Capital structure and the cost of capital
Risk, Return, and Capital Budgeting (Chapter 12)
- Business risk and financial risk
Income statement
10% increase in sales revenue
Sales Revenue10001100
FC500500OPERTING LEVERAGE
VC (20% of sales)200220
Depreciation100100
EBIT (Operating income)200280
40% INCREASE IN EBIT
Interest100100FINANCIAL LEVERAGE
EBT100180
Tax (40%)4072
EAT60108
EPS (100 Shares). 61.08
80% INCREASE IN EPS
- weighted average – pure arithmetic
Assume constant Rb, Ra, and Rb<Ra
A=B+S
Ra = (B/A) Rb + (S/A) Rs
As B/A , will Rs or or remain constant?
Assume Ra and Rb constant.
Capital structure and the cost of capital (Chapter 15,16,17)
- Value of a firm = value of equity + value of interest bearing debt
- Principle of additivity (Divide and conquer or all court press)
PV(A+B) = PV(A) + PV(b)
A, B: two cash flow streams
i.e. discounting combined CF by appropriate risk-adjusted discount rate (WACC)
is equivalent to
discounting each CF by its appropriate risk-adjusted discount rate and add them.
e.g.
A has payoff $100 in one year and a =1
B has payoff $150 in one year and b=2
Market risk premium =8%
Rf=6%
- Money machine
Suppose
M&M world (Um um sweet M&M ..)
Proceeds from short sales are fully obtained.
Two firms are in the exactly same business with possible EBIT with equal probability as follows:
RecessionNormalBoom
EBIT40012002000
Firm U has 400 shares with the price of $20 per share
Firm L has 200 shares with the price of $22 per share and debt of $4,000.
In this perfect market, P/E multiple remains constant for both firms, and equals to 10.
Interest rate for both unlimited borrowing and lending by an individual as well as firms is 10%. Can you create money machine with zero cost today, and how?
Q: Show EBIT-EPS relationship?
- Whoops!
M&M world without any taxes, again
EBIT=100
All-equity (unlevered) firm: Ro=20%
- Vu = ?
- VL =?
Sell bond $250 to repurchase stock at Rb=10%
EBIT =100
I= 25
EBT= 75
Tax= 0
EAT=75
S= 75/0.2 = 375
B= 250
VL= S + B = 625 (?)
Q: Is this the correct value of VL?
- In M&M world, what is the value of a firm of unlevered and levered firm by theory?
- What is Rs and WACC of levered firm?
- M&M irrelevance - Law of conservation of value
Sure, the value of a pie is NOT independent of how it is sliced, if slicer is also a nibbler.
- Maximizing firm value = minimizing cost of capital, if operating income is fixed.
- Comment on the following: Shareholders demand – and deserve – higher expected rates of return than bondholders do. Therefore, debt is cheaper capital source. We can reduce the WACC by borrowing more.
- A perfect capital market in which M&M theory holds. – Financial manager’s job is to find market imperfection and utilize it.
e.g. Czar of junk bond, Mikel Milken
- Effect of taxes on levered firm (Death and Taxes, Oh no!, it is Debt and Taxes)
Two equivalent approaches
- VL = after-corporate tax UCF / (1+WACC)
- VL = after-corporate tax UCF / (1 + Ro) + PV of net interest tax shields
– APV approach
Ro = Cost of unlevered equity
e.g.
Tc = 35%
EBIT = $100
Plan U – No debt, Ro =20%
Plan L - $400 permanent debt with Rb =10%
Q. What are the Vu, VL, Rs and WACC?
Note: Quirk in tax on interest income and interest expense
a)cost of interest to a firm(?):
b)return to bondholder(?):
TS is tax savings or tax shield, not tax refund from IRS.
TS is tax reduction from overall tax bills, and requires positive taxable income (earnings) for some time.
IRS total tax bill is reduced
c)Norwegian quirk on person loan
Tax on interest income (lender) – tax deduction on all personal loans (borrower)
IRS total tax billl remains the same
1)Vu = ?
2)VL =?
3)Rs = ?
4)WACC = ?
PV(B+S) =PV(B) +PV(S)
After-tax UCF from Asset + TS
= after-tax CF to bondholders + after-tax CF to stockholders
5)Will stockholders accept the bond issue when total equity value declines? How many shares will be repurchased?
Suppose 100 shares for unlevered firm, and issue bond and repruchase stocks.