FM211 Flashcards
NPV
- Costs + FCFs
stand alone principle: accept project if its NPV > 0
mutually exclusive principle: accept the highest NPV project
sunk costs, financing costs, externalities, and opportunity costs are NOT included
Net income
+ overhead
+ depr
- CAPEX
- increase in NWC
(+) accounts for the time value of money and the compensation of bearing risk
Book rate of return
Book income/book assets
(-) the components reflect tax and accounting figures and aren’t market values/ CFs
(-) time value of money is ignored
(-) only considers averages and risk is ignored
Payback period
(-) ignores time value of money
(-) ignores all CFs after the payback period
Firm A
C0 = -2000
C1 = 500
C2 = 500
C3 = 5000
Payback = 2 + (2000 - 1000)/5000 = 2.2
IRR
when NPV = 0
(-) for financing type projects, IRR should be reversed (IRR < cost of capital)
(-) multiple IRRs
(-) no IRRs
(-) can sometimes result in incorrect decisions when projects differ in scale and/or timing of their CFs
(-) different timing of CFs
what is the depreciation tax shield? using FCF formula
FCF = EBIT(1-tax) + depr - change in NWC - CAPEX + salvage
since EBIT = EBITDA - depr
FCF = (EBITDA - depr)(1-tax) + depr - change in NWC - CAPEX + Salvage
why does depr appear twice? it is a non-cash expense that reduces a firm’s bill
FCF = EBITDA(1-tax) + depr(tax) - change in NWC - CAPEX + salvage
where depr(tax) is the depreciation tax shield
salvage value
used equipment can sometimes be sold. If the sale price of the asset > book value of it, then we need to pay tax on the gain.
The after tax proceeds of this sale (“the salvage value”) is a CF that increases FCF
salvage value = sale price - (gain on sale x tax)
gain on sale = sale price - BV
BV = initial investment - AD
inflation
1 + r(real) = (1+rnormal)/(1+inflation)
profitability index
NPV/investment
Equivalent annual CF
equivalent annual CF (EAC) of a project is the equal CF per period with the same PV as the actual CFs of the project. When the CFs are costs, this is called equivalent annual costs.
EAC = PV(CFs)/ annuity factor
Real option
the right but not the obligation to modify a project in the future
- the abandonment option
- the growth option
- the timing option
CAPM formula
E(Ri) = rf + Bi(Erm - rf)
Option pricing theory
- an early exercise of an american call on a non-divident paying stock is never optimal i.e. it’s better to wait
- early exercise might be optimal for a dividend paying stock (foregone dividend = cost of waiting)
real options are valuable. In this case, the value came from avoiding bad projects. Actions that create real options are also valuable. Waiting can be costly if valuable production opportunities (e.g. revenues) are sacrificed -> similar to losing dividends when delaying the exercise of an American Call Option.
The abandonment option + its steps
the project may no longer be profitable going forward, value comes from reducing/avoiding future losses
-> use backwards induction! give optimal abandonment decision at t=1, what is the t=0 value?
1) draw a decision tree
2) find E(P1) and E(P2)
3) work out the NPV by doing cost - currently selling for all CFs (NPV without option)
4) avoid scenarios that produce negative net CFs
5) insert zeros at nodes where CF is negative and recalculate NPV
6) find all distinct scenarios and multiply by CFs
IF given permanent abandonment option (option to sell):
1) work out CFs at each node and compare with cost of selling
2) use backwards induction and decide if you should sell the company today/next year
3) the node with the positive cash flow can be plotted against the selling option on a decision tree and be used to work out Vfirm.
expected PV gain of abandonment option
= selling price - alternative option x probability/(discount rate)
option to grow/expand with steps
investment may turn out to be more profitable than expected. value comes from being able to capitalise on additional earning opportunities.
1) plot a decision tree
2) find E(CF1) and E(CF2) and E(CF1|first year high) etc…
3) workout NPV using E(CF1) and E(CF2)
4) work out the NPV for both high and low nodes of the alternative strategy
5) find the new E(CFs) and new NPV and compare without the option to expand
6) subtract both high and low demands and find the overall NPV
PV of option to grow/expand
= (Pr of opportunity x NPV) / discount rate
Option to wait + steps
even if a project has a +ve NPV today, delaying it might yield an even greater value
- intrinsic value: the profit/NPV if project is exercised immediately
- extrinsic value: the profit/NPV if you wait to exercise it
overall option value = 1+2+ time premium
(-) BUT waiting may incur lost revenues or extra costs.
Cash dividend
firm pays cash to shareholders on a pro-rate (proportionate) basis. e.g. shareholders receives $0.50 for each share held
- regular cash dividend: quarterly, semi-annual
- special cash dividend: one off
stock dividend
firm pays additional stock to shareholders on a pro-rate basis, e.g. 10% stock dividend -> shareholders receive 10 additional shares for every 100 currently held
- no actual transfer of cash to shareholders
- essentially a stock split with a much smaller split factor
declaration date
board authorises payment of dividend and announces the dividend amount
record date
only people recorded as shareholders on this date receive a dividend
ex dividend date
normally 1-2 days before record date; anyone purchasing shares on/after this date will NOT be eligible to receive the dividend
cum dividend date
the day before the ex dividend date
payment date
firm distributes dividend