholders of the firm.

This required rate of return is obtained through the use of the Capital Asset Pricing Model (CAPM), which

describes that the cost of equity is equal to the risk free rate within the market plus beta. Its equation is given

by:

The model clearly conveys a relationship between the expected return of a stock and its specific risk, which is

provided by the risk free rate plus the product of the market risk premium and beta (! ). Therefore, when the

values given are substituted into the equation, we attain the following discount rate for Cicero Mines:

! !! = 0.07+E(0.12-0.07)x0.06/0.25! = 0.118

= 11.8%

Hence, the discount rate applied to the NPV analysis is 11.8%. The NPV of the project is then calculated as

the sum of free cash flows generated throughout each year in present values minus the current cost of the

project:

!"#!"#!!"# ! = −290,000 +114,1001.118

+114,1001.118!

+114,1001.118!

+114,1001.118!

+114,1001.118!

+121,1001.118!

= 185,365.53

! !! = !! + !(!! − !!)!!

NPV of Machine B:

Annual tax paid with Machine B:

Cash flows for the following years are calculated as follows:

!"#!"#!!"# ! = −328,000 +157,5001.118

+157,5001.118!

+⋯+157,5001.118!

+161,0001.118!"

= 570,390.52

Due to a maximisation of total return to shareholders, the project with the higher NPV should be chosen

(Brealey, Myers and Allen (2011)). Thus, Cicero Mines should choose Machine B as it has a higher NPV than

Machine A. It should be noted that NPV fails to account for the differing useful lives of each machine.

According to Brigham and Ehrhardt (1998) the NPV method has the capability of leading to incorrect

conclusions when considering two projects with unlike useful lives. To overcome this problem, Brealey, Myers

and Allen (2011) propose to convert the present value of each project to an Equivalent Annual Value (EAV). It

should be noted that this method relies on the assumption that the project will be replaced with a similar cash

flow pattern. Therefore in this situation, we are able to assume that both Machines A and B have the ability to

be replaced by another machine at the end of the useful life. The EAV for each machine is calculated as

follows:

$185,365.53 = EAV!"#!!"# ! =[!! !!!.!!" !!]

!.!!" = $44,830.57

Year 1-5 6


Salvage Value 5,000




Annual Tax at 30% 59,760 61,260


Year 0 1-9 10

Machine Cost (250,000)

Installation cost (8,000)

Working Capital (70,000) 70,000


Salvage Value 5,000

Plus Depreciation 25,800 25,800

Free Cash Flow before Tax (328,000) 225,000 230,000

Less Tax 67,500 69,000

Free Cash Flow (328,000) 157,500 161,000

$570,390.52 = EAV!"#!!"# ! =

[!! !!!.!!" !!"]!.!!"

= $100,125.03

Therefore, Machine B appears to be the better option as it has a higher EAV than Machine A.

IRR Method

Alternate methods of project valuation must to be considered. Brealey, Myers and Allen (2011) describes that

the Interest Rate of Return (IRR) is the discount rate at which a project’s NPV is equal to zero. Among other

considerations, the higher IRR should be chosen when comparing two mutually exclusive projects. Therefore,

the IRR of Cicero Mines project options can be calculated as the following:

Machine A IRR:

0 = −290,000 +114,100(1 + !"")

+114,100(1 + !"")!

+114,100(1 + !"")!

+114,100(1 + !"")!

+114,100(1 + !"")!

+121,100(1 + !"")!

Therefore the IRR of Machine A is approximately 32.08%

Machine B IRR:

0 = −328,000 +157,5001 + !""

+157,5001 + !"" ! +⋯+

157,500(1 + !"")!

+161,000(1 + !"")!"

Therefore the IRR of Machine B is approximately 47.01%

Thus, due to the higher internal rate of return (IRR) and NPV, Machine B seems to be the machine most likely

to be chosen.

