Corporate Finance
Chapter 12 | Risk, Cost of Capital and Capital
Budgeting
12.1 The Cost of Equity Capital
Expected Return:
𝑅𝐸 = 𝑅𝐹 + β × (𝑅𝑀 − 𝑅𝐹)
● 𝑅𝐹 = risk-free rate
● 𝑅𝑀 − 𝑅𝐹 = expected excess market return or market risk premium
● β = company beta
12.2 Estimation of Beta
𝐶𝑜𝑣(𝑅𝑖, 𝑅𝑀) σ𝑖𝑀
β𝑖 = 𝑉𝑎𝑟(𝑅𝑀)
= 2
σ𝑀
If you believe that the operations of a firm are similar to the operations of the rest of the
industry, you should use the industry beta simply to reduce estimation error. However, if an
executive believes that the operations of the firm are fundamentally different from those in
the rest of the industry, the firm’s beta should be used.
12.3 Determinants of Beta
A beta is determined by the characteristics of the firm. We consider three factors: the clinical
nature of revenues, operating leverage and financial leverage.
Cyclicality of revenues
The revenues of some firms are quite cyclical. That is, these firms do well in the expansion
phase of the business cycle and do poorly in the contraction phase. Highly cycling securities
have high betas.
Operating Leverage
Operating leverage magnifies the effect of cyclicality on beta. Projects whose revenues
appear strongly cyclical and whose operating leverage appears high are likely to have high
betas. Conversely, weak cyclicality and low operating leverage imply low betas.
Financial leverage
Financial leverage refers to the firm’s fixed costs of finance, because a levered firm must
make interest payments regardless of the firm’s sales.
𝐸 𝐷
β𝐴𝑠𝑠𝑒𝑡 = 𝐷+𝐸
× β𝐸𝑞𝑢𝑖𝑡𝑦 + 𝐷+𝐸
× β𝐷𝑒𝑏𝑡
,The asset beta can also be viewed as the beta of the company’s shares had the firm been
all equity.
𝐸
β𝐴𝑠𝑠𝑒𝑡 = 𝐷+𝐸
× β𝐸𝑞𝑢𝑖𝑡𝑦
𝐸
Because 𝐷+𝐸
,ust e below 1 for a levered firm, it follows that β𝐴𝑠𝑠𝑒𝑡< β𝐸𝑞𝑢𝑖𝑡𝑦.
𝐷
β𝐸𝑞𝑢𝑖𝑡𝑦 = β (1 + 𝐸
)
𝐴𝑠𝑠𝑒𝑡
The equity bea will always be higher than the asset bea with financial leverage (assuming
the asset beta is positive).
12.4 Extensions of the Basic Model
If a project’s beta differs from that of the firm, the project should be discounted at the rate
that reflects project’s risk rather than firm risk.
Suppose a firm uses both debt and equity to finance its investments.
The cost of debt is the firm’s borrowing rate, 𝑅𝐷, which we can often observe by looking at
the yield to maturity on the firm’s debt.
𝐶𝑜𝑠𝑡 𝑜𝑓 𝑑𝑒𝑏𝑡 (𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥) = 𝑅𝐷 × (1 − 𝑡𝑐)
The weighted average cost of capital is:
𝐸 𝐷
𝑅𝑊𝐴𝐶𝐶 = 𝐷+𝐸
× 𝑅𝐸 + 𝐷+𝐸
× 𝑅𝐷 × (1 − 𝑡𝑐)
12.5 Estimating Carrefour Group’s Cost of Capital
,12.6 Reducing the Cost of Capital
A firm can lower its cost of capital through liquidity enhancement. Here, we speak of the
costs of buying and selling. Equities that are expensive to trade are considered less liquid
than those that trade cheaply. We generally think of three costs here: brokerage fees, the
bid-ask spread and market impact costs.
Investors demand a high expected return when investing in equities with high trading costs -
that is, with low liquidity. This high expected return implies a high cost of capital to the firm.
12.7 How Do Corporations Estimate Cost of Capital in Practice?
The most commonly used method is CAPM and beta. The return investors received in the
past is the best predictor of the return investors will receive in the future.
, 12.8 Economic Value Added and the Measurement of Financial
Performance
Economic Value Added (EVA) can be calculated by:
𝐸𝑉𝐴 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 − 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 × 𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
EVA can increase investment for firms that are currently underinvesting. However, there are
many firms in the reverse situation. EVA has the advantage that it is so stark: the number is
either positive or negative. EVA analysis makes liquidation harder to ignore.
There are also some criticisms of EVA. It has little to offer for capital budgeting because it
focuses only on current earnings. Another problem is that it may increase the
shortsightedness of managers. Managers tend to have an incentive for short-term value
instead of long-term due to personal reward.
