Letter number 101 of February 2017

  • NEW

News : Calculating the cost of capital in an emerging country: the case of Ivory Coast

Our readers are aware of how important the cost of capital is, both for:

  • valuing a company using an indirect approach (equity value as the difference between the value of capital employed and the value of net debt and other borrowings[1]),
  • choosing investments, whether the cost of capital is the discount rate used to determine the net present value of the investment or the minimum rate that the internal rate of return must exceed if the investment is to be considered as financially worthwhile[2].

Three key data are required to perform this calculation:

  • the risk-free rate,
  • the risk premium that will be added to the risk-free rate because the project or the company is not risk free,
  • and the beta coefficient which will reveal the relative volatility of the investment compared with the volatility of the market as a whole. This beta is then multiplied by the equity risk premium, and we take the resulting product and add it to the risk-free rate to get the cost of capital: 


This is the CAPM[3] formula which is applied, not to shares as in most cases, but to capital employed. Which is where we get the term bA  which is not the beta coefficient of shares, but the asset beta or the beta of capital employed, which is what the “A” in bA stands for. It is sometimes referred to by specialists as unlevered beta.  

This is what we call calculating the cost of capital using the direct method. Some people calculate the cost of capital using the indirect method where the cost of capital is the weighted average cost of equity and the cost of debt, weighted by their relative share of the financial structure in value. And so we get this formula:

The two formulae for calculating the cost of capital yield the same result, providing that the calculations are performed correctly. We prefer the direct approach because in our experience, there are far fewer opportunities to make mistakes when this method is used[4].

In countries with well-established economies, where studies and vast data bases abound, where billions of financial data have been recorded and stored for over a hundred years, none of the three data required for calculating the cost of capital present any major problems in themselves, for a rigorous analyst who has been well trained and who has access to the appropriate financial data bases. 

In emerging countries where there are no studies or vast data bases, where billions of financial data have not been recorded or stored for over a hundred years, each of the three data required for calculating the cost of capital present major problems in themselves.

However, it is possible to overcome these problems and, what’s more, to do so without being ethnocentric about it.

* * *

Let’s start with the risk-free rate which is, after all, a relative notion in many emerging countries (and only very recently introduced). In Ivory Coast, a civil war was still raging only six years ago. Luckily for us, the Ivorian Republic has issued bonds in euros, dollars and in its own currency, the CFA franc, and regularly issues new bonds. For example, a CFAF 50bn (€76m) 7-year bond with a yield to maturity of 5.82% was issued in September 2016. It is rated B+ by Moody’s, Ba3 by Moody’s and A- by Bloomfield (for its loans in CFA francs). If it hadn’t been rated, we’d have had to take the yields on government bonds of countries that are rated, such as Ivory Coast and that have similar economic features.

Given the existence of a debt in CFA francs and regular issues (six issues 2016) in the form of an auction, a relevant market price is obtained on a regular basis, in the absence of an active secondary market.

So, we are able to calculate a cost of capital for a company which is considering a project in Ivory Coast with cash-flows in CFA francs. We’ll see below what we have to do to translate this cost of capital which applies to CFA francs into an Ivorian cost of capital which would apply to flows converted into euros for example.

* * *

Let’s take a look at the asset betas. In developed countries, we’ll just say that all we need to do is choose from among the numerous peer companies and regress the returns on the shares in question against those of the index. Now that we’ve found the beta of the shares, we calculate the beta of the debt (if it’s significant) as the spread of the debt divided by the market risk premium. We can then calculate the asset betas which is the weighted average of these two betas, weighted by the relative share of debt and equity of the capital structure in enterprise value[5]. Having thus worked out a company’s asset beta, we repeat the operation as many times as there are companies in the sample. Then, we take the average of the asset betas that we have calculated for the comparable companies in order to arrive at the asset beta of our project or our company.

Although there is a stock exchange in West Africa, the BRVM, on which 41 companies from the eight countries making up the WAEMU region (with a combined market capitalisation of €11bn) are listed, most of their shares are not very liquid. The volume of monthly transactions since the start of 2016 is €50m a month, making an average of €55,000 per stock per trading day. Once banks have been eliminated, there are only around 10 sectors covered by this stock exchange.

