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Investment analysis

This type of analysis gives the client direct information regarding the investments profitability, and its influence on company value.

An important part of the investment analysis is cost. Especially in complex and demanding projects, there is significant risk related to investing. We have developed a method that clearly assesses and explains the relationship between uncertainty raised by each cost element, and which effect it has on the investment’s total risk.

In a complex project there is often a set of cost elements that triggers follow-up costs. If one cost element exceed budget, the total cost increase can be significant, even though the isolated increase in the original cost element seemed small.

We have focused on visualizing for the client, the scope of uncertainty in the investment, and which probability distributions that exist for each single cost element overstep.

We focus especially on those cost elements that should be subject to strong control and follow-up. Such that the likelihood for excess cost can be reduced.

We see it as crucial that the client has solid analysis describing and explaining the possible total cost outcomes, and their probability distributions at time of decision. With this method and these results the client can discuss the premises for the investment and decide whether or not carry out the investment with the revealed uncertainties.

Below we present three graphs that shows the sensitivity in a project related to changes in demand for return on capital. For all three graphs the reference point is set in the projects IRR which is the point where the projects discounted revenues equal the value of the projects discounted cost payments (Project inflow/outflow ratio = 1).

The curves are ideal for comparing investments with different profiles. When the X-axes is equal, curves for different projects can be overlapped to give information on whether one project is better than the other.

It is also possible to estimate the probability distribution for the projects net present value, or its effect on the distribution of company value.

15/02/2009
The Probability of Gain and Loss

Every item written into a firm’s profit and loss account and its balance sheet is a stochastic variable with a probability distribution derived from probability distributions for each factor of production. Using this approach we are able to derive a probability distribution for any measure used in valuing companies and in evaluating strategic investment decisions. Indeed, using this evaluation approach we are able to calculate expected gain, loss and their probability when investing in a company where the capitalized value (price) is known.

For a closer study, please download Corporate-risk-analysis.

The Probability Distribution for the Value of Equity

The simulation creates frequency and cumulative probability distributions as shown in the figure below.

We can use the information contained in the figure to calculate the risk of investing in the company for different levels of the company’s market capitalization. The expected value of the company is 10.35 read from the intersection between probability curve and a line drawn from the 50% probability point on the left Y-axis.

The Probability Distribution for Gain and Loss

The shape of the probability curve provides concise information concerning uncertainty in calculating expected values of equity. Uncertainty is reduced the steeper the probability curve, whereas the flatter the curve so uncertainty is more evident. The figures below depicts the value of this type of information enabling calculation of expected gains or losses from investments in a company for differing levels of market capitalization.

We have calculated expected Gain or Loss as the difference between expected values of equity and the market capitalization; the ‘S’ curve in the graph shows this. The X-axis gives different levels of market capitalization; the right Y-axis gives the expected gain (loss) and the left y-axis the probability. Drawing a line from the 50% probability point to the probability curve and further to the right Y-axis point to the position where the expected gain (loss) is zero. At this point there is a 50/50 chance of realising or loosing money through investing in the company capitalized at 10.35, which is exactly the expected value of the company’s equity.

To the left of this point is the investment area. The green lines indicate a situation where the company is capitalized at 5.00 indicating an expected gain of 5.35 or more with a probability of 59% (100%-41%).

The figure to the right describes a situation where a company is capitalized above the expected value.

To the right is the speculative area where an industrial investor, with perhaps synergistic possibilities, could reasonably argue a valid case when paying a price higher than expected value. The red line in the figure indicates a situation where the company is capitalized at 25.00 – giving a loss of 14.65 or more with 78% probability.

To a financial investor it is obviously the left part – the investment area – that is of interest. It is this area that expected gain is higher than expected loss.

11/02/2009
Corporate Risk Analysis

This entry is part 2 of 6 in the series Balance simulation

Strategy @Risk has developed a radical and new approach to the way risk is assessed and measured when considering current and future investment. A key part of our activity in this sensitive arena has been the development of a series of financial models that facilitate understanding and measurement of risk set against a variety of operating scenarios.

We have written a paper which outlines our approach to Corporate Risk Analysis to outline our approach. Read it here.

