Week 1
Basic principles of investing
- Investor perspective: investors provide equity for an expected return and debt for a
“promised yield”
- Firm perspective: to receive equity, firms have to offer a return that reflects the riskiness
of the investment, this return is referred to as the cost of equity. To receive debt, firms
have to pay interest, the expected cost related to interest payment is referred to as cost
of debt
- An investment is attractive if it at least earns the cost of equity and debt, and creates
(shareholder) value if it earns more than the weighted average of cost of equity and cost
of debt
Intrinsic value
If the project is financed with debt, then calculate the present value for equity and debt
separately by adding the required return to the asset class and use the discount rate for that
asset class. It does not matter how the project is financed, the present value stays the same
Income statement
Sales
- COGS (cost of goods sold)
= EBITDA
- Depreciation
= EBIT
- Interest expense
= Pretax income
- Taxes
= Net income
Interest expenses reduce taxable income, so taxes go down by interest expense × tax rate.
This reduction in taxes is usually referred to as tax shield
Tax shield in valuation
- Method 1: adjust discount rate (DCF-WACC)
o Forecast cash flows for 100% equity-financed firm
o Discount at weighted average cost of capital (WACC)
- Method 2: adjust cash flows (Adjusted Present Value)
o Forecast cash flows for 100% equity-financed firm, discount at unlevered cost of
capital (is equal to the cost of capital)
o Forecast tax shield based on actual leverage. If leverage stays constant, discount
at unlevered cost of capital (tax shield as risky as firm value). If leverage does not
stay constant, discount at cost of debt because debt has a different risk profile than
firm value
- Alternative method: Free Cash Flow to Equity
o Forecast cash flows to equity holders, i.e. subtract interest expense
o Discount at cost of equity
Valuation methods
$#$ $#$ $#$
𝑉!"#$%&'## = ()* ! + (()* % )% + ⋯ + (()* & )& + ⋯
"#$$ "#$$ "#$$
$#$ $#$ $#$ /0! /0% /0&
𝑉!'-. = ()*! + (()* %)% + ⋯ + (()* &)& + ⋯ + ()* + % + ⋯+ & +⋯
' ' ' '_)*_+ 1()*'_)*_+ 2 1()*'_)*_+ 2
$#$3! $#$3% $#$3&
𝐸!$#$3 = + (()* %
+ ⋯ + (()* &
+⋯
()*, ,) ,)
FCFs grow at constant rate
If both the growth rate and the discount rate remain stable, we have
, ()4 5 $#$!
𝑃𝑉! = 𝐹𝐶𝐹! ∗ ∑6
57( 6 ()* 7 = *%4
if 𝑟 > 𝑔. If the leverage stays constant, use the unlevered
cost of capital as 𝑟
Free cash flows
Free cash flows = cash inflow – cash outflow
Cash inflow = sales – cost of goods sold
Cash outflow = capital expenditure (CAPEX) + investment in working capital + taxes
Forecast cash flows
Always start with sales as of today. If it is a future project: start with assumption.
- Step 1: forecast sales growth, immediate and perpetual growth rate
- Step 2: express other cash flow relevant items in % of sales
- Step 3: compute FCFs
Calculate discount rated
We have the cost of debt (𝑟" ), cost of equity (𝑟3 ), tax rate (𝜏8 ) and leverage (𝐷/𝑉).
3 "
WACC: 𝑟&'## = 𝑟3 + 𝑟" (1 − 𝜏8 )
. .
3 "
Unlevered cost of capital (equal to return on assets): 𝑟9 = 𝑟3 . + 𝑟" .
Cash flow computation
Step 1: calculate taxes Step 2: calculate cash flows
Sales in 𝑡 = 1 EBIT
- COGS - Taxes
= EBITDA = EBIAT
- Depreciation + Depreciation
= EBIT - CAPEX
× Tax rate - Investment in WC
= Taxes = 𝐹𝐶𝐹9 (unlevered firm)
- Depreciation is first subtracted to calculate earnings and taxable income
- After that all non-cash items are added back to calculate cash flows
- PPE is Property, Plant and Equipment: illiquid assets
- Working capital = current assets – current liabilities: net liquid assets
- CAPEX = depreciation + change in PPE
- Change in net PPE is the new PPE (old PPE x growth rate) minus old PPE
- Investment in WC is new WC (old WC x growth rate) minus old WC
Immediate and perpetual growth rate
If there is for example an immediate growth rate for the first three years and a perpetual
$#$ $#$ $#$ )/.
growth rate for the years after that, then 𝑉! = ()* ! + (()* % )% + (()* - -)- , where 𝑇𝑉:
"#$$ "#$$ "#$$
is the total value after year 3
Debt capacity
The debt capacity of a project when the debt-equity ratio stays the same is the present value
of that project times the leverage
APV vs DCF-WACC vs FCFE
WACC is the easiest to use when the firm will maintain a fixed debt-to-value ratio. APV is more
complex to calculate, because it requires solving for the project’s debt and value
simultaneously. However, APV is better in situations where the leverage changes over time.
