Chapter 18 Flashcards
Value of an investment at time V0 with WACC
V0^L = E(FCF)/(1+rWacc)^1 + E(FCF2)/(1+rWacc)^2 … E(FCFn)/(1+rWacc)^n
Value of an investment at time V0 with WACC procedure:
- Determine the expected FCF stream of the investment (unlevered!)
- Compute the weighted average cost of capital
- Compute the value of the investment, including the tax benefit of leverage, by
discounting the expected FCF stream using the WACC
value of an investment at time V0 with WACC (continuous growth)
V^L= deltaFCF/rWAAC -g
g = growth
Debt capacity
The amount of debt at a particular date that is required in order to maintain the firm’starget debt
ratio (= debt/value), given the firm’srwacc
Debt capacity formula
◦ The amount of debt at a particular date that is required in order to maintain the firm’starget debt
ratio (= debt/value), given the firm’srwacc
Dt =d∙Vt^L
d = firmst target debt ratio
Vt^L = FCFt+1 +Vt+1^L / 1+rWAAC
Free cash flows + levered value / rWAAC
Adjusted Present Value method of determining the value of an investment
Calculate the unlevered value:
- Obtain the unlevered cost of capital for the firm rU
- Discount the FCF stream at this unlevered cost of capital
Add the value of the interest tax shield
Unlevered firm value
ru = rwaac (for calculation)
Unlevered cost of capital = rU = (0.50)(0.10) + (0.50)(0.06) = 8.0%
◦ Unlevered value = PV(FCF, at 8.0%) = 59.62
VU = 59.62
Interest tax shield =
Interest payments * corporate income tax
Interest payments = cost of debt * debt previous year end (rd * Dt+1)
Target leverage ratio
When a firm adjusts its debt proportionally to a project’svalue or its cash flows
The proportion need not remain constant over time, as long as it is a proportion
A constant debt-equity ratio is a special case of a target leverage ratio
what discount rate to use to determine PV(ITS) ((interest tax shield)
When the firm maintains a target leverage ratio, its future interest tax shields have similar risk to the
project’scash flows (see previous slide)
◦ So the ITS stream should be discounted at the project’sunlevered cost of capital (rU = 8%)
Total project value APV method
VL = FCF/unlevered cost of capital + PV(Interest tax shield) (discounted at waac)
APV method project value method summary
- Determine the FCF stream of the investment (unlevered!)
- Derive the unlevered cost of capital from the pre-tax weighted average cost of capital
- Obtain the unlevered value by discounting the FCF stream at the unleveredcost of capital
- Determine the present value of the interest tax shield◦ Determine the expected interest tax shield amounts
◦ Determine the appropriate discount rate to use for the interest tax shield amounts
◦ Discount the interest tax shield amounts to obtain PV(ITS) - Add the unlevered value to the present value of the interest tax shield in order to determine the value of the investment with leverage
When is APV method better than WACC method
The APV method can be easier to apply when the firm does not maintain a constant debt-equity ratio
The APV method also explicitly values market imperfections and therefore
allows to measure their contribution to firm value
Flow to equity method of project value
- Calculate the free cash flow available to equity holders (FCFE)
◦ This takes not only operational free cash flows into account, but also all payments to and from any
other financiers (i.e. debt holders) - Discount the FCFE stream at the equity cost of capital
FCFE formula
FCF - (1+Tc)*interest + delta(debt capacity)
or
Net borrowing - Free cash flows
PV(FCFE) =
NPV
Advantages and disadvantages of FCF method
It may be simpler to use when calculating the value of equity for the entire firm
◦ If the firm’scapital structure is complex (many different securities with their own cost of capital)
◦ The market values of the other securities in the firm’scapital structure are unknown
◦ It may be viewed as a more transparant method for discussing a project’sbenefit by emphasizing a
project’simplication for equity holders
We must compute the project’sdebt capacity in order to determine the interest and net borrowing
before we can make the capital budgeting decision
◦ More precisely: we must know the future market value of debt in the project before we can assess
the project’saddition to market value (circular argument)
◦ This is also a disadvantage of the APV method. The WACC method does not suffer from this
limitation
peer group” analysis
Define a group of companies that operate in the same business as the new division
◦ Obtain the unlevered cost of capital for each of these companies
◦ Estimate the unlevered cost of capital for our firm by the average of the peer group
cost of equity capital formula
rE = ru + (ru -rd)*D/E
ru = pretax WAAC
incremental leverage
This is the change in the firm’sdebt (net of cash) with the project versus without the project
Predetermined debt levels
No target debt-equity ratio, leverage ratio or interest coverage ratio. The firm
adjusts its debt according to a fixed schedule that is known in advance
Issuance costs
Intermediairies such as banks charge underwriting fees
These should be included as part of the project’srequired investment, reducing its NPV
Security mispricing
If management believes that securities are being mispriced by outsiders, then it should exploit this in
the interest of existing shareholders
◦ The gains from e.g. issuing overpriced securities should be included in the NPV of the project
◦ On the other hand, issuing underpriced securities reduces the NPV