Our purpose in this paper is to show that every item written into a firm’s profit and loss account and its balance sheet is a stochastic variable with a probability distribution derived from probability distributions for each factor of production. Using this approach we are able to derive a probability distribution for any measure used in valuing companies and in evaluating strategic investment decisions. Indeed, using this evaluation approach we are able to calculate expected gain, loss and probability when investing in a company where the capitalized value (price) is known.

03/02/2009
The weighted average cost of capital
This entry is part 1 of 2 in the series The Weighted Average Cost of Capital

A more extensive version of this article can be read here in .pdf format.

The weighted cost of capital (WACC) and the return on invested capital (ROIC) are the most important elements in company valuation, and the basis for most strategy and performance evaluation methods.

WACC is the discount rate (time value of money) used to convert expected future cash flow into present value for all investors. Usually it is calculated both assuming a constant cost of capital and a fixed set of target market value weights ((Valuation, Measuring and Managing the Value of Companies. Tom Copeland et al.)) , throughout the time frame of the analysis. As this simplifies the calculations, it also imposes severe restrictions on how a company’s financial strategy can be simulated.

Now, to be able to calculate WACC we need to know the value of the company, but to calculate that value we need to know WACC. So we have a circularity problem involving the simultaneous solution of WACC and company value.

In addition all the variables and parameters determining the company value will be stochastic, either by themselves or by being functions of other stochastic variables. As such WACC is a stochastic variable– determined by the probability distributions for yield curves, exchange rates, sale, prices, costs and investments. But this also enables us – by Monte Carlo simulation –to estimate a confidence interval for WACC.

Some researchers have claimed that the free cash flow value only in special cases will be equal to the economic profit value. By solving the simultaneous equations, giving a different WACC for every period, we will always satisfy the identity between free cash flow and economic profit value. In fact we will use this to check that the calculations are consistent.

We will use the most probable value for variables/parameters in the calculations. Since most of the probability distributions involved are non-symmetric (sale, prices etc), the expected values will in general not be equal to the most probable values. And as we shall see, this is also the case for the individual values of WACC.

WACC

To be consistent with the free cash flow or economic profit approach, the estimated cost of capital must comprise a weighted average of the marginal cost of all sources of capital that involves cash payment – excluding non-interest bearing liabilities (in simple form):

WACC = ${C_d}(1-t)*{D/V} + {C_e}*{E/V}$

${C_d}$ = Pre-tax debt nominal interest rate
${C_e}$ = Opportunity cost of equity,
t = Corporate marginal tax rate
D = Market value debt
E = Market value of equity
V = Market value of entity (V=D+E).

The weights used in the calculation are the ratio between the market value of each type of debt and equity in the capital structure, and the market value of the company. To estimate WACC we then first need to establish the opportunity cost of equity and non-equity financing and then the market value weights for the capital structure.

THE OPPORTUNITY COST OF EQUITY AND NON-EQUITY FINANCING

To have a consistent WACC, the estimated cost of capital must:
1. Use interest rates and cost of equity of new financing at current market rates,
2. Be computed after corporate taxes,
3. Be adjusted for systematic risk born by each provider of capital,
4. Use nominal rates built from real rates and expected inflation.
However we need to forecast the future risk free rates. They can usually be found from the yield curve for treasury notes, by calculating the implicit forward rates.

THE OPPORTUNITY COST OF EQUITY

The equation for the cost of equity (pre investor tax), using the capital asset pricing model (CAPM) is:

C =

R = risk-free rate,
= the levered systematic risk of equity,
M = market risk premium,
L = liquidity premium.

If tax on dividend and interest income differs, the risk-free rate and the market premium has to be adjusted, assuming tax rate -ti, for interest income:

R = (1-)*R and M = M+*R.

= Investor tax rate,
R = tax adjusted risk-free rate,
M = tax adjusted market premium

The pre-tax cost of equity can then be computed as:

$R/(1-t_d)+{beta}*{M/(1-t_d)}+{LP/(1-t_d)}$

(pre-tax) = = $R/(1-t_d)+{beta}*{M/(1-t_d)}+{LP/(1-t_d)}$

Where the first line applies for an investor with a tax rate of -td, on capital income, the second line for an investor when tax on dividend and interest differs ((See also: Wacc and a Generalized Tax Code, Sven Husmann et al., Diskussionspapier 243 (2001), Universität Hannover)) .

