NPV = PVinflows – PVoutflows
IRR = i that makes NPV = 0
UAS – annuity that = PV of irregular cash flow pattern
Ri = realized asset = expected return
ß=1 ⇒ average risk ß<1 ⇒ below average risk ß>1 ⇒ above average risk
CAPM relates a security's relevant risk (ß) to expected return.
NPV (loan) = Amount borrowed – PV (all after-tax payments)
APV (Adjusted PV) = All equity value – PV(FC) + NPV(loan)
- Calculate NPV for all-equity financing
- Adjust NPV for flotation costs
- Adjust NPV for tax shield + subsidization
WACC (weighted average cost of capital)
{D + E = V}
Pure Play Method
- Find publicly traded company with business similar to proposed project.
- Determine equity beta (ße) for pre-play firm's stock.
- Calculate pure-play assets ßA
Loan $ = Gross Proceeds (1 – FC%)
When to Lease?
If there is a tax differential or if the lease lowers transaction costs and/or reduces uncertainty
RRRD = Rf + ßD[Rm – Rf]
RRRA = Rf + ßA[Rm – Rf]
ROE = ROA + D/E[ROA – Rf]
ROA = RRREu = Rf + ßA[Rm – Rf] - expected return on an un-levered firm's assets
RRREl = RRREu + D/E [RRREu – RRRD]
ROA = [E/(D+E)](ROE) + [D/(D+E)](Rf)
ßA = [D/(D+E)]( bD) + [E/(D+E)]( ßE)
ßE = ßA + D/E(ßA – ßD)
E(RE) = Rf + ßE [E(Rm) – Rf] - M&M CAPM (Equity)
Payout Ratio = % Earnings paid as dividends
Retention Ratio = 1 – Payout Ratio
g = (Retention Ratio)(ROE)
ROE = NI/Earnings = Earnings/Book Equity
PVGO = PV[PV(cash inflows at time t) – PV(cash outflows at time t)] – present value growth option
Valuefirm = Cost of Assets + PV(OCF)
E = VF – D {D = amount borrowed/rD}
Pre-Offer Post-Offer
# shares 600,000 750,000
Value of Equity $60,000,000 $70,500,000
Price/Share $100 $94
{$94 figure calculated based on offering price}
1 share offered for $70 + 4 rights {150,000 new shares offered ⇒ $10,500,000 add'l equity}
⇒ 4 rights = $94 - $70 = $24
⇒ 1 right = $6
M&M (Modigliani and Miller)
Proposition 1: method of structuring D/E has no effect on firm value
Proposition 2: cost of equity capital increases as amount of debt increases
Assumes:
- No taxes
- No transaction costs
- No changes in investment policy
