Chapter 18

Question 1

Value of an investment at time V0 with WACC

Answer 1

V0^L = E(FCF)/(1+rWacc)^1 + E(FCF2)/(1+rWacc)^2 … E(FCFn)/(1+rWacc)^n

Question 2

Value of an investment at time V0 with WACC procedure:

Answer 2

1. Determine the expected FCF stream of the investment (unlevered!)
2. Compute the weighted average cost of capital
3. Compute the value of the investment, including the tax benefit of leverage, by
   discounting the expected FCF stream using the WACC

Question 3

value of an investment at time V0 with WACC (continuous growth)

Answer 3

V^L= deltaFCF/rWAAC -g

g = growth

Question 4

Debt capacity

Answer 4

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

Question 5

Debt capacity formula

Answer 5

◦ 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

Question 6

Adjusted Present Value method of determining the value of an investment

Answer 6

Calculate the unlevered value:

1. Obtain the unlevered cost of capital for the firm rU
2. Discount the FCF stream at this unlevered cost of capital
   Add the value of the interest tax shield

Question 7

Unlevered firm value
ru = rwaac (for calculation)

Answer 7

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

Question 8

Interest tax shield =

Answer 8

Interest payments * corporate income tax

Interest payments = cost of debt * debt previous year end (rd * Dt+1)

Question 9

Target leverage ratio

Answer 9

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

Question 10

what discount rate to use to determine PV(ITS) ((interest tax shield)

Answer 10

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%)

Question 11

Total project value APV method

Answer 11

VL = FCF/unlevered cost of capital + PV(Interest tax shield) (discounted at waac)

Question 12

APV method project value method summary

Answer 12

1. Determine the FCF stream of the investment (unlevered!)
2. Derive the unlevered cost of capital from the pre-tax weighted average cost of capital
3. Obtain the unlevered value by discounting the FCF stream at the unleveredcost of capital
4. 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)
5. Add the unlevered value to the present value of the interest tax shield in order to determine the value of the investment with leverage

Question 13

When is APV method better than WACC method

Answer 13

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

Question 14

Flow to equity method of project value

Answer 14

1. 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)
2. Discount the FCFE stream at the equity cost of capital

Question 15

FCFE formula

Answer 15

FCF - (1+Tc)*interest + delta(debt capacity)

or

Net borrowing - Free cash flows

Question 16

PV(FCFE) =

Answer 16

NPV

Question 17

Advantages and disadvantages of FCF method

Answer 17

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

Question 18

peer group” analysis

Answer 18

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

Question 19

cost of equity capital formula

Answer 19

rE = ru + (ru -rd)*D/E

ru = pretax WAAC

Question 20

incremental leverage

Answer 20

This is the change in the firm’sdebt (net of cash) with the project versus without the project

Question 21

Predetermined debt levels

Answer 21

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

Question 22

Issuance costs

Answer 22

Intermediairies such as banks charge underwriting fees

These should be included as part of the project’srequired investment, reducing its NPV

Question 23

Security mispricing

Answer 23

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