C12 Capital structure and valuation

Question 1

Valuation with constant debt-to-value ratio D/V

Answer 1

Determine the levered value of an investment by

(1) Calculate unlevered value and
(2) add the value of interest tax shield
* VL = APV = VU + PV*(interest tax shield)

Question 2

D/V constant: (1) Calculate unlevered value

Answer 2

VU = CFs/(1+rU)t
with rU = (E/V)rE + (D/V)rD

Question 3

D/V constant: (2) Add PV(interest tax shield)

Answer 3

(a) Determine Debt Capacity Dt = target D/V x VtL
(b) Determine Interest Paid in year t = rD x Dt-1
(c) Determine Interest Tax Shield = rD x Dt-1 x tC
(d) Get PV: Discount for each year the Interest Tax Shield with unlevered cost of capital (=pre-tax WACC)
(e) Add this PV (d) to VU (from (1)): VL = APV = VU + PV(interest tax shield)

Question 4

Valuation with constant interest coverage ratio k

Answer 4

constant interest coverage: interest payments are equal to a target fraction k of its cash flows
VL = VU + PV(interest tax shield) = (1+tCk)VU
with (1)VU = CFs/(1+rU)t, rU=pre-tax WACC
and (2) PV(tax shield) = tCk x VU

Question 5

Valuation with predetermined debt levels

Answer 5

VL = VU + PV(interest tax shield)
with VU = CFs/(1+rU)t
and rU = (E/V)rE + (D/V)rD
and PV(interest tax shield) = int. tax shieldt / (1+rD)
IMPORTANT: discount the predetermined interest tax shields via the debt cost of capital rD instead of pre-tax WACC

Question 6

Valuation with predetermined debt levels: special case permanent fixed debt

Answer 6

VL = VU + tC x D
with VU = CFs/(1+rU)t
and rU = (E/V)rE + (D/V)rD

Question 7

Which risk for the tax shield?

Answer 7

D is predetermined: rD
D/V is constant: rA

Question 8

Extending the APV method

Answer 8

Take into account other financing effects: e.g. cost of financial distress or bankruptcy, loan subsidies.
-> find appropriate discount rate and simply add PV of this factor

Question 9

+/- APV

Answer 9

+ implicit assumptions are clear, no contamination
+ works even if debt is not permanent
+ easy if level of future debt is known
+ takes into account which factors are creating value
+ flexibility: add different financing effects as separate terms
— requires to calculate future debt levels

Question 10

+/- WACC

Answer 10

+ inputs easy to get
+ easy and relatively accurate for precise debt-to-value policy
— mixes up the effects of assets and liabilities
— not flexible regarding other effects of financing, riskiness of debt, and accurate costs of hybrid securities
D/V as the target capital structure requires continous rebalancing
— assumes interest tax shields used in year they occur

Question 11

Practical implications (D/V constant, D constant)

Answer 11

If debt is rebalanced (D/V constant): Use WACC
If debt is predetermined (D constant): Use APV

Question 12

Unlevering and relevering with taxes: 3 steps

Answer 12

(1) Find comparables
(2) Unlevering
(3) Relevering

Question 13

Unlevering and relevering with taxes: (2) Unlevering

Answer 13

Question 14

Unlevering and relevering with taxes: (3) Relevering

Answer 14

Question 15

Comparison of financing options

Answer 15

all-equity (simple DCF) and constant debt (APV):
differences in project value can be explained by PV(interest tax shield)
constant debt (APV) and target debt ratio (WACC): differences in project value can be explained by 1) the amount of debt (-\> different values of the tax shield) and 2) different discount rates used