QUESTION

MPF753/MPF953 – T1, 2012 Assignment 2 (20% of total assessment)

Free Cash Flow (FCF) is the cash that is left over in the firm’s coffers from its net after-tax income
after providing for all planned capital expenditure and working capital requirements. It measures the
cash generated by a firm prior to servicing the debt-holders and paying any dividends to equityholders.

As per the FCF-based firm valuation model, the value of a firm can be estimated as the
present value of all future expected FCFs. The formal model is as follows (see page 279 of textbook):

V
0
= FCF
1
/(1 + r
wacc
) + FCF
2
/(1 + r
wacc
)
2
+ … + FCF
n
/(1 + r
wacc
)
n
+ V
n
/(1 + r
… (i)

Here V
0
is the present value of the firm, FCF
n
is the FCF for the n-th year, V
is the value of the firm in
the n-th year and r
wacc
is the firm’s weighted average cost of capital. Assuming g
n
to be a constant
growth rate of FCFs beyond the n-th year, V
may be estimated using the following formula:

V
n
= FCF
n
n
x (1 + g
FCF
)/(r
wacc
– g
)                                                   … (ii)

Substituting for V
n
FCF
from equation (ii), one may choose to re-write equation (i) as follows:

V
0
= FCF
= FCF
1
1
/(1 + r
/(1 + r
wacc
wacc
) + FCF
) + FCF
2
2
/(1 + r
/(1 + r
wacc
wacc
)
)
2
2
+ … + FCF
+ … + [FCF
n
/(1 + r
n
wacc
)
n
+ [FCF
n
x (1 + g
FCF
)/(r
wacc
wacc
FCF
– g
FCF
)
n
n

/(1 + r
wacc
)
n
)]                     … (iii)

][1 + (1 + g
FCF
)/(r
wacc
– g
FCF
What you are required to do:
I. Derive the FCF-based valuation model as stated in equation (iii): Your methodology can be
EITHER formal/mathematical OR descriptive/argumentative. If you are going for a
formal/mathematical derivation you will need to clearly state the underlying assumptions of the
model, clearly explain each of the terms involved and give a detailed, step-by-step algebraic
exposition that mathematically justifies the exact form in which equation (iii) has been expressed.

On the other hand, if you choose to go for a descriptive/argumentative derivation, you will still need
to clearly state the underlying assumptions of the model and clearly explain each of the terms
involved. But instead of providing a step-by-step algebraic exposition, you will justify; using lucid
arguments; why the firm valuation model essentially needs to be a sum of discounted cash flows.
You are also required to supply a hypothetical numerical example using an Excel spreadsheet
demonstrating that the value of the firm in year n indeed ‘converges’ to FCF
n
x (1 + g
)
if one assumes a constant rate of growth of the free cash flows beyond the n-th year.         (50 marks)

II. Compare and contrast the FCF-based valuation with the dividend discount model: The FCFbased
valuation
model
has
been
advanced
as
a
better
alternative
to
the
dividend
discount
model
of

valuation.

The former takes into account future expected streams of all free cash flows to the firm
whereas the latter only takes into account future expected streams of dividends to equity holders.
Clearly explain where the two models are similar and where they differ. Which one do most analysts
seem to prefer? Is a FCF-based model necessarily always better than the dividend discount model?
You are strongly encouraged to provide suitable numerical examples to make your point.  (25 marks)

)]/(1 + r
FCF
)/(r
wacc
wacc
)
– g
FCF
III. Identify & suggest remedies to some of the biggest limitations of a FCF-based valuation model:
The FCF-based valuation model has some obvious drawbacks. Perform some background research
on the model to identify these drawbacks; and then suggest ways to remedy them. You could either
suggest ‘improvements’ to the existing model or posit/advocate another model. Justify your criticism
of the FCF model and make use of logical arguments to defend your suggested remedies.  (25 marks)

The resources that you will need:
You will need to read and understand textbook chapters 3, 4 and 9. These will be covered in the first
few weeks of lectures but the purpose of this assignment is to take you beyond just the lecture
materials and give you a ‘hands on’ exposure to finance research. While the textbook and lecture
materials will give you some initial inputs to start off with, you will need to (and are expected to) do
substantial research of your own using library/online sources to gather the required information and
then process & apply that information to write well-thought responses to the assignment questions.

Some useful online resources that you might tap into are provided below but this is not exhaustive:

http://people.stern.nyu.edu/igiddy/valuationmethods.htm

https://www2.bc.edu/peter-ireland/ec261/chapter7.pdf

http://pages.stern.nyu.edu/~adamodar/pdfiles/damodaran2ed/ch5.pdf

http://people.stern.nyu.edu/adamodar/pdfiles/ddm.pdf

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/opt.html

Important information:
This assignment has an overall word limit of 2000 words (not counting mathematical equations,
charts, tables and references). How the allotted words are to be apportioned between the three
sections will depend on the adopted approach & writing style and so is up to the students to decide.