FCFE is typically used only in complicated settings for which the values of other securities in
the firm’s capital structure or the interest tax shield are themselves difficult to determine
Free cash flow to equity (FCFE)
The free cash flow that remains after adjusting for interest payments, debt issuance, and debt
repayment. 𝐹𝐶𝐹𝐸 = 𝐹𝐶𝐹 − (1 − 𝜏8 ) × (interest payment) + net borrowing
Basic principles of investing
- Investor perspective: investors provide equity for an expected return and debt for a
“promised yield”
- Firm perspective: to receive equity, firms have to offer a return that reflects the riskiness
of the investment, this return is referred to as the cost of equity. To receive debt, firms
have to pay interest, the expected cost related to interest payment is referred to as cost
of debt
- An investment is attractive if it at least earns the cost of equity and debt, and creates
(shareholder) value if it earns more than the weighted average of cost of equity and cost
of debt
Intrinsic value
If the project is financed with debt, then calculate the present value for equity and debt
separately by adding the required return to the asset class and use the discount rate for that
asset class. It does not matter how the project is financed, the present value stays the same
Income statement
Sales
- COGS (cost of goods sold)
= EBITDA
- Depreciation
= EBIT
- Interest expense
= Pretax income
- Taxes
= Net income
Interest expenses reduce taxable income, so taxes go down by interest expense × tax rate.
This reduction in taxes is usually referred to as tax shield
Tax shield in valuation
- Method 1: adjust discount rate (DCF-WACC)
o Forecast cash flows for 100% equity-financed firm
o Discount at weighted average cost of capital (WACC)
- Method 2: adjust cash flows (Adjusted Present Value)
o Forecast cash flows for 100% equity-financed firm, discount at unlevered cost of
capital (is equal to the cost of capital)
o Forecast tax shield based on actual leverage. If leverage stays constant, discount
at unlevered cost of capital (tax shield as risky as firm value). If leverage does not
stay constant, discount at cost of debt because debt has a different risk profile than
firm value
- Alternative method: Free Cash Flow to Equity
o Forecast cash flows to equity holders, i.e. subtract interest expense
o Discount at cost of equity
Valuation methods
$#$ $#$ $#$
𝑉!"#$%&'## = ()* ! + (()* % )% + ⋯ + (()* & )& + ⋯
"#$$ "#$$ "#$$
$#$ $#$ $#$ /0! /0% /0&
𝑉!'-. = ()*! + (()* %)% + ⋯ + (()* &)& + ⋯ + ()* + % + ⋯+ & +⋯
' ' ' '_)*_+ 1()*'_)*_+ 2 1()*'_)*_+ 2
$#$3! $#$3% $#$3&
𝐸!$#$3 = + (()* %
+ ⋯ + (()* &
+⋯
()*, ,) ,)
FCFs grow at constant rate
If both the growth rate and the discount rate remain stable, we have
, ()4 5 $#$!
𝑃𝑉! = 𝐹𝐶𝐹! ∗ ∑6
57( 6 ()* 7 = *%4
if 𝑟 > 𝑔. If the leverage stays constant, use the unlevered
cost of capital as 𝑟
Free cash flows
Free cash flows = cash inflow – cash outflow
Cash inflow = sales – cost of goods sold
Cash outflow = capital expenditure (CAPEX) + investment in working capital + taxes
Forecast cash flows
Always start with sales as of today. If it is a future project: start with assumption.
- Step 1: forecast sales growth, immediate and perpetual growth rate
- Step 2: express other cash flow relevant items in % of sales
- Step 3: compute FCFs
Calculate discount rated
We have the cost of debt (𝑟" ), cost of equity (𝑟3 ), tax rate (𝜏8 ) and leverage (𝐷/𝑉).
3 "
WACC: 𝑟&'## = 𝑟3 + 𝑟" (1 − 𝜏8 )
. .
3 "
Unlevered cost of capital (equal to return on assets): 𝑟9 = 𝑟3 . + 𝑟" .
Cash flow computation
Step 1: calculate taxes Step 2: calculate cash flows
Sales in 𝑡 = 1 EBIT
- COGS - Taxes
= EBITDA = EBIAT
- Depreciation + Depreciation
= EBIT - CAPEX
× Tax rate - Investment in WC
= Taxes = 𝐹𝐶𝐹9 (unlevered firm)
- Depreciation is first subtracted to calculate earnings and taxable income
- After that all non-cash items are added back to calculate cash flows
- PPE is Property, Plant and Equipment: illiquid assets
- Working capital = current assets – current liabilities: net liquid assets
- CAPEX = depreciation + change in PPE
- Change in net PPE is the new PPE (old PPE x growth rate) minus old PPE
- Investment in WC is new WC (old WC x growth rate) minus old WC
Immediate and perpetual growth rate
If there is for example an immediate growth rate for the first three years and a perpetual
$#$ $#$ $#$ )/.
growth rate for the years after that, then 𝑉! = ()* ! + (()* % )% + (()* - -)- , where 𝑇𝑉:
"#$$ "#$$ "#$$
is the total value after year 3
Debt capacity
The debt capacity of a project when the debt-equity ratio stays the same is the present value
of that project times the leverage
APV vs DCF-WACC vs FCFE
WACC is the easiest to use when the firm will maintain a fixed debt-to-value ratio. APV is more
complex to calculate, because it requires solving for the project’s debt and value
simultaneously. However, APV is better in situations where the leverage changes over time.
FCFE is typically used only in complicated settings for which the values of other securities in
the firm’s capital structure or the interest tax shield are themselves difficult to determine
Free cash flow to equity (FCFE)
The free cash flow that remains after adjusting for interest payments, debt issuance, and debt
repayment. 𝐹𝐶𝐹𝐸 = 𝐹𝐶𝐹 − (1 − 𝜏8 ) × (interest payment) + net borrowing
