David Hillier's Finance Classroom

Making Finance Easy

Finance Reference Lists: 2012 Update

It’s been some time, but I’ve now completed the reference lists for 2012 and they are fully updated in their respective pages.  I personally read each paper to ensure they are an appropriate level for Masters and Undergraduate degree students who wish to learn more about each topic.  Doctoral students will likely use this list as a base before going into more advanced research papers.

I realise the update is only 2012. Because I read each paper, it takes me a while to go through a full year. A shorter list of references but updated to much more recently can be found in my textbooks.

On to 2013!

New Video: An Introduction to Firm Valuation – Price Multiples and Free Cash Flow to the Firm (FCFF) Methods

This video finishes my series (for now) on equity and firm valuation.  I focus on three different methods to close the course:

  • Discounted Cash Flows
  • Price/Earnings Multiples
  • Free Cash Flow to the Firm (FCFF)

In a 17 minute video, I obviously can’t cover everything in detail but I hope the video gives you a good introduction into each of the methods listed above.

I’ll be back in a few weeks with a completely new course. Stay tuned!


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Video: How to Read Financial Information on Websites

This is a quick video to address some requests I’ve had on how to read financial information on websites.  It can be really daunting to people who are new to Finance when they have to collect financial information on companies for research. I’m hoping that this video will be of some help to you.

My favourite websites (not including the financial databases the university subscribes to) are:

Video: Reconciling the Dividend Growth and NPVGO Models of Equity Valuation

This isn’t my most riveting video (are any?), but very important nevertheless.

In my recent videos I’ve shown how to value equities using both Dividend Growth and Net Present Value of Growth Opportunities (NPVGO) models.  This video shows that both methods are equivalent and should lead to the same equity valuation.

I sometime include this as an exam question and ask students to show that both approaches lead to the same equity value.  Don’t say you haven’t been warned!

If you wish to subscribe to the Finance Classroom Newsletter, please supply your e-mail address at the side of the page (or the bottom if you’re using a mobile phone or tablet) and click the ‘subscribe’ button.  You will receive an e-mail notification each time a new article has been posted and exclusive posts based on subscriber requests.


Finance Reference Lists 2011 Update

A substantial part of writing Finance textbooks is the background reading that goes into each topic. My reference lists are given at the end of each chapter but because of space issues, I can only include only a subset of all the papers I read.

In the Reference Lists page, I have created curated reference lists for all the main topics in the book and they are very useful when undertaking new research into an area.

The process of reading each paper is slow, so in recreating my full lists, I have reread the papers to ensure they are relevant for the topic and make a substantial contribution to the literature.  I’ve completed the year 2011 and will now start on 2012 papers.

The topics I cover are:

  1. Asset Pricing
  2. Behavioural Finance
  3. Bonds
  4. Capital Structure
  5. Corporate Governance
  6. Corporate Restructuring
  7. Derivatives
  8. Dividends
  9. Executive Compensation
  10. Financial Analysis
  11. Financial Distress
  12. Insider Trading
  13. International Corporate Finance
  14. Investments
  15. Private Financing
  16. Security Issues

I hope these are helpful to researchers and as more years are included their usefulness should be even greater.

Video: How to Calculate the Net Present Value of Growth Opportunities

Now we’re really in 2017, I’ll be starting back on a regular delivery of videos in Corporate Finance.  This video concerns growth opportunities and how to calculate the proportion of a company’s share price that comes from growth.

It’s important to remember that share prices are forward-looking and reflect today’s expectations of everything that is going to affect a company in the future.

When President Trump tweets about automakers or companies who are producing goods in Mexico, share prices react immediately because investors incorporate changes in expectations of future cash flow into today’s price.  President Trump may or may not carry through with actions, but prices have changed nevertheless.

In this regard, share prices reflect what the market today believes will happen in the future.  In this video, I’ll show you how one can calculate the value of future events.  I’ll also spend a little time looking at non-dividend paying firms as well as showing why companies can continue to grow dividends even though they are investing in poor projects.  Enjoy!

