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Comments on the Cost of Capital

by Jozef De Mey�

1. Introduction

Increasingly over the last ten years we have seen in Europe the development and use ofconcepts related to value such as `̀ shareholder value'', `̀ value-based analysis'' or `̀ value-based management''. At the same time the determination of the cost of capital has becomemore and more important, given that it is a key element in the valuation process.

Executives of our industry, just as in others, should pay a lot of attention to the conceptsand not leave them to their CFOs, to the ®nancial analysts or to the investors: business strategy,value creation and cost of capital are intimately related.

At the corporate and business unit levels, decision-makers need to assess the value ofalternative strategies. New market entries, capital expenditures especially for the insuranceindustry in communication and information technology, new product introduction orharvesting some businesses are typical examples where value assessment is requested. Thesame is true when considering restructurings, mergers, acquisitions, divestments, jointventures, alliances, or use of different ®nancing instruments. The fact that 50 per cent ofacquisitions fail to meet their expected targets, that only 17 per cent of transactions result insigni®cant increases in shareholder value, and that 50 per cent of transactions do actuallydestroy shareholder value, gives an indication of the importance of correct valuationassessment.

At the operational level, value-based management (VBM) has proved to be an excellenttool to review, target or benchmark the performance of business operations. Is it not of vitalimportance to know whether a business or part of it is creating value? A better understandingof what performance variables, the so-called value drivers, actually drive the value of thebusiness, allows management to ®nd solutions in order to correct a poor pro®t-makingsituation or to impose, at least temporarily, higher ®nancial targets on other parts of theportfolio. Choices and decisions are easier to make and implement if they are supported bysome quantitative evidence!

It is worth noting that by reducing the value drivers from aggregated amounts likeoperating margins, down to the business level, in terms of customer segmentation forinstance, and further down to the operating level where ef®ciency and effectiveness aremonitored, the linkage is made with what has become a new standard in businessmanagement, i.e. the Balanced Business Score Card (BSCC).

Finally, and this aspect is surely not the least important one, executives need to install amanaging value mindset throughout their organizations and to communicate with theshareholders about the value of the business, the shareholders' value. One of the challenges isto develop and implement performance measurement and reward systems, not only for top

� Chief Executive Of®cer, AG 1824, S.A., Brussels.

The Geneva Papers on Risk and Insurance Vol. 25 No. 1 (January 2000) 25±33

# 2000 The International Association for the Study of Insurance Economics.

Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK.

executives, in order to drive all the activities of the organization by the concept of valuecreation. It is clear that corporations who do not maximize the shareholder's value will seecapital ¯ow to competitors either in the same industry or in other more pro®table industries.The free circulation of capital in Europe and around the world as well as the EuropeanMonetary Union will further reinforce this trend in the future.

So far I have mentioned value-based management, value creation and shareholders'value but two basic questions have not yet been answered: what is value? and why is value soimportant?

The answer to the ®rst question is quite simple: `̀ value'' equals the discounted futurecash-¯ows generated by a business, by an investment or a portfolio of investments. And valueis created when businesses invest in projects that earn returns in excess of the cost of capital.Therefore, determining the latter is of crucial importance in assessing the creation ordestruction of value.

The answer to the second question is also simple: `̀ value'' is the best measure ofcorporate performance as it is the only one that is comprehensive in terms of informationcontent. Discounted Cash Flows (DCFs) take into account cash ¯ows, different time periods,the cost of capital and all sources of revenue, whereas other measures, like return on equityand earnings growth, tend to focus on managing the income statement and overemphasize theshort term.

2. Cost of capital

The cost of capital of a corporation is the yield below which the said corporation starts todestroy value and above which it starts to create value. In the valuation assessment the cost ofcapital is the discount rate used to convert expected future cash ¯ows into present value.

Determining the cost of capital is a complex exercise as it is dependent on the capitalstructure of the company (equity, debt, preferred stocks, etc.), the effect of taxation and thecost of the sources of capital used. The evolution of these different elements over time and theinternal and external environment can have major effects on the estimate. A general formulawhich catches these factors is the Weighted Average Cost of Capital (WACC). In a simpli®edform:

WACC � Ke 3E

E� D� Kd 3

D

E� D3 (1ÿ t)

where

E � market value of equity,D � market value of debt,t � corporate tax rate,Kd � cost of debt,Ke � cost of equity.

This equation states that the cost of capital is a mix of the costs of various ®nancinginstruments used by the company with basically two components: an equity component and adebt (or debt-type) component.

A few questions show how carefully one should handle this concept:

· What is debt? What should be included in the debt component?· What is the cost of debt? The cost of raising new debt? Short-term debt or long-term debt?


