FCFF and FCFE difference

FCFF - Free cash flow to firm
FCFE - Free cash flow to equity

FCFF is the cash available to bond holders and stock holders after all expense and investments have taken place.

FCFE is the cash available to stock holders after all expense, investments and interest payments to debt-holders on an after tax basis.

What is difference between FCFF and FCFE ?

The difference is the interest payment in FCFE. In FCFE you subtract the interest expense from the cash flow to do valuations. FCFF shows the obligations for both stockholders as well as bondholders whereas FCFE consider only the obligations for stockholders.

Apart from the difference mentioned above, there are two more differences which are basically related to the approach that we will use while doing valuation. How do we calculate the FCFF and FCFE?

** FCFF can be calculated by using the formulae as mentioned below:-

FCFF = EBIT (1- t) + Depreciation/Amortization – Change in Non- Cash Working Capital – Capital Expenditure

Where,
EBIT = Earnings before income tax
t  = Corporate tax rates

** FCFE can be calculated by using formula mentioned below,

FCFE = Net Income + Depreciation/Amortization – Change in Non- Cash Working Capital*(1-D) – Capital Expenditure*(1-D)

Where,
D  = Debt ratio

Now, there lies two important points about these formulas, those are as follows:-

1)      In FCFF, we use EBIT (1-t) whereas in FCFE, we use Net Income; this is because while using EBIT (1-t) in FCFF we do not consider the effect of interest payment as mentioned above.

2)      IN FCFE, we use Change in Non-Cash Working Capital*(1-D) – Capital expenditure*(1-D) whereas in FCFF we use  Change in Non-Cash Working Capital – Capital Expenditure. This is because in FCFE, we just want to concentrate on cash flow due to equity only.

To summarise:

Factors :  FCFF
Cash Flows :  Pre Debt Cash Flows
Expected Growth : Growth in Operating Income = Reinvestment rate * ROC
Discount Rate : WACC

Factors : FCFE
Cash Flows : post Debt Cash Flows
Expected Growth : Growth in Net Income = Retention ratio * ROE
Discount Rate : Cost of Equity

Leverage and Cost of Capital

Leverage
- the effects that fixed costs have on the returns that shareholders earn
- magnify returns and risks

Operating leverage
- relationship between sales revenue and EBIT

Financial leverage
- relationship between EBIT and EPS

Total leverage
- relationship between sales revenue and EPS

operating leverage and financial leverage influence a firm's beta

breakeven point = fixed costs / contribution margin
                             = fixed costs / (price - variable costs)

When contribution margin (CM) is higher, profit rises faster
The higher the fixed costs, and low variable cost, the higher the beta

Operating leverage
- comes from mix of fixed and variable cost

			if sales up by 10%
	Lite	heavy	Lite	heavy
sales volume	10000	10000	11000	11000
price	1000	1000	1000	1000
total revenue	10000000	10000000	11000000	11000000
fixed cost	5000000	2000000	5000000	2000000
variable cost (per unit)	400	700	400	700
total cost	9000000	9000000	9400000	9700000
EBIT	1000000	1000000	1600000	1300000

Degree of Operating leverage = %ΔEBIT / %ΔSales

if sales up by 10%,
DOL of Lite = 60%/10% = 6
DOL of heavy = 30%/10% = 3
- more fixed cost , DOL increases

if DOL > 1, the firm has operating leverage

Financial leverage
- comes from use of debt

	Unlevered	levered
debt	0	10000
equity	20000	10000
asset	20000	20000
tax rate	0.4	0.4
interest rate	0.12	0.12
EBIT	3000	3000
interest(12%)	0	1200
EBT	3000	1800
tax	1200	720
NI	1800	1080
ROE	9%	11%

- more EBIT goes to investors in levered firm (as in NI + interest)

- for financially leveraged firm, NI is lower, but equity base is lower too, so ROE is higher

Basic Earning Power
BEP = EBIT/total assets
- BEP is not affected by financial leverage, because EBIT is the same whether you borrow or not
- BEP is affected by operating leverage, because change in EBIT is affected by DOL

Implications
- for leverage to be positive (increase ROE), BEP must be > rd
- for firms with high profit , use more debt, to shield the profit using debt (tax shield)