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Valuation Multiples: Carnival plc

How to Value Companies: Valuation Multiples

The Valuation Multiples method is one of the most common approaches to valuation because it is quick and does not require detailed analysis of a company’s annual accounts

It is also an excellent approach when a company is private and the share price is not available.

Which Valuation Multiple to Use?

The best multiple for a particular company will depend on its industry and growth opportunities.  Common multiples include:

Enterprise Value/Sales Price/Earnings Sales/Assets
Enterprise Value/EBITDA Price/Book Value of Equity Sales/EBIT
Enterprise Value/EBIT Price/Sales Price/Sales

Note: Enterprise Value = Market value of equity + Debt – Cash and Cash Equivalents

Four Key Steps

  1. Identify peers/benchmarks for the company.
  2. Find valuation multiples for the comparator firms.
  3. Calculate the median or mean multiples of the peer group.
  4. Calculate the expected multiple for your chosen firm and use to value equity.

Given we are in December and the weather is dreadful outside, let’s use the Cruise firm, Carnival plc as a case study for the Valuation Multiple approach.

Step 1: Identify peers/benchmarks

Carnival plc is an international leisure and cruise firm with operations throughout the world.  You can find out more about the company on their corporate website.

Our first step is to find Carnival’s peers.  For a listed firm it’s as easy as searching for “company name peers” in Google. I did this and got the following set of results:

Carnival plc Benchmark Companies

I went with the first entry in the list above and found that Carnival had two main competitors:

Carnival peers screenshot from csimarket.com

We have two peers: Norwegian Cruise Line Holdings Ltd, and Royal Carribean Cruises Ltd – both private firms.

Step 2: Find valuation multiples for the comparator firms.

Given we have private firms, there will be no share price available so we will use Enterprise Value ratios

*** For clarity, I don’t know anything about the Hotels and Leisure industry sector.  To check, I did another search on google with the following request, “what are the best valuation multiples for hotels and leisure?”.  The first result that came up was Enterprise Value/EBITDA, which is one of our ratios so we are on the right track ****

Step 3: Calculate the median or mean multiples of the peers

Simply calculate the average of the peer ratios and compare it to your target firm.

For our case study, let’s focus only on Enterprise Value/EBITDA.  If you are doing a full analysis, you should use other ratios as well to triangulate your values.

The internet is a wonderful resource. I did another search on google for “Carnival plc Enterprise Value/EBITDA“.  Our old friend, gurufocus.com, came to the rescue:

Doing the same thing for Norwegian Cruise Line Holdings, we get:

For Royal Caribbean Cruises Ltd we get:

Let’s bring the data together.


Enterprise Value/EBITDA
Carnival plc 10.94
Norwegian Cruise Line Holdings Ltd 12.25
Royal Caribbean Cruises Ltd 11.63
Average of Norwegian and Royal 11.94


Step 4: Calculate the expected multiple for your chosen firm and use to value firm

From Gurufocus.com, Carnival has an Enterprise Value of $48.451 billion and an EBITDA of $4.430 billion.

On the basis of the comparator EV/EBITDA figure, you would expect the Enterprise Value for Carnival to be 11.94 x $4.430 billion = $52.894 billion, which is higher than the actual Enterprise Value of $48.451 billion.

It would look as if Carnival is underpriced compared to its two peers.

Strengths and Weaknesses of the Valuation Multiple Approach


  1. There is a massive number of different multiples you could look at and so you have different ways to carry out firm valuations.
  2. Ratios are simple to calculate and easy to interpret.
  3. You are valuing a firm based on other companies in the same sector. Differences between the actual share price and estimated values can provide much insight into where the company could improve its operations.
  4. This method is used for private firms and each industry will have standard valuation multiples to arrive at an expected value for a company. This is important when you are looking to sell your firm.