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· Is the cost of capital calculated on an after-tax basis and which tax rate must beconsidered? The marginal statutory rate or an average rate?

· How to estimate the market values of equity and debt in order to know the capitalstructure?

· Is there an optimal gearing level between debt and equity which de®nes a target capitalstructure to be dealt with?

· What is the cost of equity and how to determine it?

In the following section I shall concentrate on the equity component of the WACC, morespeci®cally the cost of equity capital (Ke).

3. The cost of equity capital

Methods of estimating the cost of equity

Harry M. Markowitz (1959) laid the foundations and built much of the structure of whatwe now know as Modern Portfolio Theory (MPT). It formalizes the risk-return framework forinvestment decision-making: investors choose their securities on the basis of both theexpected rate of return and the standard deviation (or variance) of the rate of return, regardedas the relevant measure of risk. In the case of a portfolio of securities a second measure of riskis considered by computing the correlation (or covariance) of said security with the others.

Two major contributions of the MPT are the elimination of risk through diversi®cationand the concept of ef®cient frontier. The inconvenience, surely, in the early 1960s, was thegreat amount of calculations to be performed to calculate the statistics.

In the mid-1960s, Sharpe, Lintner and Mossin extended the MPT by assuming theexistence of a risk-free asset with a ®xed return and by taking the market as comparator. Theirmodel was called the Capital Asset Pricing Model (CAPM). The CAPM divide the total returnof an investment into a risk-free component and a risk-related component.

Other methods of calculating the cost of equity are also used and each has its own merits.Without being exhaustive I would cite three of them:

· Use of historical returns dividends and stock prices ± for the related sector or industry;· Use of the market itself: the Gordon growth model calculates the cost of equity as the sum

of the dividend yield and the dividend growth rate;· Use of option-pricing models.

CAPM

The CAPM formalizes the notion that the cost of equity can be estimated as thecombination of the cost of a risk-free asset and the cost of the risk premium. The riskcomponent for an individual security can be divided into two parts:

· A non-diversi®able or systematic or market risk; and· A diversi®able or speci®c company risk.

Only market risk is important because you cannot get rid of it by diversi®cation.The equation for the CAPM cost of equity is:

Ke � R f � â 3 (Rm ÿ R f )

where


COMMENTS ON THE COST OF CAPITAL 27

R f � risk-free interest rate,Rm � expected rate of return of the market,Rm ÿ R f � the market risk premium (MRP),â� a measure of the systematic risk of the equity; the beta measures the non-diversi®ablerisk of the equity, relative to the risk of the market.

Stated in words:

Cost of equity � Risk-free rate� â 3 market risk premium

where

â � Share Risk

Market Risk3 correlation of share to market movement:

Shares that have, compared to the market, average systematic risk, have betas equal to1.00. Shares with greater, respectively smaller, average systematic risk, have betas greater orsmaller than 1.00. Investors judge investing in given shares to be more or less risky thaninvesting in the market overall, therefore requiring a higher or smaller return.

To implement the CAPM we need to estimate three factors: the risk-free rate, the marketrisk premium and the systematic risk. It is not the aim of this contribution to elaborate on thedifferent approaches leading to the determination of these factors, as well as their limitations,assumptions and constraints. That is an important part of corporate ®nance research and justas for the determination of the cost of capital, there are more questions than answers!However, the concepts handled in CAPM are useful and CAPM works well for analysingreturns of shares highly correlated with the market and for mature and liquid markets. Theinsurance industry in developed countries, and more generally the ®nance industry, can becharacterized as such.

The insurance industry: speci®cities

Compared to other industries, and especially the manufacturing industry, the insuranceindustry has some peculiarities and faces challenges due to a rapidly changing environment.These affect the capital requirements and the cost of equity.

(a) Why is capital needed?

· To absorb risks related to the insurer's activities: underwriting and business risks as well asrisks in the asset-liabilities management positions. It is important to remember here thatinsurance companies have an inverse production cycle and that, on the balance sheet, mostof the liabilities are long term compared to the assets.

· To satisfy legal solvency and rating agencies' requirements.· To meet policyholders' and intermediaries' `̀ con®dence'' expectations.· To ®nance growth, organic (cf. solvency regulations) or through acquisitions (see below).

(b) The industry is in an accelerated reorganization process. Although players are becomingmore and more international, the majority of today's groups have still a strong domesticbase. The ®rst wave of acquisitions has generally occurred at national level in aconsolidation wave. Now some insurers are making acquisitions of companies with alarge national market share outside their home country. A third wave will seeconcentrations at the top of the insurance industry, either by mergers or by alliances.