Financial Derivatives

Forward and Futures

pricing:
F(t, T) = S(t) e ^ (r + u - d -y) (T-t)
where T: expiration date
r : risk free rate
u : storage cost
d : dividend yield
y : convenience yield

OTC central clearing to lower counterparty risk, such as London clearing house (LCH)

futures contracts are settled by cash settlement
futures contracts are closed  by entering into an offsetting position relative to your original position

Interest Rate Forward

notation:
2f1 - 1 year from now, 6 month rate
14f6 - 7 year from now, 3 year rate

By the principle of no arbitrage,
 (1+r1/2)(1+1f1 /2) = (1+r2/2)2, solve for 1f1
r1: 6 month spot
r2: 1 year spot

Interest Rate Swap

interest rate is implied in swap
USD/THB spot
USD LIBOR
# of days
swap point = fwd - spot
Σ PV (fixed) = Σ PV(floating)

money market rate, and bond rate affect swap rate

bank use PV01 to calculate risk
if gap > threshold, bank charge more

DV01 or PVBP
- 30 yr bond with 5.5% coupon
at yield of 5.5%, price = 100
at yield of 5.51%, price = 99.8540
DV01 = 0.146% of par
or DV01(per $1 mm par) = $1460

** take note **
- PV01 is change in market value from bumping the coupon rate by 1 bp
- DV01 is the change in market value for a 1 bp parallel shift of the yield curve

**hedge bond investment with bond futures
- use DV01
DV01 of 6 year bond with coupon of 5.5%: 712.5 per $1million par value
DV01 of 6 year bond with coupon of 5.0%: 613.1 per $1million par value
- the hedge ratio  (futures contract to sell) of 6 year bond investment against interest rate risk is
  hedge ratio = 712.5/613.1

Cross Currency Swap

- agreement between two parties to exchange principal and interest payments in two currencies over specified period
- may have or my not have initial principal exchange
- interest payments are usually not netted

basis swap (floating vs floating)

FX Forward

EUR/USD  ; ieur < iusd
EUR/USD forward, EUR appreciate
=> swap point +ve
=> EUR/USD > spot

AUD/USD  ; iaud > iusd
AUD/USD forward, AUD depreciate

=> swap point -ve
=> AUD/USD < spot

Case study:
Delox imports machine from Japan. Its revenue is in EUR, while its expense is in JPY. It expects to pay JPY 1000 million in 6 months. How to manage its FX risk?
Ans: one way is to buy JPY forward
EURJPY spot rate 129.45
6 month EURJPY forward rate 128.26

forward: bank charge bid offer spread
swap: bank will not charge bid offer spread

Financial Options

Options

components of option price

m.v of option = time premium + intrinsic value
intrinsic value: the difference of m.v of underlying and strike price of call option

Minimum value of call
American call : Ca(S0, T, X) >= max(0, S0 - X)
European call : Ce(S0, T, X) >= max(0, S0 - X(1+r)^-T)

Minimum value of put
American put : max(0, X - S0 )
European put : max(0, X(1+r)^-T - S0 )

Ca(S0, T, X) > Ce(S0, T, X) 

but prior to expiration, S0 - X(1+r)^-T > S0 - X

early exercise?

- for call , if dividend > time premium, then you exercise the call option

- for put , if interest rat is large enough

Maximum value of put

American put : X

European put: X(1+r)^-T

Put call parity

S0 = C(S0, T, X) - P(S0, T, X) + X/(1 + r )

ATM european call or ATM european put, which one has higher price?
S = c - p + pv(x)
c - p = S - pv(x)   ;   S=X for ATM option
c - p =  S - pv(S)  ;  S - pv(S) > 0
So : c > p

Put call forward parity
S0 = C(S0, T, X) - P(S0, T, X) + X/(1 + r )
F = S0(1+r)
S0 = F/(1+r)
So : F/(1+r)  = C(S0, T, X) - P(S0, T, X) + X/(1 + r )
  P(S0, T, X) = C(S0, T, X) + (X-F)/(1+r)

Binomial Model
- discrete time model
- if infinite samples, converges to BSM model
- if interval time getting smaller, converges to BSM model
p = (1+r-d) / (u -d)
c = [ pCu + (1-p)Cd ] / (1+r)
if stock price up by 20%, and down by 10%, then: u = 1.2, d = 0.9
S⁺ = Su; S^- = Sd, find Cu, Cd, then find c

