FIN 401 Lecture Notes - Put Option, Net Present Value, Call Option
30 Apr 2018
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Chapter 8,9,12 Capital Budgeting/Cost of Capital
• NPV = – initial cost + PV(CFs) | NPV = (CF1 / r) – CF0
• NPV = PV(bene.) – PV(costs) | PV = FV / (1+r) | FV = PV (1+i)n |
PBP = CF0 / CF | IRR 0 = (CF1 / r) – CF0 Solve for I% on Calc
o IRR’s the return dat makes NPV = 0 | Dec. Rule: Accept proj. if IRR > req. return
• Crossover Rate = Disc Rate that is indiff. b/w 2 proj.
o Enter difference of two project cash flows, CALC IRR
• CCA Deduction in Year1 = {(0.5)(UCC)} x (CCA Rate)
• (OCF) = (Annual Savings) x (1 – TC) | PV(OCF) = PMT = OCF, I% & N
• PV(Salvage Value) = Salvage Value/(1+r)n
• PV(NCS/Net CapEx) = – CapEx + PV(Salv. Val) – PV(Cap Gain Tax)
• PV(NWC) = (–NWC + PV(NWC Recaptured))recap. calc as pv(salvage)
• NPV(Replacement) = PV (OCF) + PV (NCS) + PV (CCATS)
Market Values
• E = MV of equity = (Price Per Share) (# O/S shares)
• D = MV of debt = (Price per Bond) (# O/S bonds)
o MVD = BVD x Cost of Trading at BV | V = MV of firm = E + D
• wE = E/V = % fin. w/ equity | wD = D/V = % fin. w/ debt
• CPN = (CPN Rate x Face Val.) / #CPN PMTS per year
• Cost of Debt Capital: RD = YTM(calc. bond i%) → convert to APR
• “After-Tax” Eff. Cost of Debt = (RD) x (1 – tax rate)
Cost of Equity Capital
WACC
WACC = WERE + (WDRD)(1-TC) [+
WPFDRPFD]
• Weighted Floatation Costs = WE (Fc of E) + WD (Fc of D)
Amt to Raise (Debt) = Proj. Cost / (1 – Fc), Then cont. w. reg. NPV
Chapter 6 → Capital Structure
Debt:Value Ratio = D / V | PV(Equity) = MV of Unlevered Equity
Levered Equity = Expected Cashflows – Debt Repayment
o Leverage does not increase value, but rather, increases the risk of the equity and
raises the equity cost of capital sdsdsds
MM#1 (No Taxes) 2. = VL = VU = E + D → Value is same with or
without leverage, not affected by capital structure!
1. VU = EBIT / RU | 3. E = VL – D | 4. RE = RU + (RU/RD) (D/E)
WACCPreTax = WERE + WDRD | WACCPre-Tax = RU (unlevered costof capital)
MM#2 (Taxes) and Val. Levered Firm
1. VU= [(EBIT)(1 – TC)] / RE | 2. VL= VU + D(TC) | 3. Levered Eq.: E = VL – D
4. RE = RU + (RU – RD)(D/E)(1-Tc) | 5. WACCTax = WERE + WDRD (1-Tc)
5. Value of Levered Firm = FCF / WACC
Expected Return of RE = Levered Equity / Debt – 1
MM Case 2 = Cost of Capital of Levered Equity: A higher D/E ratio leads
to higher req. return on equity, because of higher risk involved for equity-
E = MV – D | E = VL – D | Equity Div. = FCF – Interest PMT
Unlevered Equity = Debt + Levered Equity
EPS = Net Inc. / # Shares O/S | (ROE) = Net Inc. / Total Equity
Net Inc. (CFshare) = (EBIT – Int.)(1 – TC) | Inter. = Debt x Cost of Debt
Interest Tax Shield = Corp. Tax x Int. Exp.
VL = VU + PV(Interest Tax Shield) | PV(Int. Tax Shield) = Tc x D
RD → Return on Debt = Risk-Free Rate | Int. Earn. = Amt. paidto Bondholders
Higher the firm’s leverage, more the firm exploits tax advan. of debt & lower its WACC. WACC declines with lever.