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(c) Due to national regulations and culture, however, the approach to the market is multi-domestic and not yet truly multi-national, except for commercial-type risks.

(d) The insurance industry has huge growth potential, more speci®cally in the pensions andhealth sector, as governments seek to move more responsibilities to the individual.

(e) The change in products offered by insurance companies ± saving, universal life and unit-linked products ± has intensi®ed the competition (or co-operation) between banks andinsurers. Asset management has become `̀ the quest for the Holy Grail''.

Which risk-free rate?

Basically three methods of estimating the risk-free rate can be used:

· Short-term government debt;· Short-term government debt adjusted for future in¯ation expectations;· Long-term government debt (ten years and beyond).

The ten-year rate will be considered as it approximates to the duration of the stock marketindex portfolio and its use is therefore consistent with the Beta and MRP estimates.

The LTyield should re¯ect the long-term forecasts of nominal Gross Domestic Product(GDP) growth plus some spread for country default risk and other risks (e.g. taxation policy).These uncertainties increase with the duration of debt considered. In developed countries thereal GDP growth is around 2 to 3 per cent. Adding in¯ation expectations of 1.5 to 2 per centand 0.5 per cent for other risks gives a total range of 4 to 5.5 per cent.

Today's LT government bonds in Europe and the United States are in this range (Table 1).

These low rates are historically not abnormal. In the period from 1926 until 1960, the 20-yearU.S. government bond was under 4 per cent with an average level of 2.8 per cent. Only in the1970s and 1980s, when in¯ation and public de®cits were high, were the LT rates above 6 percent and even more than 10 per cent.

Thelaunchoftheeuroatthebeginningofthisyearencouragestheuseofonesinglerisk-freerate for the euro zone even if today there are still somesmalldifferencesbetweencountries. Theconvergence will be reinforced with the disappearance of the different national currencies, thecontinuous reduction in public de®cits and the reduction in in¯ation spread between countries.

With these considerations and

· taking into account the spread in in¯ation between the U.S. and Europe,· expecting Europe to grow somewhat faster in the coming years,· and the U.S. somewhat slower than in the recent past,

Table 1

10-Year bonds� 30-Year bonds�Belgium 4.09% 5.03%Netherlands 3.96% 4.86%Germany 3.83% 4.83%France 3.95% 4.88%Switzerland 2.37% 3.73%United States 5.21% 5.52%

�As at 30 April 1999.



LT risk-free rates of respectively 4.5 per cent for Europe and 5.3 per cent for the U.S. arereasonable estimates.

Which market risk premium?

The market risk premium (MRP) or equity risk premium is the difference between theexpected rate of return on the market portfolio and the risk-free rate. It is important to note thatthe risk premium is a forward-looking concept, that is, the risk premium should be re¯ectiveof what investors think, namely that the risk premium will be going forward.

There are two general ways to estimate the MRP:

· Using historical data;· Using market projections.

Most equity risk premium models use historical data and assume that the past provides thebest indicator of what the future will hold. Future projections models are based on analysts'estimates (IBES : Institutional Brokers Estimate System) of expected growth in earnings overdifferent periods of time. Differences in market risk premium for different countries havebeen very important in the past. There are also substantial variations over time.

For the U.S. market, data exist back as far as the late 1800s. Therefore it is possible tomeasure the historical equity risk premium for roughly the past 100 years. Based on the riskpremium for the return on the S & P 500 versus the long-term Treasury bonds, IbottsomAssociates have calculated equity risk premium for time windows starting in 1926. Over thevery long period from 1926 to 1995, which encompasses stock market crashes, expansions,recessions and two world wars, the geometric average equity risk premium is 5 per cent.

For Europe, statistics are not available for the same period but for a period covering thelast 40 years the equity risk premium has been 3.2 per cent in Belgium, and between 4.4 and 6per cent in France, the U.K. and Sweden.

Using a dividend discount model CSFB (Credit Suisse First Boston) computes themarket risk premium using IBES forecasts for earnings growth in Europe. In January 1999 theweighted average for Europe (15 countries) was 5.2 per cent.

Comparisons for some countries in November 1997 and January 1999 are given inTable 2.

Here also it is interesting to note the convergence of the market risk premium across theEuropean countries over the last ®ve years. This is consistent with the economic evolution ofEurope:

Table 2

November1997

January1999

Belgium 4.3% 4.6%Netherlands 3.4% 5.2%Germany 3.3% 5.2%France 4.9% 5.5%U.K. 4.9% 6.1%Switzerland 5.9% 6.4%


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· A single market means synchronized economic cycles;· The same currency means similar or convergent monetary and ®scal policies;· A more `̀ liberal'' climate ± deregulation, privatization, international competition on a

worldwide scale, consolidation of industries, etc. ± has fundamentally changed anduni®ed the attitude towards capital and the reward of risk.

