
Tutorial:
RISK & CAPITAL ASSET PRICING
MODEL

Every financial investment contains some level of financial risk. This risk is usually expressed through the discount rate used in the financial analysis.
Since the risk varies from investment to investment, the discount rate needs to vary as well.
FinanceIsland's ROI analysis tool
with Monte Carlo simulation enhances your typical net present value (NPV) analysis not only by embedding Monte Carlo
simulation, but also by helping you to choose a projectspecific discount rate. This projectspecific discount rate allows for "applestoapples"
comparison of independent investments competing for the same resources.
The framework to calculate a projectspecific discount rate is based on the Capital Asset Pricing Model. To simplify the use of this framework,
FinanceIsland's ROI analysis provides a risk matrix to determine an appropriate projectspecific discount rate.


To see how the risk matrix (see below) described in this tutorial is used, please take a look at FinanceIsland's
ROI analysis tool.

Capital Asset Pricing Model (CAPM)
The financial risk is usually translated into a projectspecific, riskadjusted discount rate using the Capital Asset Pricing Model, a cornerstone of
modern financial theory. Although this model has been developed by economists to help with investment decisions in the stock market, it is also used for
investment analysis in the business world, including research & development (R&D) or marketing investments.
CAPM defines the relationship between risk and return. The premise of the model is that the expected investment return varies in direct proportion to
its risk, i.e., the riskier the investment  whether in the stock market or in R&D  the higher the return you should expect.
CAPM calculates the riskadjusted discount rate with the riskfree rate, the market risk premium, and beta:
riskadjusted rate = riskfree rate + market risk premium * beta
As the name suggests, the riskfree rate is the discount rate for riskfree investments. In the United States, it's often approximated by the rate of
shortterm (3month) Treasury bills, which can be found in major on and offline news publications. Although Treasury bills are not completely riskfree,
they are riskless enough for CAPM's purposes. In the past ten years, the 3month Treasury bills have varied in the U.S. between almost 0% and 6%.
The market risk premium describes how much riskier the market as a whole is in comparison with a riskfree investment. In the U.S., this risk premium can
be approximated through the average premium above the riskfree rate returned by the Standard & Poor's 500 index. For the purpose of calculating the riskadjusted
discount rate, the market risk premium has been historically in the 5% to 8% range.
Both the riskfree rate and the market risk premium are usually projectindependent. They vary, however, with the economy and can be substantially different
from country to country. They often change when central banks change key interest rates.
Beta (β), on the other hand, is investmentspecific. It's a relative factor that measures how risky an individual investment is relative
to the market. A beta of 1 means that an investment has exactly the same risk as the market. Businesses with relatively stable earnings tend to have lower betas
than those with cyclical results or short lifecycle products. Betas for established companies usually range from 0.2 to 2, but they can go up to 5 and beyond for new ventures.
Risk matrix
If you know the beta of your project, you can use it with the riskfree rate and the market risk premium in the above formula to calculate your project's
riskadjusted discount rate. However, it's usually difficult to determine the appropriate beta for a project. FinanceIsland's ROI analysis tool solves this problem
by using a risk matrix.
FinanceIsland's risk matrix first captures company's risk range expressed through discount rates. This range represents the range of risk behind investments
pursued by the company. It varies from low discount rates used for low risk investments such as cost reduction projects to high discount rates used for high
risk investments such as new ventures.
The matrix identifies then two risk components: internal and external. The internal risk component accounts for how familiar the company is with the products
or services to be introduced. The external risk component addresses company's familiarity with the market they will be introduced to. The internal risk is
usually more controllable by the company than the external risk. You can weigh these two risk drivers to account for different project exposures to internal
vs. external risk. The matrix calculates then a projectspecific and riskadjusted discount rate based on these risk levels.
The risk matrix helps also to standardize how the discount rates are derived. Most likely, you will be comparing and making tradeoff decisions on several
investment projects. Hence, it's crucial to calculate NPVs with discount rates that were derived based on the same approach.
After the project's discount rate has been calculated, it's helpful to verify its correctness by comparing your project against other projects at your company
to put its risk into perspective. Many times you will find that projects can be categorized according to their risks, as depicted in the following chart.
You should expect cost reduction projects to be less risky than projects that introduce new products. Projects that develop new technologies or explore new
ventures for your company should be the most risky. It's not uncommon for these highrisk projects to have discount rates of 30% to 40%. Lowrisk projects on
the other hand usually have discount rates in the range of 2% to 8%.
Weighted average cost of capital
Larger companies with corporate finance teams should be aware of the cost of capital rate calculated by those teams. This cost of capital is the weighted
average of the cost of equity and the cost of debt for the company and represents the minimum return expected for an average capital investment. Some of these
corporate finance teams require that NPV calculations for ALL investment projects use the same weighted average cost of capital (WACC) rate as the discount rate.
FinanceIsland strongly advises against using the WACC rate since it represents the average company risk. Risks of individual projects, however, may vary significantly from
the average company risk, making WACC useless for individual project analysis. This is in particular true for investment projects that deviate
significantly from typical projects undertaken by the company so far.
Academic debate
So, now that you've determined your project's riskadjusted discount rate, you can use it to calculate and simulate your NPV. However, there is one potential
issue to keep in mind. Some academics argue that the Monte Carlo simulation already takes into account NPV risk and hence cash flows should be discounted at
the riskfree rate if the Monte Carlo simulation is used.
Although we believe that there are pros and cons for this point of view, FinanceIsland recommends using the riskadjusted discount rate when using Monte Carlo
simulation. This approach is most consistent with typical scenario analyses where riskadjusted discount rates are used.
Nevertheless, the final call is yours. FinanceIsland's ROI analysis
with Monte Carlo simulation gives you the option of ignoring the riskadjusted discount rate and using other rate you deem appropriate. Whatever call you make, it's
important to use the same approach for all financial analyses throughout your company.





