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Summary - Corporate Finance (BT2107)
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Summary of all required literature and lectures for the course Corporate Finance (Erasmus University Rotterdam)
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Week 1Chapter 12: risk, cost of capital and capital budgeting
All businesses require funding for their investments and projects. The cost of capital refers to the
cost of acquiring such funding, either through equity or debt. To an investor, the rate of return that is
expected when undertaking a project is the discount rate. For a manager, the discount rate is the
cost of acquiring capital to finance the company’s investments. To decide on which investments to
undertake, understanding the risks included in a financial decision is a prerequisite. To measure risk,
the Capital Asset Pricing Model (CAPM) and Weighted Average Cost of Capital (WACC) are used.
When a firm has extra cash, it can either pay this cash out as dividends or invest this in another
project, resulting in future cash flows that can be paid out as dividends. Shareholders will always
prefer the option that has the highest expected return. This leads to the following capital budgeting
rule: “The discount rate of a project should be at least the expected return on a financial asset
(share or bond) of comparable risk.”
The expected return on equity, which is the cost of equity capital for a firm, can be calculated under
the CAPM formula: 𝑅𝐸 = 𝑅𝐹 + β * (𝑅𝑀 − 𝑅𝐹). This formula makes two assumptions: the beta risk of
new projects is the same as the risk of the firm and the firm is fully financed with equity.
For a firm completely financed by equity, the discount rate for a new project with the same beta risk
as that of the firm is equal to 𝑅𝐸. The cash flows of a future project are discounted with this rate to
obtain its net present value (NPV). If the NPV is positive, one should accept the project. Conversely,
if the NPV is negative, one should reject the project.
The internal rate of return (IRR) is another tool used to evaluate projects. A company should invest
in a project if the IRR is greater than the discount rate.
Beta refers to the riskiness of a security compared to the risk of the entire market portfolio, detailing
how responsive a security is to movements of the market. In terms of company equity, a beta of
2.38 means that for every 1% rise in the market, the equity will increase by 2.38%. The beta of the
market itself is always 1 because beta refers to the correlation of a security with the market.
,A high beta suggests that a slight shift in the market could have a significant impact on a project’s
profitability. If the market were to fall slightly, for example, a project with a high beta would be
extremely negatively impacted. There are multiple ways to derive a project beta:
1. Use the industry beta if the operations of a firm are like the operations of its industry
2. Use the company beta if the operations of a firm differ from competitors in the industry
In many cases, the company’s beta is unknown and needs to be estimated. To estimate the beta of a
𝐶𝑜𝑣(𝑅𝑖,𝑅𝑚) σ𝑖𝑀
security, the following formula can be used: 𝐵𝑒𝑡𝑎 𝑜𝑓 𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑦 𝑖 = 𝑉𝑎𝑟(𝑅𝑚)
= 2
σ𝑀
So, beta is the covariance of a market security, divided by the variance of the market. Variance refers
to how much values in a set deviate from the average, and covariance measures the degree to
which two sets move in the same direction, looking at the relationship between, for example, two
different company equities.
Problems that occur when estimating the beta of a company:
1. The sample size could be inadequate
2. Betas are influenced by changes in financial leverage (debt-equity ratio) and business risk
3. Betas can vary over time
Solutions to these problems could be:
1. The use of more sophisticated statistical techniques
2. Incorporation of fluctuations -> adjusting for changes in business and financial risk
3. The use of industry betas
Beta is determined by the cyclical nature of revenues, operating leverage and financial leverage.
Revenues of some firms are cyclical: do well in the expansion phase of the business cycle and do
poorly in the contraction phase. High-tech firms, retailers and automotive firms fluctuate with the
business cycle. Firms in industries such as utilities and food are less dependent on the cycle. Highly
cyclical securities have high betas. Cyclicality is not the same as variability, so securities with high
standard deviations need not have high betas.
The difference between variable and fixed costs allows us to define operational leverage. A firm
has high operating leverage if it has low variable costs and high fixed costs.
,Operating leverage magnifies the effect of cyclicality on beta. Business risk depends on the
responsiveness of the firm’s revenues to the business cycle and the firm’s operating leverage.
Operating leverage refers to the firm’s fixed costs of production.
Financial leverage is the extent to which a firm relies on debt, and a levered firm is a firm with some
debt in its capital structure. Because a levered firm must make interest payments regardless of the
firm’s sales, financial leverage refers to the firm’s fixed costs of finance. The asset beta can be seen
as the beta of the firm’s shares had the firm been financed only with equity.
