Samenvatting ondernemingsfinanciering en vermogensmarkten
Introduction
NPV and market value
• Investment project within a firm
◦ Investment outlay I0 = Capital expenditure + ΔNWC
◦ Projected cash flows E(CFt ), using all-equity fiction
◦ Cost of capital, applicable to the project (rp )
• Project value = PV =
◦ = current market value of additional cash flow stream for the firm
◦ but this is only obtainable after paying the investment outlay I0
• Net Present Value = NPV = PV − I0
• NPV is identical to the increase in firm market value: NPV = ∆V
Project discount rate (rp )
• Reflects the risk embedded in the project cash flows
• As perceived by the capital market
• Only the systematic part of the risk is relevant (CAPM)
• Which is measured by the project’s beta-coefficient (β)
• The project’s risk (βp ) is not necessarily equal to that of the existing projects in the firm (β)
• Therefore
What is still missing?
• In determining expected cash flows, we continue to use the all-equity assumption
• But firms are usually financed with equity and debt -> Not in the expected cash flows, but in
the relevant cost of capital
• rwacc = weighted average cost of capital
• Use information sources in order to calculate the equity beta (βE )
• Determine the equity cost of capital (rE ) using the CAPM
• Determine the beta of debt (βD ) and the cost of debt capital (rD )
• Combine this into the weighted average cost of capital
• Use this rwacc to discount the (all-equity) expected cash flows
,Chapter 14
Condensed balance sheet
Adjusted balance sheet
• This defines (net) productive assets as closely as possible
• This asset total is financed by capital market investors by using explicit financing
agreements or securities
Case: start up a new firm
• Strategy, management team (MT)
• Business plan is ready, which includes current investment:
◦ Capital expenditures in fixed assets, i.e. CapEx
◦ Operational net working capital, i.e. ΔNWC
• It also includes expected cash flows, resulting from investing and pursuing the strategy
• However: MT-members are not able to fund the investment outlay themselves
• So they have to attract external capital and issue securities on the capital market
• What capital structure should the MT choose?
• I.e. what relative proportions (or “package”) of debt, equity and other securities should they
issue in order to finance the firm’s initial investment
• Business plan reveals:
◦ Investment outlay = 800 at time 0
◦ Cash flow at time 1 is depending on the state of the economy: 1400 (strong) or 900
(weak), with equal probability
◦ The current risk-free interest rate rf is 5%
◦ The projected cash flows depend on the state of the economy and therefore contain
market risk
◦ Capital markets are expected to demand a risk premium for this type of risk of 10%
over the current risk-free interest rate
• So rwacc is equal to 15%
,All-equity financing
• Since its NPV is positive, this is an interesting investment project
• But it can only be executed after the initial funding is provided for
• Suppose the MT resorts to all-equity financing, what amount can it raise from a share issue?
◦ We call this unlevered equity = equity in a firm with no debt
◦ The unlevered equity cash flows are equal to that of the firm
◦ Assuming that the capital markets are competitive, outside investors are willing to
pay up to 1000 in return for 100% of the equity, since
Unlevered equity returns
• Expected unlevered equity return =
• This is a fair return (expected return is the same as cost of capital)
Levered equity alternative
• Suppose the MT considers the following alternative financing package
◦ Borrow 500 (debt)
◦ Issue equity for the remainder (levered equity = equity in a firm that also has debt
outstanding)
• Even the lowest cash flow outcome is large enough to repay the debt with interest, so the
debt is entirely risk-free
◦ The MT can borrow at the risk-free rate in competitive capital markets (i.e. at 5%)
◦ And the total debt payment is 500(1.05) = 525 (= interest + repayment)
• Note that the company’s cash flow will now be divided between the debt and equity
providers
Law of One Price
• The cash flows of both debt and levered equity sum to the firm’s cash flow
• By the Law of One Price, the combined debt and equity package value must be equal to
1000
• So the levered equity value is equal to 500
Deciding between both financing packages
• The cash flows of levered equity are smaller than those of unlevered equity
• So the issue amount of levered equity is lower than with unlevered equity
• But the total financing package still yields 1000
, • And the MT will be indifferent between both packages
Leverage and return on equity
• Levered equity cash flows are not only smaller, but the spread in levered equity returns is
also higher: levered equity is more risky
• So levered equity cash flows may not be discounted at the same (unlevered) discount rate
• We should use a higher discount rate
Expect returns on (un)levered equity
• The risk premium is twice as high for levered equity
• Levered equity holders require 25% return in order to compensate them for the increased
risk
Cost of capital and leverage
• So rwacc is equal in both the unlevered and levered financing packages
• The suggested advantage of cheaper debt is annihilated by a compensating rise in the cost of
levered equity, such that for the market value of the firm
EU = 𝐕𝐔 = 𝐕𝐋 = EL + D
• There is no net present value to be created by choosing whatever financing package
• This is the famous Proposition I of Modigliani and Miller (MM I)
• rwacc does not change for different values of debt
• Cost of levered equity rises sharply for higher debt levels
Modigliani-Miller I (MM I)
• MM I holds under a set of conditions that defines a perfect capital market:
◦ Investors and firms can trade the same set of securities at competitive market prices
equal to the present value of their future cash flows
◦ There are no taxes, transaction costs or issuance costs associated with security
trading
◦ A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them
• In such a setting, the Law of One Price implies that leverage will not affect the total value of
the firm
◦ Total firm value is equal to the market value generated by its assets and is not
affected by its choice of capital structure
◦ Leverage only changes the allocation of cash flows between debt and equity, without
Introduction
NPV and market value
• Investment project within a firm
◦ Investment outlay I0 = Capital expenditure + ΔNWC
◦ Projected cash flows E(CFt ), using all-equity fiction
◦ Cost of capital, applicable to the project (rp )
• Project value = PV =
◦ = current market value of additional cash flow stream for the firm
◦ but this is only obtainable after paying the investment outlay I0
• Net Present Value = NPV = PV − I0
• NPV is identical to the increase in firm market value: NPV = ∆V
Project discount rate (rp )
• Reflects the risk embedded in the project cash flows
• As perceived by the capital market
• Only the systematic part of the risk is relevant (CAPM)
• Which is measured by the project’s beta-coefficient (β)
• The project’s risk (βp ) is not necessarily equal to that of the existing projects in the firm (β)
• Therefore
What is still missing?