  1. It can be difficult to identify appropriate peers for the company. Choose the wrong ones and your value estimates will be wrong.
  2. It is easy to focus on the wrong multiples given that there are so many to choose from.
  3. The method does not actually look at the company’s figures but uses other company data to arrive at a value.


In this series of articles, I have shown a number of different ways to value companies. The exposition was necessarily simple to ensure the central concepts are presented in a clear and concise way.

There are many factors I didn’t consider as my objective was to show you the general approach to value firms, rather than to look at the specific valuation of any one firm.

If you want to know more about valuation multiples, you should check out Chapters 12 and 13 of my book, Financial Markets and Corporate Strategy, where I explore the method in much more depth.

I’m now going to take a break for a couple of weeks and when I return in January, I will continue with my valuation videos on YouTube.

See you in a few weeks!



How to Value Companies: Focussing on the Operations

You can value companies in a number of ways. For example, use balance sheet/stock market data for the market valuation method, or you can use Cash Flow/Income Statement for FCFF valuation. In this article, we focus on the actual operations of a firm to get a valuation estimate.

Consider the basic accounting equation:

Assets = Liabilities + Equity

The method used in Part 1 of this series separately estimated the liabilities and equity of a company to arrive at an overall firm value.

Our focus shifts to the left-hand side of the accounting equation – the assets of the firm.  Theoretically, asset value should be equal to the sum of the liabilities and equity values.

Valuation Steps

The best approach to valuing a firm’s assets is to work with the company’s management to identify all future cash flows likely to come from the assets (including human capital, brands and other intangibles). If you don’t have access to the management, you will need to use websites and the financial pages.

To value your firm, follow steps 1 and 2 below.

  1. Split the company into different divisions/activities and analyse each of these separately.
  2. Carry out a discounted cash flow analysis on each of the firm’s operational lines and then sum the individual present values to arrive at a total value of the assets (and the firm).

Valuation in Practice

Consider the construction firm, Carillion plc.  From its website, the company is involved in 4 distinct operations: Support Services, Public Private Partnerships, Middle East Construction Services and Construction Services (Excluding Middle East).

Cash Flows

The Carillion Annual Report provides the following information on the firm’s operations:

How to Value Companies

It is clear  that whereas Support Services is the largest market by far for Carillion, it is fairly stagnant compared to their Construction business.

Pipeline orders for Construction (The Middle East and elsewhere) are massive compared to existing revenue streams.  In addition, the efficiency of these business lines is much better than for Support Services.

The Discount Rate

Page 93 of the Annual Report states:

Discount rates have been estimated based on pre-tax rates that reflect current market assessments of the time value of money and the risks specific to the Cash-Generating Units (CGUs). Whilst the Group has four CGUs, the risks and rewards associated with Construction services (excluding the Middle East) are consistent, and therefore one discount rate has been applied to each CGU. Similarly the risks and rewards encountered in the Support services CGUs are consistent and therefore one discount rate has been applied to each CGU. Management has derived a Weighted Average Cost of Capital (WACC) using the capital asset pricing model to determine the cost of equity and then weighting the overall cost of capital for the Group by equity and debt. The WACC was then used to determine the pre-tax discount rates for each CGU. The rate used to discount the forecast cash flows for the CGUs in the Construction services (excluding the Middle East) was 10.0 per cent (2012: 11.7 per cent) and for the CGUs in the Support services segment was 8.8 per cent (2012: 9.9 per cent).

So, from this text, we have a discount rate of 10.0% for Middle East Construction and Construction (Exc. the Middle East) and 8.8% for Support Services and Public Private Partnerships.


From this point on, it is up to the analyst to decide on the assumptions with respect to cash flow growth and future cash flows.  This is covered in much more detail in my textbooks, so, for now, I am just going to state a number of very broad (and probably unrealistic!) assumptions.


  1. For the next five years, cash flows will grow at a rate in proportion to the Pipeline/Order Book ratios for each business line.
  2. From the 5th year onwards, cash flows will remain constant.
  3. The maximum year on year growth in cash flows in any unit will be 20%.