Chapter 17 → Dividend Policy
• 1. Shareholder Wants Equal Dividends:
1. 2. Find Equal Dividend Value (PMT Calc):
2. Investor Wants1 vs Investor Gets2: i.e. (121,14 x 1000 =
$21, 140, 224 x 1000 = $24000)
Extra $2860 (use to buy
more shares)
3. 3. ALWAYS find new stock
price, use PV of Future
Dividend, 1st dividend been paid, THUS, NEW STOCK
PRICE: PV = 18/1.10 = $16.36 → If no Disc. Rate,
Subtract Stock Price by D1 Value
4. $2860 / $16.36 = BUY 174.82 shares, at T2, investor will
have 1174.82 shares receiving $18 dividend, = $21,140
5. NOT ENOUGH (SHORTAGE) = Holder will SELL SHARES,
6. MORE THAN ENOUGH (SURPLUS) = Holder will BUY SHARES
Cash, Equity for div PMT | Debt , Equity for repurchase
PPS = Firm Value / Shares O/S | = [Div / (g)] x (1-TC)
Equity = Ent. Value + Cash – Debt | Ent. Val = Mkt Cap. + Debt – Cash
Market Cap = Market PPS x # of Shares | Leverage Ratio = Debt / Equity
Stock Price = Market Capor FirmValue / # of shares O/S
Ex-Div. Stock Price = Price – Value of Div.
Shares Repurc. = Excess Cash / PPS
New Stock PPS After Repurch. = New Equity / New Shares O/S
New Shares O/S = Old# – Repurch.# | New Equity = Old Eq. – Repurch. $ Value
Expansion Value of Firm = FCFExpansion / Cost of Cap.
Before Repurc. Value of Firm = (FCFExisting / r) + repurchase $
Stock Div.: Add. shares instead of cash,
Stock Split: Stock div. of 50% or higher
Split → Div = 7:4 Split = 1.75 – 1 = 75% Stock Div.
Share Div = 10% Stock Div. = 100 shares x (1.1) = 110 shares
Shares O/S after Div = (Shares O/S) (1 + Stock Div%) |or (Stock Split)
PPS after Stock Div = Old Equity / New Shares O/S OR
(Old Price x Reverse Stock Split) → Ex: (split = 12:7) NewPPS =
$84 x (7/12) Chapter 23 → Leasing
1. After-Tax Rd (debt cost of capital) = (cost of debt) (1 –Tc)
USE IN CCA FORM.
2. ATLP = (Lease payment) x (1 – Tc) Use original TC, NOT
AFTER TAX
3. PV(ATLP) = PV (PMT = ATLP, n, I% = ATRd)
4. PV(CCATS) OR PV (DEP) = same as above, use ATRd for R
in form. & if dep, use calc. (ENDonly on ccats/maint )
a. Depreciation = (Initial Cost – SV) / n
Dep Tax Shield =
Dep x Tax Rate
use that as PMT to find PV
5. PV (Salvage) = SV / (1+ATRd)n | PV (Main) = PV(ATMP)
6. NAL = Initial Cost – PV(ATLP) – PV(CCATS) – PV(SV) +
PV(AT Maintenance) & for lessor jus flip signs
7. BreakEven Lease Rate Steps: 1. Indiff. LP: Set NAL = 0 &
solve for PV(ATLP) once found, find PMTBGN, I% = ATRd then
use BTLP formula
8. BTLP = ATLP/(1 – Tc)
9. No-Tax NAL for lessee = Initial Cost – PV(BTLP) – PV(Salvage) +
PV(Main) Same initial cost, just use untaxed lease and pre-tax rate in calculations
10. PV(BTLP) = PVAD [Initial lease, n, initial pre-tax borrowing rate%]
11. Indiff. No Tax LP: Set NAL = 0 & solve for PV(BTLP), once found,
find PMTBGN, use untaxed (original cost of capital)
Raising Capital
• Post-Money Valuation = Total Shares O/S x PPSnew investor paying
• Value of Shares = Shares Owned x PPSprice paid at last round
• Required Sales Proceedssolve for X: X(1 – UWFee) = Amt. Needed
• # of Shares Offered = Required Sales Proceeds / Offer Price
Firm Commitment IPO: The underwriter guarantees that it will sell all the
stock at the offer price
• Proceeds to FirmIPO Issuers = Total Shares x Offer Price
• Underwriter Profit = (OpenMarket Sell. Price – CostOffer Price) (total shares)
Regular Underwriting (Best Efforts Basis): The underwriter doesn’t guarantee the
stock will be sold, but instead tries to sell the stock for best possible price
• Proceeds to FirmIPO Issuers = #shares x (Open MarketSelling Price – UWFee)
• Underwriter Profit = (fee per share)(number of shares)
Rights: A right gives the shareholder an option to buy a specific number of
new shares from the firm at a
specified price within a specified
time: Ex: →
• #Shares Sold = Total Rights Issued / Rights Req. for Share Purc.
