Hoorcollege 1
NPV and market values
● Investment project within a firm
○ Investment outlay I0 = CapEX +∆𝑁𝑊𝐶
○ Projected cash flows E(CFt), using all-equity fiction
○ Cost of capital, applicable to the project (rp)
𝑇 𝐸(𝐶𝐹𝑡)
● Project value = 𝑃𝑉 = ∑ 𝑡
𝑡 = 1 (1 + 𝑟𝑝)
○ = current market value of additional cash flows 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 relevant (CAPM)
● Which is measures 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 𝑟𝑝 = 𝑟𝑓 + [𝐸(𝑅𝑚𝑘𝑡) − 𝑟𝑓]β𝑃
● 𝐸(𝑅𝑚𝑘𝑡) − 𝑟𝑓 = market risk premium
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
● Should this not be included in the (N)PV calculation?
Yes surely
● 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
● Determine the equity cost of capital using the CAPM
● Determine the beta of debt and the cost of debt capital
● Combine this into the weighted average cost of capital
𝐸 𝐷
𝑟𝑤𝑎𝑐𝑐 = 𝑟𝐴 = 𝑟𝑈 = 𝐸+𝐷
𝑟𝐸 + 𝐸+𝐷
𝑟𝐷
● Use this rwacc to discount the (all-equity) expected cash flows
In chapter 12:
● We determined the re and rd using ad hoc assumptions
● With a given financing mix of E and D amounts
● We learned that re and rd are the required returns by outside investors on equity
and debt in the company
,But don't you think that the required returns re and rd are affected by:
● The level of debt that the company already uses
● The dividend policy that the company pursues
● Tax credits or other financial subsidies that the company can exploit
● Bankruptcy threats and other financial distress
● Inside information held by board members, conveyed by their financial decisions
Expected cash flows and all-equity fiction
● Why do we determine expected cash flows using this all-equity fiction?
● This is a profound question, which relates to:
Should a company be assessed at its ability to undertake excellent real projects, or at
its qualities to make smart financial decisions?
● Many people support the first view
● But then the relevant expected cash flow definition should not include financial items
such as interest costs
● Therefore this all-equity fiction
Balance sheet presentation
● Corporate finance uses a balance sheet representation which is derived from a
‘regular’ balance sheet
● This is called the ‘adjusted balance sheet’ and it is extremely important in corporate
finance, both in this course and in practice
,Adjusted balance sheet
● Terminology
● This defines (net) productive
assets as closely as possible
● This asset total is financed by
capital market investors
● 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. ∆𝑁𝑊𝐶
● It also includes expected cash flows, resulting from the investing and pursuing the
strategy
● However: MT-members are not able to fun the investment outlay themselves
● So they have to attract external capital and issue securities on the capital market
Fundamental question
● 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
● Why is this a relevant question?
○ ‘It is just the money that is needed, so any package of securities will do as
long as it provides for the investment funding.’
○ Maybe different packages have different (net) present values!
● Lets analyse this in a highly stylized example
Business case details
● 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
Net present value
● Business plan also reveals
○ 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%
● Expected cash flow
E(CF) = ½ (1400) + ½ (900) - 1150
, ● Net present value
NPV = -800 + 1150/1.15 = -800 + 1000 = +200
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
1150
𝑃𝑉(𝑒𝑞𝑢𝑖𝑡𝑦 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑠) = 1.15
= 1000
Unlevered equity returns
● The unlevered equity value and returns are summarised below
● Fair return dat datgene wat men eist aan rendement gelijk is aan wat men krijgt
● Expected unlevered equity return = ½ (40%) + ½ (-10%) = 15%
● This is a fair return
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 + payment)
● Note that the company’s cash flow will now be divided between the debt and equity
providers:
○ Debtholders have a priority claim on this cash flow: they get paid first
○ (levered) equity holders receive the remaining cash flow: they are residual
claimholders
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
NPV and market values
● Investment project within a firm
○ Investment outlay I0 = CapEX +∆𝑁𝑊𝐶
○ Projected cash flows E(CFt), using all-equity fiction
○ Cost of capital, applicable to the project (rp)
𝑇 𝐸(𝐶𝐹𝑡)
● Project value = 𝑃𝑉 = ∑ 𝑡
𝑡 = 1 (1 + 𝑟𝑝)
○ = current market value of additional cash flows 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 relevant (CAPM)
● Which is measures 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 𝑟𝑝 = 𝑟𝑓 + [𝐸(𝑅𝑚𝑘𝑡) − 𝑟𝑓]β𝑃
● 𝐸(𝑅𝑚𝑘𝑡) − 𝑟𝑓 = market risk premium
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
● Should this not be included in the (N)PV calculation?
Yes surely
● 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
● Determine the equity cost of capital using the CAPM
● Determine the beta of debt and the cost of debt capital
● Combine this into the weighted average cost of capital
𝐸 𝐷
𝑟𝑤𝑎𝑐𝑐 = 𝑟𝐴 = 𝑟𝑈 = 𝐸+𝐷
𝑟𝐸 + 𝐸+𝐷
𝑟𝐷
● Use this rwacc to discount the (all-equity) expected cash flows
In chapter 12:
● We determined the re and rd using ad hoc assumptions
● With a given financing mix of E and D amounts
● We learned that re and rd are the required returns by outside investors on equity
and debt in the company
,But don't you think that the required returns re and rd are affected by:
● The level of debt that the company already uses
● The dividend policy that the company pursues
● Tax credits or other financial subsidies that the company can exploit
● Bankruptcy threats and other financial distress
● Inside information held by board members, conveyed by their financial decisions
Expected cash flows and all-equity fiction
● Why do we determine expected cash flows using this all-equity fiction?
● This is a profound question, which relates to:
Should a company be assessed at its ability to undertake excellent real projects, or at
its qualities to make smart financial decisions?
● Many people support the first view
● But then the relevant expected cash flow definition should not include financial items
such as interest costs
● Therefore this all-equity fiction
Balance sheet presentation
● Corporate finance uses a balance sheet representation which is derived from a
‘regular’ balance sheet
● This is called the ‘adjusted balance sheet’ and it is extremely important in corporate
finance, both in this course and in practice
,Adjusted balance sheet
● Terminology
● This defines (net) productive
assets as closely as possible
● This asset total is financed by
capital market investors
● 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. ∆𝑁𝑊𝐶
● It also includes expected cash flows, resulting from the investing and pursuing the
strategy
● However: MT-members are not able to fun the investment outlay themselves
● So they have to attract external capital and issue securities on the capital market
Fundamental question
● 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
● Why is this a relevant question?
○ ‘It is just the money that is needed, so any package of securities will do as
long as it provides for the investment funding.’
○ Maybe different packages have different (net) present values!
● Lets analyse this in a highly stylized example
Business case details
● 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
Net present value
● Business plan also reveals
○ 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%
● Expected cash flow
E(CF) = ½ (1400) + ½ (900) - 1150
, ● Net present value
NPV = -800 + 1150/1.15 = -800 + 1000 = +200
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
1150
𝑃𝑉(𝑒𝑞𝑢𝑖𝑡𝑦 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑠) = 1.15
= 1000
Unlevered equity returns
● The unlevered equity value and returns are summarised below
● Fair return dat datgene wat men eist aan rendement gelijk is aan wat men krijgt
● Expected unlevered equity return = ½ (40%) + ½ (-10%) = 15%
● This is a fair return
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 + payment)
● Note that the company’s cash flow will now be divided between the debt and equity
providers:
○ Debtholders have a priority claim on this cash flow: they get paid first
○ (levered) equity holders receive the remaining cash flow: they are residual
claimholders
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