I admit these can be criticized as being “finger in the air” assumptions.  However, without further in-depth analysis, we cannot forecast any further than five years from now. Also, from year five onwards assuming no growth is as good an estimate as any.

With the exception of Support Services, the pipeline of orders in all units are significantly higher than the existing order book.  Consequently, I am assuming 20% growth year on year for all units, excluding Support Services .

Support Services looks as if future performance will be flat.  Given that the pipeline of orders in this division is 23.5% less than the existing order book, I have chosen a negative growth rate of 23.5/10 = -2.35% for the next five years. This reflects a potential thttp://www.david-hillier.com/wp-admin/post-new.phpightening of this market over the coming period.

With these assumptions, we have the following cash flow streams for each business unit: 

We now need to estimate the terminal value for each of the Business Lines.  To do this, I simply treat the cash flows from Year 6 onwards as perpetuities and discount them at the respective discount rate for each unit (=Cash Flow@Yr 6/Discount Rate).

Company Valuation: Assets

We now have cash flows and a Terminal Value for each business unit.  These will be discounted to present values using the respective business unit discount rates.  The present values for each cash flow are given below:

Company Valuation

Summing these present values gives us an estimate of the value of Carillion plc.  The value from the Asset Valuation method is £4.089 billion.

 Strengths and Weaknesses:

The strengths of the Asset Valuation approach are:

  1. If full sight is given of the firm’s operations, it is possible to come to a completely independent estimate of firm value that does not rely on financial reports.
  2. The method (when valuing the future cash flows of operations) avoids accounting assumptions like intangibles valuation, which can be difficult to understand.

The weaknesses of the Asset Valuation approach are:

  1. It is often exceptionally difficult to get information on the firm’s operations and sales pipeline, making this method almost impossible to use.
  2. The method suffers from the need to make assumptions about future cash flows just like all other methods.

In the next installment of this Primer on Corporate Valuation, I will look at the final valuation technique, Valuation Multiples and Peer Comparisons.

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FCFF Valuation

How to Value Companies: The Free Cash Flow to a Firm (FCFF) Method

I apologise upfront as this is quite a long post that takes you step by step through the process of valuing a firm using the Free Cash Flow to the Firm (FCFF) approach.

Like all valuation methods, you need good estimates for your model and in this case, you need to forecast:

  • Future free cash flows;
  • Free cash flow growth rates; and
  • the Weighted average cost of capital, WACC.

The FCFF method requires the total cash available to all investors (equity and debt holders).  Unfortunately, there are a number of ways to calculate Free Cash Flow to a Firm (FCFF) and people often get confused regarding which one is the best.

In addition, the accounting standards a firm follows affects the formulae used to estimate free cash flows.  I am assuming your company uses International Financial Reporting Standards (IFRS), which applies to most companies outside of the US.

In keeping with the theme of my blog, I am not going to deep dive into any single approach but instead, simplify the models enough so that FCFF can easily be used by anyone. In addition, my philosophy is that more noise comes from forecasting the future than from any variation in the different approaches you meet in practice.

Step 1: Free Cash Flow

The best way to estimate free cash flows is to work with a company’s management and derive estimates of future cash flows (up to about five years). However, this isn’t practical in many cases and most times only the financial accounts are available

Free cash flow is the money left over after all operating and investment costs have been paid.  This is the amount that can be distributed to debtholders and equityholders of the firm.

Simple Estimation

Free Cash Flow to the Firm = Cash Flow from Operations + Cash Flow from Investing Activities

Important Points

  1. Normally, dividends and interest payments must be stripped out of the figures given above.  I say ‘normally’ because if a company is a bank, it may make interest payments as part of its business operations rather than through financing needs.  In addition, many companies receive interest payments or dividends from their own investments in other firms. Given that these are operating cash flows, they should be included in the Free Cash Flow estimates.
  2. When looking at the Cash Flow from Operations and Cash Flow from Investing Activities, you may consider stripping out extraordinary items or one-off special payments.  This is because you want to get an expected future free cash flow that can grow at a specific rate constantly into the future.  If your initial cash flow is unusual, your future cash flow estimates will also be out.  You can separately discount any extraordinary items as a single cash flow and add it later if required.