Black Scholes Model
- continuous time model
- assume rf and vol are constant
- no taxes and transaction fee
- assume options are european
- assume stock price is normally distributed
- S, T, X, rf, vol -> find c

calculate implied vol
- work backwards to find it
- C, S, X, T, rf ->BSM model -> find implied vol

volatility smile
- shows implied vol is not consistent
- implied vol depends on exercise price
- violates the constant vol assumption of BSM

Implied vol > forecast vol
- option overvalued
- sell option

selling options, the trade is short volatility. if actual vol is lower than what he priced it at, he makes money

Interest rate Cap
- series of interest rate call options

Interest rate Floor
- series of interest rate put options

Fiscal Policy

Fiscal policy
- automatic stabilizer: tax revenue, unemployment benefit
- discretionary policy

tax revenue is endogenous, sensitive to the state of economy than spending

fiscal policy is planned with horizon larger than monetary policy

fiscal consolidation may increase AD, eg. expansionry fiscal contraction
- people expect lower debt, lower taxes in future
- spending cut, wage cut -> labor cost down, Investment up , profit up
- structure reform complement fiscal contraction

Interaction of fiscal and monetary policy

use stackelberg game to model the interaction of policy makers

C- cooperation , Pareto efficient equilibrium 

OM -monetary leadership, OF -fiscal leadership

Government Budget Deficit

deficitt = rBt-1 + Gt -Tt
where r: real interest rate
    Bt-1: government debt at the end of year t-1

let deficitt = Bt - Bt-1
therefore:
Bt - Bt-1 = = rBt-1 + Gt -Tt
Bt = (1+r)Bt-1 + (Gt -Tt)

-if government spending is unchanged, a decrease in taxes today will have to be offset by an increase in taxes in the future.
-the longer the government waits to increase taxes, the higher the real interest rate, and higher the increase in future taxes

Debt to GDP Ratio

Bt/Yt = (1+r)Bt-1/Yt + (Gt -Tt)/Yt
after mathematics munipulation:
Bt/Yt - Bt-1/Yt-1 = (r-g)Bt-1/Yt-1 + (Gt -Tt)/Yt
where g: GDP growth rate

How countries reduced their debt ratios
- run budget surplus, (Gt -Tt) < 0
- have low real interest rate and high GDP growth, (r - g) > 0, real interest low can be low or even negative when inflation is high.
- a large part of the decrease in debt ratios was achieved by paying bond holders a negative real interest rate on the bonds

Balanced Budget

- It means Gt = Tt
If economy is good, T up -> G up -> cause overheating

If economy is not good, T down -> G down -> econ could not recover

Therefore, balanced budget is not practical

Ricardian Equivalence

David Ricardo developed a theory about government spending and private spending. When government stimulate demand bu debt financed spending, the people will save money to pat for future tax increases (to be used to pay off the debt).
- So overall demand is unchanged

Cyclically Adjusted Deficits

It is used to indicate whether tax/revenue system is going to create deficit at Yn (output at natural full employment). If it is negative at Yn, deficit is *not* going to go down.
- We never know exact Yn, and Yn changes, so Cyclically Adjusted Deficits is not useful

Money Finance
1. Debt Monetization
Fiscal dominance of monetary policy: Central bank must do what the government tells it to do. Government issues bonds and forces CB to buy. The central bank then pays the government with the money it creates, and the government uses that money to finance its deficit. This process is called debt monetization.

2. Seignorage
The amount of good and services that government can obtain by printing money. The revenue from money creation is called seignorage.

seignorage = ΔH/P = ΔH/H * H/P
seignorage/ Y =  (ΔH/H * H/P ) / Y

If government uses seinorage to finance budget deficit of 10% of GDP, seignorage/ Y = 10%, so ΔH/H = 10% and (H/P)/Y = 1,  the growth rate of nominal money must be 10%.

International Financial Systems

Balance of Payments
The BoP accounts record all transactions between residents of a country and residents of all foreign nations.

