ACCOUNTING THEORIES

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.

The due date is Monday 7
th
May 2012 by 11:59PM Melbourne time. All students must complete an
online plagiarism declaration. Assignments submitted after the due date will draw a penalty of 5
marks per day of delay. Any request for extension of the deadline must be made in writing (with
supporting documentation) to the Assignment Chair at sukanto@deakin.edu.au. Extensions may be
granted ONLY on medical or compassionate grounds or in certain work-related circumstances.

SOLUTION

Answer1:

The FCF based valuation model relies on the general principle that the financial valuation of any business enterprise should be done on the basis of how it performs in the long run or it’s earning potential in the future which is estimated on the basis of its expected cash generation capacity in future.

The cash available to the firm after paying for all the operating expenses reflects the potential of the firm in meeting the expectations of those who have supplied capital (debt, equity) in the firm. When the amount of capital expenditures made and working capital changes get deducted from this amount, free cash flow to the firm (FCFF) is calculated.

SIGNIFICANCE OF DISCOUNTED CASH FLOWS FOR VALUATION OF FIRM

In today’s scenario ,characterized by frequent unexpected turbulence in the market , the credible valuation of any business firm calls for an estimate of the present  worth of the  expected earnings which the investors( both equity and debt holders) would get  in future by investing their funds in the company. Various techniques for valuation of firm have been in use namely, asset based, earning based , market value based etc.  The earning based valuation method overcomes the limitations of traditional valuation techniques, which does not consider the future earnings  capacity of the firm as a parameter for its valuation.The discounted future cash flow approach necessarily helps in evaluating the worth of capital expenditure proposals in terms of their potential for creating NET PRESENT VALUE for the firm. (Copeland,2000)

The table above shows the computation of FCF from the net profits of the business firm.

ASSUMPTIONS OF THE MODEL:

• The discounting rate used in the model is the weighted average cost of capital  i.e. future free cash flows are discounted at weighted average coc.
• The composition of capital structure does not change frequently over a period of time
• Firms invest in long term assets and introduce working capital in the business to generate cash flows in future. Both these amounts need to be subtracted from operating profits (after tax)to compute free cash flows
• The valuation of any business firm is segregated into 2 periods. The first one is that period for which reasonably accurate forecasts of free cash flows in future can be made and is termed as explicit forecast period and the second period is one for which the free cash flows change at a constant rate.
• Firms grow at steady rate during the explicit forecast period but it cannot sustain abnormal rate of growth for an indefinite period. At the end of explicit forecast period, firms are assumed to grow at constant rate.
• The amount of  capital expenditure, depreciation and changes in working capital are  non-operating in nature and therefore subtracted from the earnings of the firm to compute the value of Free Cash Flows.

V0=

In the above formula , FCF1, FCF2, FCFn denotes the free cash flows expected for year 1, 2 and year n respectively.r wacc is the weighted average cost of capital. gfcf is the expected growth rate in the FCF till perpetuity.

The portion of the equation highlighted in red reflects the total present value of FCF generated   during the explicit forecast period ,discounted at a rate which is the weighted average cost of capital. The rationale behind using weighted average COC is that FCF reflects the amount which is available for distribution to all the investors who have contributed in the capital of the business firm by way of equity or debt.(Ireland,n.d)

NUMERICAL ILLUSTRATION:

Suppose ABC ltd has employed total capital of 1,000 (million dollars) composed of debt and equity in equal proportions:

10% debt

5 million equity shares(100$ each). k_e is 14% and  40% corporate tax. The expected FCF for next 5 years is given below:

YEAR               FCF (million dollars)

1                        300

2                        200

3                        500

4                        150

5                        600

From the 6^th year onwards the FCF increases at 5% annually.

According to FCF model of firm valuation, the value of firm at period 0 will be calculated as follows

Clearly, value of r is equal for each term , therefore it is a case of infinite geometric progression series.

The sum of infinite GP =a/1-r      ,where a is the first term in the series

=630/1-0.95

= 12600

Therefore, value of FCF after the explicit forecast period ( from year 6 till infinity)= 12600(million dollars)

VALUE OF FIRM=1288.45 + 12600=13888.45 (million dollars)

According to formula in question value of firm in year n =

FCFn x (1 + gFCF)/(rwacc – gFCF)

= 600 *(1+ .05)/ .10-0.05

=12600 (million dollars)

It clearly demonstrates that the value of the firm in year n indeed ‘converges’ to FCFn x (1 + gFCF)/(rwacc – gFCF) if one assumes a constant rate of growth of the free cash flows beyond the n-th year.