The long-term strategy is a debt-equity ratio of one, the un-levered beta is assumed to be 1.1 and the market risk premium 5.5%. The corporate tax rate is 28%, and the company pays all taxes on dividend. The company’s stock has low liquidity, and a liquidity premium of 2% has been added.

In the Monte Carlo simulation all data in the tables will be recalculated for every trial (simulation), and in the end produce the basis for estimating the probability distributions for the variables. This approach will in fact create a probability distribution for every variable in the profit and loss account as well as in the balance sheet.

THE OPPORTUNITY COST OF DEBT

It is assumed that the pre-tax debt interest rate can be calculated using risk adjusted return on capital (RAROC) as follows:

Lenders Cost =

= Lenders Funding Cost (0.5%),
= Lenders Average Expected Loss (1.5%),
= Lenders Administration Cost (0.8%),
= Lenders Risk Premium (0.5%).

The parameters (and volatility) have to be estimated for the different types of debt involved. In this case there are two types; short -term with a maturity of four years and long-term with a maturity of 10 years. The risk free rates are taken from the implicit forward rates in the yield curve and lenders cost are set to 3.3%.

In every period the cost and value of debt are recalculated using the current rates for that maturity, ensuring use of the current (future) opportunity cost of debt.

THE MARKET VALUE WEIGHTS

By solving the simultaneous equations, we find the market value for each type of debt and equity:

And the value weights:

Multiplying the value weights by the respective rate and adding, give us the periodic most probable WACC rate:

As can be seen from the table above, the rate varies slightly from year to year. The relative small differences are mainly due to the low gearing in the forecast period.

MONTE CARLO SIMULATION

In the figure below we have shown the result from simulation of the company’s operations, and the resulting WACC for year 2002. This shows that the expected value of WACC in is 17.4 %, compared with the most probable value of 18.9 %. This indicates that the company will need more capital in the future, and that an increasing part will be financed by debt. A graph of the probability distributions for the yearly capital transactions (debt and equity) in the forecast period would have confirmed this.

In the figure the red curve indicates the cumulative probability distribution for the value of WACC in this period and the blue columns the frequencies. By drawing horizontal lines on the probability axis (left), we can find confidence intervals for WACC. In this case there is only a 5% probability that WACC will be less than 15%, and a 95% probability that it will be less than 20%. So we can expect WACC for 2002 with 90% probability to fall between 15% and 20%. The variation is quite high – with a coefficient of variation of 6.8 ((Coefficient of variation = 100*st.dev/mean)).

VALUATION

The value of the company and the resulting value of equity can be calculated using either the free cash flow or the economic profit approach. Correctly done, both give the same value. This is the final test for consistency in the business model. The calculations are given in the tables below, and calculated as the value at end of every year in the forecast period.

As usual, the market value of free cash flow is the discounted value of the yearly free cash flow in the forecast period, while the continuing value is the value of continued operation after the forecast period. All surplus cash are paid, as dividend so there is no excess marketable securities.

The company started operations in 2002 after having made the initial investments. The charge on capital is the WACC rate multiplied by the value of invested capital. In this case capital at beginning of each period is used, but average capital or capital at end could have been used with a suitable definition of capital charge.
Economic profit has been calculated by multiplying RIOC – WACC with invested capital, and the market value at any period is the net present value of future economic profit. The value of debt as the net present value of future debt payments – is equal for both methods.

For both methods using the same series of WACC when discounting cash the flows, we find the same value for the both company and equity. This ensures that the calculations are both correct and consistent.

Tore Olafsen and John Martin Dervå
08/09/2008
The Value of Quality Management
Warret Buffett is recognized being one of the worlds most successful investor. What are the key issues when deciding to invest? Some of the most relevant factors are written here. If you want the source himself, please go to Warren Buffett here.

Managing the Buffett way
By Stuart Crainer

The naive figure who utters profound truths holds a perennial and universal appeal. The naïf who succeeds and mysteriously makes sense of an alien environment is the subject of movie after movie – from Peter Sellers’ Being There to Tom Hanks’ Big.

Something of the same phenomenon can be seen in the business world. Ben and Jerry fascinate because they appear so blithely straightforward and enthusiastic. Sir Richard Branson remains immune to criticism despite Virgin’s occasional misadventures. He is an engaging innocent, an enthusiast in a woolly jumper. There is a sense that these people are from a different time, an era of decency and simple pleasures. They are idiosyncratic throwbacks to bygone ways of doing business, cavaliers in an age of roundheads.