In other words, at this stage, we cannot reasonably expect to make the same sort of calculations that we do for stock exchanges in Europe, North America and Asia. The good news is that when we think about the determinants of asset betas such as sector sensitivity to the economic situation, sharing of fixed and variable costs and sector visibility[6], there is no fundamental reason for believing that these factors will differ fundamentally from one country to the next and from one geographic region to the next.

In other words, the table that we publish in the Vernimmen, to which we’ve added a few extra economic sectors and which we’ve reproduced below, is applicable regardless of the geographic region:

* * *

And now for what you’ve all been waiting for – the equity risk premium, the difference between return on equity and the risk free rate in West Africa. Well, there’s only one way of saying it: it’s quite simply impossible to calculate. Whether for the historical risk premium or the prospective risk premium (which we prefer[7]), there are just no data available. And data won’t be available in West Africa for a while yet, notwithstanding its rapid development over recent years.  

A historical premium is only meaningful if it is calculated over a very long period because what it does is calculate the average performance of the market index, by smoothing out the impact of booms and crashes, and removing the performance of the risk-free asset over the same period. It’s just not reasonable over a period of less than 50 years, and some academics would say that you need 100 to 150 years of data. 

In order to extract a prospective premium from current share prices, we need a more or less clear view of forecasts of future flows made by investors. So it’s doable when brokers publish notes and forecasts. If they don’t, then is just can’t be done.

* * *

So, what we gonna do?

Well, just ask investors which invest in West Africa, what sort of risk premium they require. It’s pragmatic, easy and efficient. It’s what PWC does every two years in the main regions of Africa, including West Africa. In its latest study[8], PWC puts the risk premium at between 7.1% and 10.2% on the basis of the range of replies it got from the 61 investors surveyed (not all of which are active in West Africa). As this survey was published in autumn of 2014, so the next one should be published soon, we’d be inclined to take the lower figure (7%).  We believe that the economic and political climate in West Africa has in fact improved and not declined, which explains the likelihood of a lower risk premium.

And PWC goes even further as it also asks investors about what sort of size or illiquidity premium they require depending on the size of the company. It’s obvious that a smaller company will has a higher market risk than a large one and this is something that the formula at the beginning of this article does not take into account. Here we see the APT or Fama & French approaches[9].

Below are the premiums that should be added to the cost of capital as per the investors surveyed by PWC, according to enterprise value:

So, we can value the cost of capital of an Ivorian pharmaceutical distributor at around $250m by taking the asset beta in this sector (0.75 in the above table): 5.9% + 0.75 x 7% + 2.8% = 14%. And an Ivorian electricity producer is worth over €1,000m: 5.9% + 1.0 x 7% + 1.1% = 14%.

We can use Bolloré, the European group currently investing the most in West Africa, as an example. In its annual report, Bolloré takes a cost of capital of 11% for its flows in this region, converted into euros. Given that inflation in Côte d’Ivoire was around 2% compared with 0% in the euro zone, this rate of 11% in euros is equal to a rate of around 13% in CFA francs. This is in line with what we’ve just seen.

* * *

This article is a summary of the paper delivered by one of us in Abidjan on the invitation of the Ivorian members of ICCF@HEC Paris and a copy of which is available on the vernimmen.net and ICCF@HEC Paris websites.          

  • the risk-free rate,
  • the risk premium that will be added to the risk-free rate because the project or the company is not risk free,
  • and the beta coefficient which will reveal the relative volatility of the investment compared with the volatility of the market as a whole. This beta is then multiplied by the equity risk premium, and we take the resulting product and add it to the risk-free rate to get the cost of capital:

Statistics : Non-performing loans as percentage of total loans to non-financial corporations in Southern Europe

They continue to fall in Spain and have stabilized in Italy, Portugal and Belgium, according to Moody’s:

Source: Moody’s

Nevertheless, the Italian figure (close to 18%) is no stranger to the fact that the largest Italian bank, Unicredit, is currently trying to raise as much as €13bn of fresh equity i.e. around 80% of its current market capitalisation.