Chapter 12 | Risk, Cost of Capital and Capital
Budgeting
12.1 The Cost of Equity Capital
Expected Return:
𝑅𝐸 = 𝑅𝐹 + β × (𝑅𝑀 − 𝑅𝐹)
● 𝑅𝐹 = risk-free rate
● 𝑅𝑀 − 𝑅𝐹 = expected excess market return or market risk premium
● β = company beta
12.2 Estimation of Beta
𝐶𝑜𝑣(𝑅𝑖, 𝑅𝑀) σ𝑖𝑀
β𝑖 = 𝑉𝑎𝑟(𝑅𝑀)
= 2
σ𝑀
If you believe that the operations of a firm are similar to the operations of the rest of the
industry, you should use the industry beta simply to reduce estimation error. However, if an
executive believes that the operations of the firm are fundamentally different from those in
the rest of the industry, the firm’s beta should be used.
12.3 Determinants of Beta
A beta is determined by the characteristics of the firm. We consider three factors: the clinical
nature of revenues, operating leverage and financial leverage.
Cyclicality of revenues
The revenues of some firms are quite cyclical. That is, these firms do well in the expansion
phase of the business cycle and do poorly in the contraction phase. Highly cycling securities
have high betas.
Operating Leverage
Operating leverage magnifies the effect of cyclicality on beta. Projects whose revenues
appear strongly cyclical and whose operating leverage appears high are likely to have high
betas. Conversely, weak cyclicality and low operating leverage imply low betas.
Financial leverage
Financial leverage refers to the firm’s fixed costs of finance, because a levered firm must
make interest payments regardless of the firm’s sales.
𝐸 𝐷
β𝐴𝑠𝑠𝑒𝑡 = 𝐷+𝐸
× β𝐸𝑞𝑢𝑖𝑡𝑦 + 𝐷+𝐸
× β𝐷𝑒𝑏𝑡
,The asset beta can also be viewed as the beta of the company’s shares had the firm been
all equity.
𝐸
β𝐴𝑠𝑠𝑒𝑡 = 𝐷+𝐸
× β𝐸𝑞𝑢𝑖𝑡𝑦
𝐸
Because 𝐷+𝐸
,ust e below 1 for a levered firm, it follows that β𝐴𝑠𝑠𝑒𝑡< β𝐸𝑞𝑢𝑖𝑡𝑦.
𝐷
β𝐸𝑞𝑢𝑖𝑡𝑦 = β (1 + 𝐸
)
𝐴𝑠𝑠𝑒𝑡
The equity bea will always be higher than the asset bea with financial leverage (assuming
the asset beta is positive).
12.4 Extensions of the Basic Model
If a project’s beta differs from that of the firm, the project should be discounted at the rate
that reflects project’s risk rather than firm risk.
Suppose a firm uses both debt and equity to finance its investments.
The cost of debt is the firm’s borrowing rate, 𝑅𝐷, which we can often observe by looking at
the yield to maturity on the firm’s debt.
𝐶𝑜𝑠𝑡 𝑜𝑓 𝑑𝑒𝑏𝑡 (𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥) = 𝑅𝐷 × (1 − 𝑡𝑐)
The weighted average cost of capital is:
𝐸 𝐷
𝑅𝑊𝐴𝐶𝐶 = 𝐷+𝐸
× 𝑅𝐸 + 𝐷+𝐸
× 𝑅𝐷 × (1 − 𝑡𝑐)
12.5 Estimating Carrefour Group’s Cost of Capital
,12.6 Reducing the Cost of Capital
A firm can lower its cost of capital through liquidity enhancement. Here, we speak of the
costs of buying and selling. Equities that are expensive to trade are considered less liquid
than those that trade cheaply. We generally think of three costs here: brokerage fees, the
bid-ask spread and market impact costs.
Investors demand a high expected return when investing in equities with high trading costs -
that is, with low liquidity. This high expected return implies a high cost of capital to the firm.
12.7 How Do Corporations Estimate Cost of Capital in Practice?
The most commonly used method is CAPM and beta. The return investors received in the
past is the best predictor of the return investors will receive in the future.
, 12.8 Economic Value Added and the Measurement of Financial
Performance
Economic Value Added (EVA) can be calculated by:
𝐸𝑉𝐴 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 − 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 × 𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
EVA can increase investment for firms that are currently underinvesting. However, there are
many firms in the reverse situation. EVA has the advantage that it is so stark: the number is
either positive or negative. EVA analysis makes liquidation harder to ignore.
There are also some criticisms of EVA. It has little to offer for capital budgeting because it
focuses only on current earnings. Another problem is that it may increase the
shortsightedness of managers. Managers tend to have an incentive for short-term value
instead of long-term due to personal reward.