FCFF Case Study: BP plc

We will look at the global energy firm, BP plc. The most recent annual results (31st December 2015) can be found from BP’s Investor Relations page.

The BP plc Cash Flow Forecast is presented below:

FCFF BPHow to Value Companies FCFF

A quick scan of the figures shows BP reported a major loss of $9.5 billion that was caused by an accounting provision to pay fines linked to Gulf of Mexico oil spill in 2010. There was also a general downturn in its business because of low oil prices (read this Reuters news report for more information on BP’s results).

To keep things simple, we will go with the overall figures without correcting them for any items.

Free Cash Flow to the Firm (FCFF) = Cash Flow from Operations + Cash Flow from Investing Activities

FCFF = $19.133 billion + (-$17.300 billion) = $1.833 billion

You will see that the operating cash flows (the cash flows that arise from everyday business) are positive, whereas the investment cash flows are negative. You would expect this because the underlying operations should make money and the company should also be investing to grow.

We now have an FCFF estimate. Time to estimate growth rates.

Step 2: Free Cash Flow Growth Rate

A simplifying assumption that I am going to make here is that the FCFF grows at a steady rate forever.  Clearly, this is unrealistic.  However, it is good as a starting point and a launchpad for more complex analyses.

If you want to look at different approaches to modelling future growth rates, check out YouTube video on Equity Valuation or any of my books.

Growth rates are notoriously difficult to estimate as they are based completely on subjective forecasts.  My favoured approach is to simply use analyst forecasts as an initial estimate, and iterate further once initial firm values have been calculated.

Looking at the BP page on FT.Com (search for the name in the FT.Com website and click on forecasts tab):

FCFF Valuation Model BP plc

Source: FT.Com, December 2016.

Two forecasts are provided for the growth rate: 1.27% and -3.50%. These aren’t particularly valuable because there is no consistency between the two short-term estimates.  We need to look elsewhere!

A good site for current company data is www.gurufocus.com, which calculates these figures automatically from data.  According to Gurufocus:

During the past 13 years, BP PLC’s highest 3-Year average Free Cash Flow per Share Growth Rate was 52.60% per year. The lowest was -35.90% per year. And the median was 5.80% per year.

Let’s go for the Gurufocus growth rate of 5.80% since it is based on 13 years of data and is an average.  Clearly, you should investigate these figures more using different growth rate models, but for our purposes, 5.80% will do.

Step 3: Weighted Average Cost of Capital (WACC)

The fastest way to find out BP’s Weighted Average Cost of Capital is to search Google to see if an analyst has estimated the figure already (sometimes, the company itself will provide the WACC.   I’ve found two estimates:

www.finbox.io: range 7.8% – 8.8%; Midpoint: 8.3%

www.Gurufocus.com: 7.17%

Given we went with Gurufocus for growth rate, we will stick with them for the WACC estimate.

Step 4: Estimate Value of Firm.

There are many ways to work with cash flows in discounted cash flow analysis and much of what is calculated comes down to simplifying assumptions.  In my analysis here, I am assuming that cash flows will grow at a constant rate forever.

The formula I am using is then:

Value of Firm = FCFF(1+g)/(WACC-g) = $1.833(1+.058)/(.0717-.058) = $101.16 billion

According to the FCFF model and our estimates, BP is worth over $100 billion.


Our estimate is quite a bit lower than the current market value of BP based on share price and book debt value ($150 billion), so clearly we have either underestimated the cash flow and/or growth rate or overestimated the WACC.  More research is needed into these estimates.

Does this mean FCFF is a poor method? Definitely not!

For example, Finbox.io used a number of different estimates to arrive at a range of WACCs, as did Gurufocus.