The investor Warren Buffett is part of this phenomenon. He successfully ignored the new economy bubble and emerged to tell a tale of even greater riches. The Sage of Omaha has been enormously successful in a field where competition is ruthless. As you’d expect, Buffett’s achievement has been examined from every angle. Yet, if emulation is a measure of understanding, it appears little understood.

Buffett, a man of resolutely simple tastes, someone who oozes old-fashioned decency from every pore, stands above the maelstrom of analysts, commentators, and private investors. As he has become more famous and his investment company Berkshire Hathaway ever more successful, Buffett’s public utterances and writings have become more playful.

As happens in Wall Street all too often, what the wise do in the beginning, fools do in the end,” he wrote in 1989. This was followed in 1990 by: “Lethargy bordering on sloth remains the cornerstone of our investment style”. Of all the markets he has conquered, the one in homespun wisdom may be his surprising legacy.

Investors buy books on the great man in their millions (there is a book called Buffettology though the most useful is The Essays of Warren Buffett) and pore through them in search of a formulaic approach to investing. They will, of course, be disappointed. It is not that Buffett does not have a formula. He does.

Buffett advocates “focused investing”. When gauging the wisdom of an investment, investors should look at five features:
1. The certainty with which the long-term economic characteristics of the business can be evaluated.
2. The certainty with which management can be evaluated, both as to its ability to realize the full potential of the business and to wisely employ its cash flows.
3. The certainty with which management can be counted on to channel the reward from the business to the shareholders rather than to itself.
4. The purchase price of the business.
5. The levels of taxation and inflation that will be experienced and that will determine the degree by which an investor’s purchasing-power return is reduced from his gross return.
Buffett admits that many will find such criteria “unbearably fuzzy”. This is only partly the case. Analysis can lead to conclusions about the long-term economic prospects of a business. Analysis can also establish what is a reasonable purchase price and help predict future macroeconomic conditions likely to impact on the investment. Where analysis falls down and things do begin to become fuzzy is in assessing the incumbent management.

Time and time again in his wry annual letters to shareholders, Buffett returns to the issue of sound management. Given the right conditions, good managers produce good companies. Never invest in badly managed companies.

The trouble, it seems, is that there are a great many poor managers. “The supreme irony of business management is that it is far easier for an inadequate CEO to keep his job than it is for an inadequate subordinate,” lamented Buffet in 1988, going on to criticize the comfortable conspiracies of too many boardrooms. “At board meetings, criticism of the CEO’s performance is often viewed as the social equivalent of belching.”

Buffett believes that executives should think and behave as owners of their businesses. He is critical, therefore, of the “indiscriminate use” of stock options for senior executives. “Managers actually apply a double standard to options,” Buffet writes. “Nowhere in the business world are 10-year, fixed-price options on all or a portion of a business granted to outsiders. Ten months, in fact, would be regarded as extreme.”

Such long-term options, argues Buffet, “ignore the fact that retained earnings automatically build value and, second, ignore the carrying cost of capital”.

Buffett is a slow-moving minimalist in an age of hyperactive behemoths. In the Berkshire Hathaway boardroom, belches are welcomed.

Copyright © 2000 FT Knowledge Limited
04/09/2008
The Challenge

This entry is part 2 of 6 in the series Monte Carlo Simulation

Whenever you take a decision where you can loose or gain something, value is at risk. Most decision makers want a situation where they maximize the value, and if everything goes wrong have a minimum of regret.

Intuition based decisions are the most common type of decisions we make in our daily life, what we seem to forget is that the intuition is the sum of all our experiences gained through years of hard work and often at a high cost. So what seemed to be an easy decision might be the result of years of gathered information. The decision maker has in fact very little uncertainty since the information is known.

When the decision involves other people that need to be convinced and the complexity is vast and the potential loss is bigger than the individual can bear other methods than intuition is required. This was the situation for the team in The Manhattan project building the first atomic bomb. They needed to know and they did not have the experience to know and there was no place to gather information.

They had to take decisions with a great deal of uncertainty. In order to understand the risk involved in every single decision and the total risk, they needed a method to calculate the risk. Most decisions related to investments and business development does not face this huge challenge similar to The Manhattan project but the same method can be used.

01/09/2008