Other elements like the increasing trend towards institutionalization of funds and sectorialapproaches by asset managers instead of geographical analyses also encourage the conver-gence of equity risk premium. The signature as recently as 4 May 1999 of a `̀ memorandum ofunderstanding'' by eight European Stock Exchanges (London, Frankfurt, Paris, Milan,Madrid, Amsterdam, Zurich and Brussels) in order to create a common electronic quotationplatform for 250 to 300 important European securities is a tangible sign of this rapid evolution.

In summary, a market risk premium of 5 per cent is a reasonable estimate for Europe andthe United States.

Which â?

The â of an equity measures the non-diversi®able risk relative to the risk of the market.To determine this factor there are two methods:

· Calculate â for the security considered with data of stockprice evolution;· Compare with the â of the industry or activity sector; this method refers to the peer group

analysis.

Some problems may occur in establishing the appropriate â:

· Finding a suitable set of analogues;· Some adjustment is required to take into account the equity/debt gearing: the impact of

increasing debt is to increase equity volatility and hence â;· â is sensitive to observation frequency (daily, weekly, monthly) and the window size of the

observation;· The precision of the â estimate increases with the number of `̀ pure plays'' but there are

not so many!

Table 3 gives â for a certain number of industries for European and American equities:

Table 3

Industry â (Europe) â (U.S.)

Wholesale trade ± durable goods 1.32 1.28Automobile 1.25 1.38Paper 1.12 1.01Telecoms 1.03 0.89Chemicals 0.98 1.20Electric and gas utilities 0.93 0.50Food 0.88 0.71Holdings 0.80 ±

Banks 1.10 1.60Insurance 1.01 0.93



For the insurance industry as a whole â is equal to 1.00 which, at least for the past, con®rmsthat this industry is neither more nor less risky than the overall stock market. Looking now tomajor insurance groups in Europe, measured relatively to the Dow Jones Euro Stoxx 50 over aperiod of ®ve years we have (Table 4):

Regressing the returns of Fortis (B) against the FTSE Eurotop 300 index gives a â of 1.08 on ahistorical basis over the period 1989±1999 and 1.15 on a ®ve-year rollover basis. This re¯ectsFortis' greater volatility in the stock returns compared to the market. Fortis (NL) followed thesame pattern going from 0.91 to 1.16. The history of Fortis over the last few years showsaccelerated growth in revenues and pro®ts. Fortis shares have become `̀ growth''shares whichis re¯ected in P and the requirement of higher returns from investors.

Cost of equity capital for the insurance industry

Based on above results we can determine the cost of equity capital for different sets ofvalues of risk-free rate, market premium and â:

Ke � R f � â 3 MRP

The shaded area in Table 5 shows values which are our current best estimates ± the cost ofequity capital is around 10 per cent.

The evolution of Fortis (B) cost of capital over the period 1994±1998 is given in Figure 1below: extreme values over this time frame are 11.5 and 7.9 per cent. It must be noted thatFortis is not a pure insurance company but is diversi®ed in banking and asset management.This however is true for other large companies too, except perhaps that banking activity isrelatively smaller.

Table 4

Company âAegon 0.96Allianz 1.02Fortis (B) 1.07Fortis (NL) 1.17AXA 1.15

Table 5

MRP 4.5% 5.0% 5.5% 6.0%

â 0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.24.0% 8.05 8.50 8.95 9.40 8.50 9.00 9.50 10.00 8.95 9.50 10.05 10.60 9.40 10.00 10.60 11.204.5% 8.55 9.00 9.45 9.90 9.00 9.50 10.00 10.50 9.45 10.00 10.55 11.10 9.90 10.50 11.10 11.705.0% 9.05 9.50 9.95 10.40 9.50 10.00 10.50 11.00 9.95 10.50 11.05 11.60 10.40 11 11.60 12.205.5% 9.55 10.00 10.45 10.90 10.00 10.50 11.00 11.50 10.45 11.00 11.55 12.10 10.90 11.50 12.10 12.706.0% 10.05 10.50 10.95 11.40 10.50 11.50 11.50 12.00 10.95 11.50 12.05 12.60 11.40 12.00 12.60 13.20

:Rf


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Figure 1: Evolution cost of capital for Fortis, 1994±1998



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