Part 2: Tax Rate Change

With the introduction of a carbon and mining tax, the company tax is expected to increase to 38% before the

project can be implemented. This could impact the decision between Machine A and B, as an increased tax

expense will decrease free cash flows of the project, creating a difference in calculated NPV’s. Hence, the

adjusted cash flows for both Machines A and B are as follows:

Machine A: Calculation of income tax for years 1-6:

Year 1-5 6






Annual Tax at 38% 42,940 46,740


Annual cash flows for Machine A:

Year 0 1-5 6

Free Cash Flow (290,000) 105,060 111,260

Assuming that the discount rate calculated in Part 1 remains the same, the NPV of Machine A is $147,577.25

and the IRR of Machine A is approximately 28.2%

Machine B: Calculation of income tax for years 1-10:

Annual cash flows for Machine B:

Assuming all factors remain the same, the NPV of Machine B is $523,568.57 and the IRR of Machine B is

approximately 44.37%

If taxes were to increase before the investment decision occurs, the decision should still remain with Machine

B, as it provides a higher NPV than Machine A. Furthermore, Machine B delivers a higher IRR than Machine

A.

Part 3: Proxy Company

Since the values that were used to estimate the required rate of return in Parts 1 and 2 have not been updated

for several years, they could prove to be false and as a result distort the true discount rate of return

appropriate to Cicero Mines, therefore affecting the analysis of investment. As Cicero Mines is not listed on the

ASX, a similar proxy company in the same industry as Cicero Mines and of an equivalent size is required.

Since we are told that Cicero Mines is a large mining firm, we can assume that BHP Billiton is a suitable proxy

for this analysis.

Year 1-5 6


Salvage Value 5,000




Annual Tax at 38% 75,696 77,596


Year 0 1-9 10

Free Cash Flow (328000) 149,304 152404

Brealey, Myers and Allen (2011) announce that in order to determine a companies securities expected return,

approximations are required for the current risk free rate, the expected excess returns of the market and beta

(!). The CAPM can then be utilised to determine the rate required by Cicero Mines shareholders, in turn

offering a suitable discount rate to calculate the NPV of each machine.

Risk-Free Rate:

Brigham and Ehrhardt (1998) define the risk free rate (!!) as the rate at which a security has no risk to carry. It

should be noted that a risk free rate is only a hypothetical term as it is very difficult to achieve. Therefore,

securities with low risk rates are frequently used. Government bonds are an example of a security, as the

government backs the returns. Nevertheless, Brealey, Myers and Allen (2011) proclaim that interest rate

changes influence securities such as bonds, and as a result cannot be risk free.

Ten year Australian Treasury Bonds are used as a proxy for the risk free rate, due to this project being of a

long-term nature. The rate on these ten-year treasury bonds was 5.55% for the month of October 20121. As

such, this rate will be used as a proxy for the risk free rate in the CAPM.

Market Risk Premium:

The market risk premium is the second component of the CAPM equation and is conveyed mathematically as

!(!! − !!). According to Brealey, Myers and Allen (2011) this value is attained on the basis of long term

historical returns on the market above the risk free rate, with the underlying assumption that the monthly

market returns will predict future returns. Historical data suggests that since World War 2, the average market

risk premium is 8.6%2, which will be used when calculating the discount rate.

Proxy Beta:

Beta is the third and final part of the CAPM and since Cicero Mines is not a publically listed company, beta

cannot be directly calculated from its share price data. In order to find beta, Bowman and Bush (2006) declare

that the beta of a comparable publically listed company is needed as a proxy. In this situation, the comparable

company is BHP Billiton and their levered beta equates to 1.773. Consequently, beta must be unlevered to

account for the fact that, unlike Cicero Mines, BHP Billiton is not 100% equity financed and therefore its

shareholders have a lower market risk. With BHP Billiton’s debt to equity ratio being 0.32 4, the following

formula allows the unlevered beta to be calculated as follows:

!!"#$%$&$' =1.77

1 + 1 − 0.3 x0.32= 1.446

1 Risk Free Rate for month of October 2012 www.rba.gov.au/ 2 Historical Data of market risk premium was obtained from www.rcrawford.wordpress.com/ 2 Historical Data of market risk premium was obtained from www.rcrawford.wordpress.com/ 3 BHP Billiton Beta was obtained from www.au.finance.yahoo.com/ 4 Average Debt to Equity ratios (5 year average) were obtained from www.forbes.com/

Discount Rate and NPV Calculations:

When using the CAPM formula, the adjusted discount rate of Cicero Mines is calculated by utilising the data

obtained from the proxy company as follows:

!! + !(!! − !!)!