It is composed of
- current account
- capital and finance account
- official reserve account
- statistical discrepancy : net errors and omission

Current Account
- export/import of goods and services
- net income: interest earned on foreign assets, interest paid on foreign debt
- Unilateral transfers: workers remittances from abroad, official grants

Capital and Finance Account
- capital transfer: debt forgiveness, transfer of ownership of fixed assets (it is in capital account and the amount is small)
- direct investment: greenfield investments, FDI
- portfolio investment:  debt and equity securities
- other investments: deposits and loans
- financial derivatives

CA + KA = Δ reserve

Under a flexible exchange rate regime
CA + KA = 0

BoP is a double entry system of accounts

CA: Surplus + / Deficit -
  export + / import -
KA: Net borrowing + / Net lending -
  increase in financial assets -   ; because money going out
  increase in financial liabilities +

Example: import oil
import - ; increase in financial assets +

Example: company export
export + ; increase in financial assets -

Example: borrowing from abroad
 increase in financial liabilities +
 increase in financial assets -

BoP effect on exchange rate
export ↑ -> CA surplus ↑ -> FX rate ↑

KA surplus ↑ -> demand for local currency ↑ -> FX rate ↑

reduce appreciating pressure on local currency, sell local currency, buy USD
-> reserve ↑

Interpretation of CA
- Trade balance: CA deficits reflect living beyond one's mean
- Difference in national savings and investment
Y = C + I + X - M ; ignore G
Y - C - I = X - M
S - I = X - M
it reflects high investment and low savings rate

- Timing of trade
CA deficit means choose to consume now by borrowing from abroad
CA surplus means choose to consume later by lending to abroad

consumption smoothing
- borrow from future income, and spend today

Role of International Reserves
- reduces currency speculation
- precautionary purpose, as insurance cover to smooth temporary stops in capital flows

FX Intervention
Unsterilized FX intervention
- domestic currency is sold to purchase foreign assets -> increase in international reserves - > increase in money supply -> domestic currency depreciation
Sterilized FX intervention
To counter the effect of FX intervention above, CB sells gov bond, reduces the money supply

Reserves adequacy
Traditional measures:
- Trade based : reserves to monthly import , 3-4 months
- Debt based : reserves to ST external debt ,  > 100%
- Money based : reserves to M2 ; 5-10% if flexible exchange rate
 (flexible exchange rate act as automatic stabilizer)

Drawbacks of Traditional measures
- reserves to months of imports, neglect international financial linkages
- reserves to ST external debt, neglect other liabilities (stock holdings, bond holdings)
- reserves to broad money, neglect external drain on reserves

Having reserves means intervening in FX market?

New approaches:
- BoP stress testing: scenarios looking at all BoP items
- insurance model : cost benefits of holding reserves, eg. negative carry, valuation loss
- balance sheet analysis

**BoP is flow concept, need to look at stock holdings

Case study: China's FX reserves
China's exports are larger than its imports, it is running a positive trade balance. Foreign currency flows into China via trade flows and investment flows. The more foreign currency is floating in its economy, the lower the price of that currency relative to domestic currency will be. This will have appreciation pressure on domestic currency.  To offset, the CB will sell domestic currency and buys up the foreign currency. The intervention will build up the FX reserves.

Capital Controls
- produces misallocation and corruption
- not effective in the long run (people will find a way to circumvent the restrictions)
- delay reform, money flow out because domestic investment opportunity maybe not attractive
- better to strengthen econ fundamentals, and improve bank regulation

Working Capital

Operating capital: capital used in daily operations of a business
Working capital: includes inventory, cash, raw materials, and A/R
Net Operating Working capital: measure operating liquidity of a business

NWC = CA - CL
NOWC = (CA - Cash) - CL
NWCInv (for calculating FCF) = does not include cash, cash equivalent, notes payable and current portion of debt

CA are Inventory, A/R, Prepaid expense
-- Cash, marketable securities are considered non-operating assets, not included in CA
CL is A/P, Accruals, non interesting bearing liabilities
-- Notes payable is not included in CL


When finding the net increase in working capital for the purpose of calculating free cash flow, we define working capital to exclude cash and cash equivalents as well as notes payable and the current portion of long-term debt. Cash and cash equivalents are excluded because a change in cash is what we are trying to explain. Notes payable and the current portion of long-term debt are excluded because they are liabilities with explicit interest costs that make them financing items rather than operating items.