Our Cash Flow estimates were also quite simplistic and we could have looked at the components of the Cash Flow Statement to identify any one-off items that should be stripped out.

Strengths and Weaknesses of FCFF


  1. The method is applicable for all firms (public and private firms) and useful when the company to be valued has no stock price data.
  2. The method is based on a company’s financial accounts and thus based on audited financial figures.
  3. It is a good model for companies with stable cash flows and constant capital structures.



  1. It doesn’t use stock price information, which is the most timely information.
  2. It is very sensitive to inputs such as Free Cash Flow Estimates, Growth Rates, and Discount Rate.

Admittedly, the method hasn’t been particularly effective in valuing BP plc. I would definitely attempt to come up with a more refined set of cash flow forecasts.  I would also look again at the growth rates we used in this example and identify the most appropriate measure.

Interested readers can find out much more about valuation in my YouTube videos and any of my textbooks.

If you have got this far, you’re clearly a finance enthusiast! Please leave a comment with your thoughts or even requests for future posts.

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How to Value Companies: The Market Valuation Approach

In this four-part series on valuation, I will describe different approaches to valuing a firm.

My advice is to start off with the methods given in this post, adapt them to the specific industry and corporate conditions, and then come to a consensus view based on all four approaches.

The Four Valuation Methods:

  1. Market Valuation, where actual market information is gathered on the debt and equity of a firm.
  2. Free Cash Flow to the Firm, where the present value of future cash flows to the firm are calculated.
  3. Asset Approach, where the company’s assets are valued.
  4. Valuation Multiples, where information is used on peer firms in the same industry to arrive at a valuation of the firm.

To show valuation in action, I will use the global pharmaceutical firm, AstraZeneca plc, as an example.

The Market Valuation Approach   

The Market Valuation method takes data from the stock market to value a firm.


  1. Find Equity Value: Visit any financial webpage (such as FT.Com, Yahoo! Finance, etc.) and find the market capitalization of equity. I went to FT.Com’s webpage for AstraZeneca plc and got the information below: AstraZeneca Market Capitalisation Figure 1: Summary data on AstraZeneca, 26 November 2016 (source: FT.Com)

The Market Capitalisation of equity is £54.30 billion.

  1. Find Debt Value: In most countries, corporate debt is traded irregularly. This means that the prices you get from financial pages can be out of date by a long way. The fastest way to find the value of a company’s debt is to get the total value of its liabilities from the most recent set of accounts. Don’t worry about any bond issues or loans issued since the most recent report because the cash raised will be reflected in the equity market capitalization.


Figure 2: AstraZeneca Balance Sheet (Source: AstraZeneca 2016 Q3 Results)

From Figure 2, the value of the Debt is equal to total liabilities = $48.31 billion.

At an exchange rate of $1.2478/£ (source: XE.com, 26 November 2016), AstraZeneca’s debt is worth £38.72 billion.

The total value of AstraZeneca plc according to the market valuation method is £93.02 billion.

Value of Equity + Value of Debt = £54.30 billion + £38.72= £93.02 billion.

Strengths and Weaknesses

The strengths of the market valuation method are as follows:

  1. Share prices contain all available information in the stock market including future growth prospects, intangible assets and the quality of a firm’s management, among other factors.
  2. The information you are using is the most up to date out of all the valuation approaches. Other methods use figures that can be many months old.
  3. The method makes no theoretical assumptions and is based entirely on observed market valuations.


  1. Market prices may not reflect value fundamentals. This can occur if a firm is the target of a takeover and the price has responded to the potential bid.
  2. If the company is not publicly traded there will be no market prices. Most valuations are carried out for private companies with no share price, which makes it impossible to use this method.
  3. The company may be small and traded infrequently leading to stale market prices. Out of date information can cause as many issues as poorly estimated information.

If a company is large and traded on the stock market, the market valuation method can be used quickly and easily to arrive at a firm value.

In my next post, I will explain the Free Cash Flow to the Firm method, which is also known as the income approach to corporate valuation.

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