Research : Disasters and the psychology of managers

With Simon Gueguen, lecturer and researcher at the University of Paris-Dauphine

When making decisions, managers are required to assess the probability of various future scenarios and events occurring. This applies to investment choices, but also when they make decisions relating to financial policy. According to the main theories of corporate finance, the assumption is that the managers calculate probabilities rationally, based on information available to them. However, psychologists, as well as behavioural economics specialists, are of the view that the perception of probabilities is subjective. More specifically, individuals assess risks on the basis of heuristics, mind maps that help them to assess probability more quickly, although there is often a degree of bias involved. The most frequently cited case is the proximity of the occurrence of a shock, or salient event. The article we look at this month[1] shows that managers tend to overestimate the probability of a salient event when they observe such an event in close proximity, in the same way as drivers will temporarily fear being involved in an accident when they see a car crash in the adjacent traffic lane.

Seeking to demonstrate this, Dessaint and Matray collected data on hurricanes in the USA. These data present a number of advantages in terms of statistics. Firstly, the risk of hurricanes is a stationary risk, which means that the probability of a hurricane occurring in the future is not modified when a hurricane occurs in a given area (unlike the risk of an earthquake for example). So, any modification in the perception of this risk after a hurricane has occurred is irrational. Next, since the path of a hurricane can be accurately plotted, it is possible to define a proximity area and to compare changes in the behaviour of managers in this area with such changes simultaneously outside this area (the difference-in difference method, which we looked at previously in this Newsletter).

The study covers 15 major hurricanes (property damage exceeding $5bn) in the USA between 1989 and 2008. Dessaint and Matray show that firms located in the vicinity of the hurricane (but not impacted by the disaster) will see a 1.1 point increase in their cash and cash equivalents of total assets, i.e. $15m in the year following the disaster. This increase is economically significant. The size of the increase is more or less equal to the effective loss suffered by firms that were impacted. In other words, the behaviour of the managers of these firms is compatible with the perception of a future risk of a hurricane of almost 100% (even though the annual risk is not altered and remains 6%). It is also temporary and disappears two years after the disaster.

Dessaint and Matray also note that the accounting documents published by these companies mention the hurricane risk nearly twice as often in the year following the disaster. Two years later, these references are back to normal, just as the cash and cash equivalents position is. This return to normality means that we can exclude the assumption that managers were unaware of (or underestimated) the hurricane risk before witnessing one in the vicinity, in which case the variation should be permanent. Dessaint and Matray’s assumption (a temporary and irrational increase in probability of this risk occurring) is supported by these results.

This decision to increase the amount of their cash and cash equivalents, which seems to be irrational, is also expensive. Dessaint and Matray show, in particular that this surplus cash in undervalued by shareholders. So this article provided solid empirical evidence of the existence of a behavioural bias on the part of managers that is the source of value-destroying decisions. One of the operational consequences of these results impacts on the decision-making process at the firm. Salient events of all types are likely to alter managers’ risk perception. It would be interesting to analyse to what degree corporate governance structures (role of external directors) could reduce this bias.


[1] O.DESSAINT et A.MATRAY (2016), Do managers overreact to salient risks? Evidence from hurricane strikes, Journal of Financial Economics, pending.

Q&A : What are CNAV, VNAV and LVNAV funds? Or just a little bit more than rounding off figures

Accros the world, money market funds (MMFs) are split into two main categories: 

- Constant Net Asset Value (CNAV) funds, which value the securities in which they invest on the basis of depreciated cost, and for which the value of shares/units is $1.00, €1.00, £1.00, etc., calculated to two decimal places, which means that any variation in their net asset value per share (as they calculate it) will only be reflected if it exceeds 0.5% (0.994 for example which is rounded down to 0.99). Which is a lot for an MMF that, in theory, is invested in short-term assets with a low credit risk. A deviation on the constant unit value has only occurred twice, in 1994 and in 2008, following the Lehman bankruptcy. Valuation at depreciated cost means that a share bought by the fund at 99.7% and redeemed at 100%, is valued by the fund every day at the initial purchase price (99.7%) plus 0.3% pro-rated to the time lapsed compared with the total time period between the purchase of the share and its redemption. It is only if the difference between the depreciated cost and the value of this title exceeds a given threshold that a corrective mechanism is triggered.