All external sources of information must be appropriately referenced & a reference list appended.
No particular referencing style is mandated – any style is acceptable as long as it is used consistently.

This assignment MUST be submitted as a single MS Word document. All Excel illustrations need to
be embedded in the Word document – please DO NOT submit separate Excel files with your work.

This assignment may be done either as an individual assignment or as a group assignment
(preferred) with no more than two members per group. However MPF953 students MUST do this as
an individual assignment. If done as a group, ONLY ONE member must make the final submission
online via the D2L drop-box. The first page of the submitted assignment MUST show the full names
and student ID numbers of both group members. E-mailed submissions won’t normally be accepted.

SOLUTION

Derivation of free Cash Flow

The Free cash flow is the measure of the cash generated by a company in a given year. It thus shows the financial stability of a company. It is given by the formula as shown below:

PAT + Depreciation – Capital Expenditure – Net working capital _ Debt payment + New Debt

Where PAT is the profit after tax of the company.

Thus considering that the cash flow for each year be FCF1 in t1, FCF2 in t2 and so on.

But the free cash flow has to be discounted with the discount rate or the cost of capital for a company to get the present value of the cash flow.

This has been shown below.

V₀ = FCF1/(1 + r) + FCF2/(1 + r)² + … + FCFn/(1 + r)ⁿ + Vn/(1 + r)ⁿ

Thus it can be said that the free cash low will give the value of the firm in each year. Or in other words the total valuation is the sum of valuation over the years for each year

V₀= V₁ + V₂… + V_n

If the company is growing by g% the free cash flow can be given as

FCF₁= FCF₀(1+g)

FCF₂=FCF₁(1+g) = FCF₀ (1+g)²

Thus the value of the company will be

V₀ = FCF₀ + FCF₀(1+g)/(1+r) + FCF₀(1+g)²/(1+r)²… FCF₀(1+g)ⁿ/(1+r)ⁿ

further solving the equation we get

V₀ = FCF₀ (1+ (1+g)/( 1+r) + (1+g)²/(1+r)²… (1+g)ⁿ/(1+r)ⁿ)

This is a Geometric Progression series and thus the sum of GP can be done as shown below

V₀ = FCF₀ (1+g)/(r-g)

Thus we get the valuation of the company based on the free cash flow of the company.

The only point of consideration is that in the derivation of the formula it has been considered that the series for free cash flow is infinite and thus the valuation can actually be different in case of limited life of the project(Damodaran, 2008).

Difference between Free Cash Flow and Dividend Discount Method

The two of the most popular models of the valuation of equity is the Dividend Discount model and the Free Cash Flow model. Both the models are similar but not same. Although both models are based on the cash flows for the shareholders of the company but differ on how the cash flow is calculated or generated for the company.

The difference between the both the models may be highlighted by the fact that the cash flow for the company may be reaching zero in the long run due to the discounting of the cash flow but the firm pays dividend as per constant growth. Thus the valuation method differs in both the cases.

The Valuation as per Dividend Discount Model is given by

V_E= D₀ (1+g)/ (K_E-g)

And in case of free cash flow the valuation is given by

V_E= FCF₀ (1+g)/ (K_E-g)

Where K_E is the cost of equity and g is the growth rate

It can be said from the above two formulas that in order that both the models give the same valuation for the company the dividend must be equal to the free cash flow of the firm.

Dividends as is clear is derived from the net income of the firm and the Free Cash flow is obtained by the formula given below

PAT + Depreciation – Capital Expenditure – Net working capital _ Debt payment + New Debt

Thus this is the baseline for the difference between the valuation method for the dividend discount method and the free cash flow method.

The dividend discount model is preferred in case of large companies that pay dividends to the shareholders on annual basis (Damodaran, 2008). Whereas the small and medium companies may not give the dividend on annual basis thus the Gordon dividend discount model may not apply.

Thus it can be said that the dividend discount model at times give better results as the free cash flow of the company may vary as per the situation in the company for example it may be in the growth phase and has made huge investments in the merger and acquisition of the other company.

An example has been shown below:

As shown above the total cash flow of the company is calculated after the Net inflow for the company is known. This net inflow is based on the formula that has been shown above which includes components such as depreciation, capital expenditure and working capital requirement.

Limitations of FCF model

1. High dependency on assumptions:

There is high level of dependence of this model on the inputs and the assumptions made for the future cash flows of the company. This includes the projections for sales, expenses, taxes rebate, working capital etc. Thus the future estimations of the working capital requirements and the other factors need to be assumed based on effective reasoning supporting it

1. Requires Experience

In preparing the free cash flow for a company an estimation of the future cash flow can be made more accurately with the experience associated with doing the f=cash flow analysis. It will be more accurately measured by someone who is associated with the company for which the free cash flow is being measured as that person is more aware about the operations of the company, its working capital requirements and the sales generated by the company over the period of time.