Answer 2:

When the discounted cash flow technique is applied to dividends , it is called DIVIDEND  DISCOUNT MODEL. On the contrary, when discounted cash flow technique is applied to Free cash flows in business , it is termed as FCF valuation model.( pages.stern.nyu.edu,n.d)

Although the two models differ in the ways mentioned above, there are few points of similarities between the two of them as both are viewed as an extension of Discounted Cash Flow Technique of valuation of firm. Under the FCF model, as explained previously the firm is valued under two periods of time i.e. during and after the explicit forecast period. In the latter case the formula for deriving the present value of firm is the replica of what is used in Dividend Discount Model (for the case of constant growth in dividend) except the fact that in FCF method the cash available as free cash flow to investors is discounted using the weighted average cost of capital whereas in the DDM the equity dividends are discounted using cost of equity.( people.stern.nyu.edu,n.d)

Most financial analyst seem to prefer FCF valuation model over DDM valuation as the former serves as a comprehensive statistical tool used in forecasting purposes.

As compared to dividends, Free Cash Flows is a more optimistic unit of measuring the value of firm .As FCF model provides figure of cash available for distribution to all the stakeholders in the firm(debt, equity, preference) , the figure of the value of firm computed by employing FCF  has a wider acceptance.

Under the circumstances mentioned below, financial analysts seem to prefer free cash flow valuation model over dividend discount model:

• When the firm does not pay dividend to its stakeholders rather follows the policy of reinvesting  the profits  back into the business
• Where the firm though pays dividends to the shareholders but the amount of dividends paid does not reflect the true capacity of the firm to pay dividend
• Free cash flows align with the profitability of the business during the forecasted period with reasonable accuracy
• When the creditors of capital (equity and debt) intends to take a control perspective over business valuation.
• Where firm intends to strengthen its credit standing in the eyes of investors with a view to raise further capital from the market.

Let’s take a look at the following illustration to make the understanding of both the approaches more clear:

ABC ltd has 20,000 equity shares of 100 dollar each outstanding at the beginning of the period 1. It has a 10%debt capital 2,000,000 (dollar) in its balance sheet on the same date.

Suppose the dividend paid is 100,000; 200,000;300,000;400,000 for year1, 2 , 3 and 4 respectively . weighted average coc is 10%

Cost of equity is 14%

Cost of equity is Following is the income statement:

Value of debt at present= 2,000,000

Value of equity =21,957,000-2,000,000= 19,957,000(dollars)

According to Dividend discount model:

Present value of equity stock is equal to the value of the expected future stream of dividends discounted at cost of equity.

P= 100,000*0.877+200,000*0.769+ 300,000*0.675+ 400,000*0.592

=87700+153800+202500+236800

=680800(dollars)

Value of equity = 680,800(dollars)

Value of debt = $2,000,000

Value of firm = $2,680,800

This clearly shows that the valuation on the basis of dividend discount model may give very conservative estimates of firm’s value when dividend paid is a small fraction of earnings and major portion of the earnings are reinvested in the business.

Answer 3:

Although the FCF model provides a significant technique for valuation of firm but its application is limited to firms that follow a constant growth rate after the explicit forecasted period. The basic underlying assumption of the model is that, a business firm has indefinite life and it is genuinely impossible to forecast the future earnings of any business firm for its entire life. Though it is quite likely that reasonably accurate estimates of performance of a firm could be made for few initial years and after that period it is assumed to grow at a certain predetermined growth rate. This growth rate remains constant for indefinite period. But in reality, firms do have varying degrees of growth rates over their perpetual existence in the business.

Therefore, the assumption of constant growth rate is clearly UNREALISTIC in today’s volatile market conditions.

The parameter of growth rate often gets distorted because of presence of uncertain forces in the business environment like inflation. Different analysts often use different benchmark growth rates while carrying out the task of valuation. Due to such differences the comparison between different firms in their valuation becomes very difficult.

The complexity involved in calculating the amount of FCF is another limitation of this valuation model. The amount of FCF signifies the cash available for distribution to the investors, it does not mean that the entire amount is tangible for the investors. The figure of FCF is only an estimate of performance of the company and the conservative investors might claim that they cannot access these cash flows. A firm may have show huge amounts of FCF in its books but an individual investor cannot claim a right in sharing that amount.

The amount of Free Cash Flows is derived from the figure of cash from operations in the business. While calculating FCF companies often record a significant amount of gain or expense which is not directly related to the operations of the firm thereby providing a distorted picture of company’s cash generating ability.

The figure of FCF can be also be manipulated by under-reporting the capital expenditures in order to increase the credibility of firm.

There need to be a regulatory framework which could suggest guidelines for treatment of various items of capital expenditures and working capital while calculating the amount of FCF. Also,  as per the growth rate in performance of a business is concerned, there should be standard technique of calculating it for all  firms engaged in similar business so that the comparison of their valuation can be done precisely.

REFERENCES:

Copeland ,Tom,Valuation-measuring and managing the value of companies, John Wiley and Sons, New York:2000, pp. 134

Ireland, Peter  n.d,Money Banking and Financial Markets, viewed on 31^st march 2012, https://www2.bc.edu/peter-ireland/ec261/chapter7.pdf

Equity discounted Cash Flow Models, viewed on 31^st march 2012, http://pages.stern.nyu.edu/~adamodar/pdfiles/damodaran2ed/ch5.pdf

The Stable Growth DDM, viewed on 31^st march 2012, http://people.stern.nyu.edu/adamodar/pdfiles/ddm.pdf

JD75