• In determining expected cash flows, we continue to use the all-equity assumption
• But firms are usually financed with equity and debt -> Not in the expected cash flows, but in
the relevant cost of capital
• rwacc = weighted average cost of capital
• Use information sources in order to calculate the equity beta (βE )
• Determine the equity cost of capital (rE ) using the CAPM
• Determine the beta of debt (βD ) and the cost of debt capital (rD )
• Combine this into the weighted average cost of capital
• Use this rwacc to discount the (all-equity) expected cash flows
,Chapter 14
Condensed balance sheet
Adjusted balance sheet
• This defines (net) productive assets as closely as possible
• This asset total is financed by capital market investors by using explicit financing
agreements or securities
Case: start up a new firm
• Strategy, management team (MT)
• Business plan is ready, which includes current investment:
◦ Capital expenditures in fixed assets, i.e. CapEx
◦ Operational net working capital, i.e. ΔNWC
• It also includes expected cash flows, resulting from investing and pursuing the strategy
• However: MT-members are not able to fund the investment outlay themselves
• So they have to attract external capital and issue securities on the capital market
• What capital structure should the MT choose?
• I.e. what relative proportions (or “package”) of debt, equity and other securities should they
issue in order to finance the firm’s initial investment
• Business plan reveals:
◦ Investment outlay = 800 at time 0
◦ Cash flow at time 1 is depending on the state of the economy: 1400 (strong) or 900
(weak), with equal probability
◦ The current risk-free interest rate rf is 5%
◦ The projected cash flows depend on the state of the economy and therefore contain
market risk
◦ Capital markets are expected to demand a risk premium for this type of risk of 10%
over the current risk-free interest rate
• So rwacc is equal to 15%
,All-equity financing
• Since its NPV is positive, this is an interesting investment project
• But it can only be executed after the initial funding is provided for
• Suppose the MT resorts to all-equity financing, what amount can it raise from a share issue?
◦ We call this unlevered equity = equity in a firm with no debt
◦ The unlevered equity cash flows are equal to that of the firm
◦ Assuming that the capital markets are competitive, outside investors are willing to
pay up to 1000 in return for 100% of the equity, since
Unlevered equity returns
• Expected unlevered equity return =
• This is a fair return (expected return is the same as cost of capital)
Levered equity alternative
• Suppose the MT considers the following alternative financing package
◦ Borrow 500 (debt)
◦ Issue equity for the remainder (levered equity = equity in a firm that also has debt
outstanding)
• Even the lowest cash flow outcome is large enough to repay the debt with interest, so the
debt is entirely risk-free
◦ The MT can borrow at the risk-free rate in competitive capital markets (i.e. at 5%)
◦ And the total debt payment is 500(1.05) = 525 (= interest + repayment)
• Note that the company’s cash flow will now be divided between the debt and equity
providers
Law of One Price
• The cash flows of both debt and levered equity sum to the firm’s cash flow
• By the Law of One Price, the combined debt and equity package value must be equal to
1000
• So the levered equity value is equal to 500
Deciding between both financing packages
• The cash flows of levered equity are smaller than those of unlevered equity
• So the issue amount of levered equity is lower than with unlevered equity
• But the total financing package still yields 1000
, • And the MT will be indifferent between both packages
Leverage and return on equity
• Levered equity cash flows are not only smaller, but the spread in levered equity returns is
also higher: levered equity is more risky
• So levered equity cash flows may not be discounted at the same (unlevered) discount rate
• We should use a higher discount rate
Expect returns on (un)levered equity
• The risk premium is twice as high for levered equity
• Levered equity holders require 25% return in order to compensate them for the increased
risk
Cost of capital and leverage
• So rwacc is equal in both the unlevered and levered financing packages
• The suggested advantage of cheaper debt is annihilated by a compensating rise in the cost of
levered equity, such that for the market value of the firm
EU = 𝐕𝐔 = 𝐕𝐋 = EL + D
• There is no net present value to be created by choosing whatever financing package
• This is the famous Proposition I of Modigliani and Miller (MM I)
• rwacc does not change for different values of debt
• Cost of levered equity rises sharply for higher debt levels
Modigliani-Miller I (MM I)
• MM I holds under a set of conditions that defines a perfect capital market:
◦ Investors and firms can trade the same set of securities at competitive market prices
equal to the present value of their future cash flows
◦ There are no taxes, transaction costs or issuance costs associated with security
trading
◦ A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them
• In such a setting, the Law of One Price implies that leverage will not affect the total value of
the firm
◦ Total firm value is equal to the market value generated by its assets and is not
affected by its choice of capital structure
◦ Leverage only changes the allocation of cash flows between debt and equity, without