1. Periodic review required

There may be changes being done by the company in its operational activities thereby resulting in the increased or decreased cash flow for the company. Thus a periodic review of the activities is required.

1. Not suited for companies in growth phase

This type of valuation is not suited for companies that are in growth phase as during this phase the investments will be high and thus the free cash flow to the company will be less resulting in lower valuation of the concerned company, whereas it will be difficult to estimate the future cash flow of the company based on the fact that it is in the growth phase. Also in the case when the company has acquired another firm there will shortage of cash flow with the company there by the cash flow of the company will be considerably reduced. Thus this may not imply that the company is not performing well, but it will have considerably higher future cash flows. Thus such considerations should be made.

1. Not suited for short term investments

The free cash flow of any company might fluctuate. It may be reducing due to some acquisitions and may increase as a result of change in legislative for a particular place. Thus there will be high fluctuations if a small horizon is considered. However more accurate results can be drawn with regards to valuation if the investments made by the company has longer horizons.

1. Not suitable for company that pays dividend

This type of valuation is favorable for those countries that are not paying dividend as the dependency or the variance of cash flow due to change in dividend policy of the company. Only in cases when the dividend being paid is significantly different from the free cash flow to equity this valuation method is favored.

Positioning of Australian Dollar

As per the data available there is variation seen in the value of Australian dollar as against the given currencies of the world. The graphs drawn have shown a decrease in value of the Australian dollar during the period of December 2008 to February 2009 and whereas the currency has appreciated lately wherein it has superseded almost all the currencies mentioned in the dataset. Below is the analysis for the appreciation and depreciation in the currency when compared to the currency of other countries of the world. The analysis will be done in phased manner starting with the basic understanding and then the main points discussed in the scholarly articles.

The main trend that has been observed in the comparison is that the currency that is mentioned in the dataset includes some of those that are dependent on the US economy. Thus when there is slump in the US economy and the uncertainty prevails and the currency has appreciated. The uncertainty in the US market has led to the depreciation in the economy of the other countries like Singapore and Malaysia. This can be observed from the trend and the graph that has been drawn. There is a loop when there is depreciation in the currency when compared to US dollars, Singapore dollar and the Chinese currency. Similarly the similar economic conditions prevailed for Euro and the Great Britain pound and thus both the currencies revealed the similar trend.

However the Australian economy has been different from the economies of United States and that of the Eurozone and the Asian market. Thus the relation between the markets is not always positive for all of them rather the currency appreciation of Australia is much dependent on the prevailing conditions in Australia and its foreign policies.

The researchers have analysed the factors that have led to the appreciation in the currency as compared to the deficit in the early 1980s. The depreciation as stated by the experts is due to the amateur market conditions in Australia and the rise of United States as the world power which has led to the downfall of the soviet union and the emergence of the US as the major driver of the world economy.

The factors that have been in favor of Australia is the current account deficit of United States and thus Australia is attracting investors from around the world. There has been weakening of the US economy. Another major factor is the rising of the commodity prices of the resources that are in abundance in Australia. For example, the coal prices have been rising globally (Dobson, 2011). Thus there has been exodus of investors going in for joint venture in Australia. All these factors led to the appreciation of the Australian Dollar against almost all the currencies in the world and thus the appreciation has been so much that it has overpowered US dollars also. In case of Euro it has been benefited by the Eurozone crisis and the declining growth rate of the UK economy. These all factors have benefited Australia along with the monetary policy changes in Australia, which has led to lifting of Australian dollar and thus making it expensive the exports from the country. Another reason for the weakening of the US dollar is the lowering of the interest rates in United States.

In 2008 the Australian economy was trapped in the global financial crisis and thus this led to the downfall and thus the weakening of the currency.

References:

Damodaran, A. (2008). The Dividend Discount Model. Retrieved 02nd may 2012, from http://pages.stern.nyu.edu/~adamodar/pdfiles/eqnotes/ddm.pdf

W, M. C., L, E. M., Mario, M., & Amit, P. (2005). Adjusted Free Cash Flow and Capital Expenditures of the S&P 100: What Is the Source of Growth in Adjusted Free Cash Flow?. Retrieved 02nd May 2012, from http://smartech.gatech.edu/handle/1853/10667

Betzkorn (2010). Gordon Dividend Discount Model versus FCF Valuation Model. Retrieved 02nd May 2012, from www. betzkorn.com

Olivia (2011). Difference between DDM and DCF. Retrieved from www.difference between.com

Reserve Bank of Australia (2010). Appreciation of Australia’s real exchange rate: causes and effects. Retrieved 02nd May 2012, from www.rba.gov.in

Dobson, P. (2011). Australian Dollar may appreciate to 28-Year high on Coal, BNP Paribas Says. Retrieved 02nd May 2012, from www.bloomber.com

Pettinger, T. (2008). Australian Dollar Appreciation. Retrieved 02nd May 2012, from www.economicshelp.org

KG11

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