Revenues net of management costs result not in an increase in the value of the share, because this value is fixed, but in the allocation of additional shares to subscribers.

- Variable Net Asset Value (VNAV) funds, which value the securities in which they invest on the basis of their market value and of which the value of shares/units is calculated very precisely to 3 to 4 decimal points.

CNAV funds are criticised because their rounding-off rule and their method for booking their assets could incite savvy subscribers to rush in and demand a payment of 1.00 when their assets are only worth 0.996, for example, before these assets fall to 0.994, which would lead to a price of 0.99 being displayed. This sort of incitement is naturally pro-cyclical, of a systemic nature and it harms the less lively subscribers who bear the cost of the speedy investors’ exit at 1.00, when the market value of the share is in reality only 0.996.

In the USA and the UK, monetary funds are mostly CNAV type funds, even though, for example, AVIVA abandoned CNAV funds for VNAV funds a few years ago. In India, CNAV funds are banned while in France, VNAV funds predominate.

Following a request by the G20 to reform monetary funds, the European Union has finalised a directive that should be implemented in 2017 and which makes provision for CNAVs being replaced two types of funds: Government CNAVs which, five years after the implementation of the directive, will be required to hold at least 99.95% of government and similar securities, with a minimum of 80% of EU government securities, and LVNAVs, Low Variable Net Asset Value funds. LVNAVs will be CNAVs that switch to VNAVs when the market values of the shares falls by more than 0.2% compared to the constant theoretical value of the share.

Moreover, VNAV funds will be required to have a double liquidity ratio: at least 7.5% of the assets in these funds will have to mature on the day itself, making it possible to cope with as many daily withdrawals without having to sell shares in the portfolio, and 15% of the assets will have to mature within one week. CNAV funds are already subject to such ratios.

Government CNAV funds and LVNAV funds will have to apply exit fees if they do not comply with their liquidity ratios, or even put barriers in place in order to stagger exits.

Our readers who are familiar with accounting will probably be amused to notice that in this area, France is one of the proponents of fair value, and the USA and the UK of amortised cost.

All in all, we can hope for slightly fewer risks on CNAVS, expect a slightly poorer performance for VNAVs and especially, a lot more complexity. So it goes… 

New : Comments posted on Facebook

Regularly on the Vernimmen.com Facebook page[1] we publish comments on financial news that we deem to be of interest. Here are some of the comments published over the last month.

The Dow Jones has crossed the 20,000 point threshold. This may be a highly mediatised event but it is a financial non-event.

The Dow Jones, the only US index that the general public is aware of, is not relied on much in finance because its composition means that it in no way reflects he US stock market, because of two key flaws.

The first is that it is not made up of major corporates like most other indices, but of a selection of groups that reflect the past more than the present. We’ll let you be the judge: five of the 10 largest US market capitalisations are not among the 30 companies listed on the Dow Jones (Alphabet with a market cap of $582bn, the second largest US market cap), Berkshire Hathaway ($405bn, #4), Amazon ($397bn, #5), Facebook ($380bn, #6), and Wells Fargo ($284bn, #10). And seven of the top 20, adding ATT ($254bn) and Bank of America ($236bn). Caterpillar (market cap of $57bn) is listed on the Dow Jones, but not Oracle ($165bn); Travelers ($33bn), but not Citi ($164bn), etc.