𝐸 𝐷
- β𝑎𝑠𝑠𝑒𝑡 = 𝐷+𝐸
* β𝑒𝑞𝑢𝑖𝑡𝑦 + 𝐷+𝐸
* β𝑑𝑒𝑏𝑡
Because E/(D+E) must be lower than 1 for a levered firm, it follows that β𝑎𝑠𝑠𝑒𝑡< β𝑒𝑞𝑢𝑖𝑡𝑦. The equity
beta will always be higher than the asset beta with financial leverage.
𝐷
- β𝑒𝑞𝑢𝑖𝑡𝑦 = β𝑎𝑠𝑠𝑒𝑡(1 + 𝐸
)
If a project’s beta differs from that of the firm, the project should be discounted at the rate that
reflects project risk rather than firm risk. This is important as companies often speak of a corporate
discount rate (hurdle rate, cut-off rate, benchmark and cost of capital/WACC). Unless all projects in
the firm are of the same risk, choosing the same discount rate for all projects is incorrect.
𝐸 𝐷
The weighted average cost of capital (WACC) is ( 𝐷+𝐸 ) * 𝑅𝐸 + ( 𝐷+𝐸 ) * 𝑅𝐷 * (1 − 𝑡𝑐). If the firm
issues no debt, the cost of capital is equal to the cost of equity.
Market value weights are more appropriate than book value weights because the market values of
the securities are closer to the actual money that would be received from their sale. Target market
weights are the market weights expected to prevail over the life of the firm or project.
Lowering the risk of a firm is difficult and it is easier to
increase the liquidity of the firm’s equity, which lowers
the cost of capital. With the concept of liquidity, we
speak of the cost of selling and buying equities. Equities
that are expensive to trade are considered less liquid
than those that trade cheaply. With the cost to trade,
we consider brokerage fees, the bid-ask spread and
market impact costs.
Brokerage fees are the fees you have to pay the broker
in order for him to execute a trade. The bid-ask spread is the difference between the buying price
, and selling price, which is a cost that you are losing over a round-trip transaction. The price drop
associated with a large sale and the price rise with a large purchase are the market impact costs.
Investors demand a high expected return as compensation when investing in high-risk equities.
Because the expected return to the investor is the cost of capital to the firm, the cost of capital is
positively related to beta. Now, the same is for trading costs. Investors demand a high expected
return when investing in equities with high trading costs - that is, low liquidity. This high expected
return implies a high cost of capital to the firm.
One factor that influences liquidity is adverse selection: a counterparty will lose money on a trade if
the trader has information that the counterparty does not have. An option is to reduce the price at
which you are willing to buy or increase the price at which you are willing to sell -> the bid-ask
spread will widen, thereby increasing the costs of trading to all traders (informed and uninformed).
The spread should be positively related to the ratio of informed to uninformed traders. That is,
informed traders would pick off the market and uninformed traders not. Thus, informed traders
raise the required return on equity, thereby increasing the cost of capital. If the bid-ask spread is
lower, the firm’s equity will be more liquid.
- Adverse selection leads to higher bid-ask spreads
The corporation has an incentive to lower trading costs because a lower cost of capital should
result. There are two strategies:
1. Bring in more uninformed investors: stock splits can be useful here
2. Disclose more information, which narrows the gap between uninformed and informed
investors, thereby decreasing the cost of capital -> the bid-ask spread is reduced after the
release of financial data about corporate segments and more management forecasts
The economic value added (EVA) approach:
- (𝑅𝑂𝐴 − 𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙) * 𝑡𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
- 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 − 𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 * 𝑡𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙.
There are two problems:
1. If focuses only on current earnings, so little to offer for capital budgeting
2. It may increase the shortsightedness of managers
Three advantages of the approach:
1. It can help optimize a firm’s investment level
2. It takes into account the size of capital tied up to a project
3. It makes liquidation of a division harder to ignore
Lecture 1
The balance sheet has two sides, one with assets and the other one with
liabilities and owner’s equity. The asset side contains all the stuff that
belongs to a company. The right side (liabilities and owner’s equity) of the
balance sheet, the capital side, contains how a firm paid for its assets.
There are two main components in the asset side: current assets and fixed
assets. Current assets are assets that stay in the firm for less than a year ->
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