Ε !! = 0.0555 + 0.086 ×1.77 = 0.20772

Therefore, this provides a proxy discount rate of 20.8%, which substituted into NPV calculations gives the

following values:

Machine A !"#!"#$% = $84,538.05 Machine B !"#!"#$! = $315,910.10

As a result, the new proxy rate still conveys Machine B as the preferred investment.

Part 4: Sensitivity Analysis

Discussed earlier in Part 3, the beta estimated relies on various assumptions such as, historical returns that

will reflect future returns, and the market risk of Cicero Mines is similar to its competitors adjusted for leverage.

Conversely, the validity of these assumptions may not be entirely correct considering the recent volatility of

financial markets and the lack of information on Cicero Mines, and therefore is likely to influence the

investment evaluation.

As a result of this, a sensitivity analysis was undertaken in the attempt to determine how different beta values

impact Cicero Mines investment choice, with everything else remaining constant. The results are as follows:

Change to Beta Adjusted Beta Equivalent

Discount Rate

NPV (A) NPV (B) NPV (B) - (A)

1 2.77 0.29372 $17,104.79 $167,664.77 $150,559.99

0.8 2.57 0.27652 $28,880.26 $192,306.98 $163,426.72

0.6 2.37 0.25932 $41,437.32 $219,160.88 $177,723.56

0.4 2.17 0.24212 $54,846.01 $248,497.13 $193,651.12

0.2 1.97 0.22492 $69,184.08 $280,627.12 $211,443.04

0 1.77 0.20772 $84,538.05 $315,910.10 $231,372.06

-0.2 1.57 0.19052 $101,004.33 $354,761.79 $253,757.46

-0.4 1.37 0.17332 $118,690.61 $397,664.70 $278,974.09

-0.6 1.17 0.15612 $137,717.36 $445,180.62 $307,463.26

-0.8 0.97 0.13892 $158,219.63 $497,965.75 $339,746.13

-1 0.77 0.12172 $180,349.15 $556,789.10 $376,439.95

The graphical representation of the NPV’s of the projects against the range of betas are as follows:

As conveyed in the table and graph above, while both machines NPV’s are sensitive to the beta values used in

the calculations, it is not likely that it should have any influence on the investment decision. This is due to the

fact that the NPV of Machine B is significantly higher than that of Machine A, it should be noted that this is for

all beta values used in the sensitivity analysis. Therefore, the correct decision is to choose Machine B as it

provides the best outcome in all calculations undertaken throughout this investment analysis.

References:

• Bowman, R. G., and Bush, S. R., 2006, Using Comparable Companies to Estimate the Betas of Private

Companies, Journal of Applied Finance 16(2), 71-81.

• Brealey, R. A., Myers, S. C and Allen, F. 2011, Principles of Corporate Finance, 10th Ed., McGraw Hill

Irwin, New York.

• Brigham, E and Ehrhardt, M, 1998, Financial management: Theory and Practice, Harcourt College

Publishers.

• Forbes, 2012, Ratios and Returns, Forbes, Sydney, viewed 21 October 2012

http://finapps.forbes.com/finapps/jsp/finance/compinfo/Ratios.jsp?tkr=bhp

• Megginson, William L, 2005, Introduction to Corporate Finance, South Western College Pub,

Cincinnati.

• RTCrawford’s Weblog, 2008, BHP Billiton Ltd, Sydney, viewed 22 October 2012

http://rcrawford.wordpress.com/2008/05/25/bhp-billiton-ltd-bhp-buy-sell-hold-may-24-2008/

• Ross, S., Westerfield, R. and Jordan, B. 2008, Corporate Finance Fundamentals, 8th ed., McGraw Hill,

New York.

• Reserve Bank of Australia (RBA), 2012, Capital Market Yields – Government Bonds – Monthly, RBA,

Sydney, viewed 21 October 2012 http://www.rba.gov.au/statistics/tables/#govt_finance

• Yahoo Finance, 2012, BHP Billiton - Key Statistics, Yahoo, California, viewed 22 October 2012

http://au.finance.yahoo.com

0

100000

200000

300000

400000

500000

600000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Machine A

Machine B

finc2011 assignment 2012

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