Secondly, Dow Jones listed companies are not weighted on the basis of market capitalisations nor on free floats (like most indexes), but… on unit share prices. This is how Goldman Sachs accounts for 22% of the Dow Jones when its share of the DJ’s market capitalisation is 1.6% ($94bn out of $5,777bn), Boeing for 10% when its share of market cap is 1.8 %, etc. Apple, the largest US market capitalisation ($641bn) accounts for the same percentage as Travelers, the smallest market cap on the DJ ($33bn).

The popularity of the DJ is a result of the ease which it is calculated and its long, august history, compared with indices that are wider and, in particular, more widely used by professionals such as the SP 500 (500 largest US market capitalisations) which is used as a basis for trading options or futures.

For more, see the Vernimen.com Newsletter n°21, December 2006.

Finally, we note that since its previous record in March 1999 (the 10,000 point threshold), the Dow Jones’ performance excluding dividends is only 3.9% and around 6% per year by adding a rate of return of around 2%. But in March 1999, we were in the middle of the TMT bubble!


The French government has just issued €7bn in green bonds. This is both the largest amount ever issued for a green bond and for the longest maturity: 22 years. This long time to maturity, which is much longer than the average French marketable debt (7 years), is a good thing. In the current environment, it fixes a low interest rate (1.74%), which does not differ from that of a standard bond. Additionally, it consolidates the leading position of French issuers on this segment of the bond market of which they held a 17% share last year.
The fact that there was demand for €23bn does give the impression that green finance is what investors want. This is obviously rather nice, but it is what always happens when things are going well. In fact, demand is often 2 to 3 times higher than the offer for a bond issue. Investors know this and consequently inflate their demand, hoping to get what they really want. So an issue that is subscribed up to 120% would be a bit of a failure, contrary to appearances, because investors will have to subscribe more bonds than they really want. This would not be good for the price performance of this new bond on its first days of trading.
For those of you who’d like to know more about green bonds, take a look at the Vernimmen.com Newsletter for January 2016.


On ETFs and passive management, the two largest asset managers in the world, BlackRock and Vanguard, which together manage $9,000bn, have just announced that their 2016 new money was $517bn, of which $237bn for passive management in ETFs, representing 46% of new funds under management, reflecting the continued absolute and relative growth of passive management within asset management; and in all probability an increase of the market share of the major players in passive management.

If in active management, from a certain threshold, size is rather a disadvantage (because investment strategies are often concentrated on sub-compartments of the market that are not indefinitely extensible (SMEs, biotechnologies, Southeast Asia, etc.); in passive management, the opposite is true. In order to replicate the performance of the market in its entirety or in large sub-part of it (British, emerging, US equities, etc.), the boundaries are unattainable and the size that allows a better distribution of fixed management costs is clearly an advantage. Hence a low 2016 management fee as a percentage of assets: 0.22% at BlackRock, 0.18% at Vanguard or 0.16% at the European leader Amundi (over the first 9 months of 2016, annualized). The differences between these 3 figures can be explained by a mix of different kind of assets under management and different active management / passive weights.


Essilor (ophthalmic lenses) and Luxottica (prescription frames and sunglasses) announced their merger expecting €500m of synergies. The two share prices rose (+ 12% and + 8%), instantly creating €4.6bn of additional shareholder value.

Synergies are thus valued at about 13 times their amount (after an average corporate tax rate of 31%), or around half of the 2017 P/E ratio of the two groups (between 23 and 24 according to Exane BNP Paribas). This is logical and normal because groups never keep 100% of the announced synergies, even when they deliver them. Sooner or later, they must give a part to their customers, suppliers, employees. So that they have less value than current profits. A market valuation of synergies at half the P/E ratio of the groups participating in a merger is frequently seen and seems reasonable in the light of our experience.

The structure of the new group is less usual: each of the two groups will continue to be headed by its current CEO and will be fully owned by a joint holding company which will be listed. It's as if they merge without merging or as if they do not want to forbid a future divorce. However, it will be necessary to realize the announced synergies. The age difference of the two managers (81 years for Luxottica and 60 years for Essilor) will facilitate common management, although one is a manager (at Essilor) and the other one the founder (of Luxottica) and the main shareholder of the new group with 31% of the capital. Not easy.