The rate used to discount future unlevered free cash flows (UFCFs) and the terminal value (TV) to their present values should reflect the blended after-tax returns expected by the various providers of capital. The discount rate is a weighted-average of the returns expected by the different classes of capital providers (holders of different types of equity and debt), and must reflect the long-term targeted capital structure as opposed to the current capital structure. While a separate discount rate can be developed for each projection interval to reflect the changing capital structure, the discount rate is usually assumed to remain constant throughout the projection period.
In situations where projections are judged to be aggressive, it may be appropriate to use a higher discount rate than if the projections are deemed to be more reasonable. While choosing the discount rate is a matter of judgment, it is common practice to use the weighted-average cost of capital (WACC) as a starting point.
Considerations in Calculating WACC
The following are important considerations when calculating WACC:
- WACC must comprise a weighted-average of the marginal costs of all sources of capital (debt, equity, etc.) since UFCF represents cash available to all providers of capital.
- WACC must be computed after corporate taxes, since UFCFs are computed after-tax.
- WACC must use nominal rates of return built up from real rates and expected inflation, because the expected UFCFs are expressed in nominal terms.
- WACC must be adjusted for the systematic risk borne by each provider of capital, since each expects a return that compensates for the risk assumed.
- While calculating the weighted-average of the returns expected by various providers of capital, market value weights for each financing element (equity, debt, etc.) must be used, because market values reflect the true economic claim of each type of financing outstanding whereas book values may not.
- Long-term WACCs should incorporate assumptions regarding long-term debt rates, not just current debt rates.
WACC WACC
WACC |
= |
E |
× |
r_{e} |
+ |
D |
× |
(1 − t) |
× |
r_{d} |
+ |
P |
× |
r_{p} |
(E+D+P) |
(E+D+P) |
(E+D+P) |
E |
= |
Market value of
equity |
D |
= |
Market value of debt |
P |
= |
Market value of
preferred stock |
r_{e} |
= |
Cost of equity |
r_{d} |
= |
Cost of debt |
r_{p} |
= |
Cost of preferred
stock |
t |
= |
Marginal tax rate |
Calculation of the Cost of Equity
The cost of equity is usually calculated using the capital asset pricing model (CAPM), which defines the cost of equity as follows: re re re re re
r_{e} |
= |
r_{f} |
+ |
β |
× |
(r_{m} − r_{f}) |
r_{f} |
= |
Risk-free rate
(represented by 10-yr U.S. Treasury bond rate) |
β |
= |
Predicted equity
beta (levered) |
(r_{m} −
r_{f}) |
= |
Market risk premium |
Equity betas can be obtained from the Barra Book. These betas will be levered and either historical or predicted. The historical beta is based on actual trading data for the period examined (often 2 years), while the predicted beta statistically adjusts the historical beta to reflect an expectation that an individual company's beta will revert toward the mean over time. For example, if a company's historical beta is less than 1.00, then the predicted beta will be greater than the historical beta but less than 1.00. Similarly, if the historical beta is greater than 1.00, the predicted beta will be less than the historical beta but greater than 1.00. It is generally advisable to use predicted beta.
Betas of comparable companies are used to estimate re of private companies, or where the shares of the company being valued do not have a long enough trading history to provide a good estimate of the beta.
Predicted beta may be calculated using one of two methods:
(A) Using the company's beta:
- De-lever the beta using the following formula:
- Unlevered β
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
Unlevered β
=
Levered β
1 + [(D/E) × (1−t) + P/E]
=
Levered β
1 + [(D/E) × (1−t) + P/E]