Risk-Free Rate - Investment and Project Valuation

Importance of risk-free rates

The risk-free rate of return $r_f$ is the theoretical return rate of an investment with no risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. It plays a central role in financial valuation and is the planning base for return rates of risky assets.

Prospective cost of debt (return rate requirement) can be estimated by adding default spreads to the risk-free rate. This can be done by synthetic rating of the company with its interest coverage ratio and adding a default spread according to the synthetic rating of the company. Additionally, in an emerging market the country of the occuring cash flows can generate a further country default spread added to the risk free rate.

Equity return rates $r_e$ are calculated by adding risk premiums to the risk-free rate. Considering the Capital Asset Pricing Model (CAPM) the expected value of the equity return rate is:

$E \left( r_e \right)= r_f+\beta \left( E\left( r_m \right) - r_f \right)$

$\beta$ is the sensitity of the risky cash flow return rate to the efficient market protfolio return rate $r_m$ .

Risk-free rates are also very important in real options analysis. The time values of real options are weighted by risk-neutral probabilities and discounted with the risk-free rate.

Because of all these reasons it is very important to understand the risk-free rate in detail. Most books neglect that issue. In my point of view the best analysis is done by Aswath Damodaran in his book about investment valuation (2011).

Risk-free rate criteria

There are two criteria that a return rate of an asset can be considered as risk-free: 1) First the asset does not have any default risk. This excludes private entities, since even the largest and safest ones have some measure of default risk. The only securities that have a chance of being risk-free are government securities, not because governments are better than corporations, but because they usually control the printing of currency. 2) Secondly the asset must not have any reinvestment risk. The return rate has to be ensured fo the whole period of time.

Discounting Period

Government zero-coupon bonds and securities have different return rates for different time horizons. Usually the return rate increases with longer time horizons. Well-behaved term structures would include an upward-sloping yield curve, where long-term rates are at most 2 to 3 percent higher than short-term rates. For each maturity the investor gets a different guaranteed return on the investment. That means that each maturity has a specific discount rate.

Most DCF valuations use only one risk-free rate corresponding to a specific maturity. In most cases they take long term Treasury bonds, because cash flows mainly occur years away from present time $(t=0)$ of the valuation. But be aware that this is an approximation and can be false in some cases.

Currency

The risk-free rate used to come up with expected returns should be measured conisistently with how the cash flows are measured. Thus, if cash flows are estimated in nominal U.S. dollar terms, the risk-free rate will be the U.S. Treasury bond rate. This also implies that it is not where a firm is domiciled that determines the choice of a risk-free rate, but the currency in which the cash flows of the firm are estimated. If we assume purchasing power parity, then differences in interest rates reflect differences in expected inflation. Both the cash flows and the discount rate are affected by expected inflation; thus, a low discount rate arising from a low risk-free rate will be exactly offset by a decline in expected nominal growth rates for cash flows, and the value will remain unchanged. If the difference in interest rates across two currencies does not adequately reflect the difference in expected inflation in these currencies, the values obtained using the different currencies can be different.

Default Spreads

The interest rates on bonds are determined by the default risk that investors perceive in the issuer of the bonds. This default risk is often measured with a bond rating, and the interest rate that corresponds to the rating is estimated by adding a default spread to the riskless rate. An Euro government bond from Greek or Italian government has a higher default spread than a bond emitted by German government. You always have to subtract the default spread from the effective bond interest rate to get the risk-less (or better default-free) rate.

Conclusion

In most books concerning capital budgeting and DCF analysis the risk-free rate is the interest rate of a long term Treasury government bond. But also maturity, currency and default risk of the bond emitter have to be considered to get the right interest rate of a default-free asset. The investment analyst has to be aware of that and also has to know the inaccuracy when making approximations.