• Amount Raised = #Shares Sold x PPS
• New Shares O/S = Funds to be Raised / Subscription Price
• Rights Per Share = Old Shares O/S / New Shares O/S
• Value of a Right = (Pre-offer price – Sub. price) / (# of rights + 1)
Options
1. Call option – gives the owner the right, but not the obligation, to buy the underlying asset
2. Put option – gives the owner the right but not the obligation, to sell the underlying asset
Option Seller/Writer is obligated…
3. Call – option seller is obligated to SELL the asset if the option is exercised
4. Put – option seller is obligated to BUY the asset if the option is exercised
ST = MKTStockPrice @ Expiration Date | E = Exerciseor strike or locked-in
Price | P = Option Premium | Profit = Payoff – Premium
Profit Call-Option Buyer = (# options)(contract size) [Max(0, ST-E) – P]
Profit Call-Option Seller = (# options)(contract size) [P – Max(0, ST – E)]
Prof. Put-Option Buyer = (# options)(contract size) [Max(0, E-ST) – P]
Prof. Put-Option Seller = (# options)(contract size) [P – Max(0, E – ST)]
Break-Even Stock Price (Solve for ST) 0 = (#options)(contract size)[P –
max(E – ST, 0)] | Payoff = (# options)(contract size)[max(S – E, 0)]
Warrants: Security gives holder right to purchase shares at fixed price over given period
Straight Bond Value: PVA(CPNPMT, I%, n) + Par Value/(1+I%)^n
Total Value of Warrants = Bond Selling Price – SBV
Price of Warrant = Total Warrant Value / Total Warrants
Conversion Ratio = Par Value / Conversion Price
Conversion Value = Conversation Ratio x Stock Price
Minimum Bond Price = max(SBV, Conversion Value)| OPTION DETERMINANTS:
As Stock price ; call price , put price
As Exercise price ; call price , put price
As Time to expiration ; call price and put price
Greater Variance of return; call and put worth more
As Risk-free rate ; call price , put price Risk Management
Hedging: Risk reduction achieved by using contracts or trans. which provide
firm with CFs that offset its losses from price changes
Forwards / Futures Contracts:
Long position – agreeing to buy the asset at the future date (buyer)
Short position – agreeing to sell the asset at the future date (seller)
• d = CCA Rate &
r = cost of
capital
(1 )
wacc E D C
ED
rr r T
ED ED
=+-
++
For no-tax
WACC, remove
(1-Tc) and only
add PFD to
above formula if
needed
1000 stocks, $24 D1, $18 D2
Disc Rate = 10%, Current
Stock Price = $36.69
Option #2: 5 rights to buy 2 new shares for $5 each
# shares sold = (2)(100m/5) = 40 million shares
Amount raised = (40m)(5) = $200m
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Chapter 8,9,12 capital budgeting/cost of capital: npv = initial cost + pv(cfs) | npv = (cf1 / r) cf0, npv = pv(bene. ) Pv(costs) | pv = fv / (1+r) | fv = pv (1+i)n | Val) pv(cap gain tax: pv(nwc) = ( nwc + pv(nwc recaptured))recap. calc as pv(salvage) d = cca rate & r = cost of capital. E = mv d | e = vl d | equity div. Eps = net inc. / # shares o/s | (roe) = net inc. / total equity. Interest tax shield = corp. tax x int. Vl = vu + pv(interest tax shield) | pv(int. Rd return on debt = risk-free rate | int. Higher the firm"s leverage, more the firm exploits tax advan. of debt & lower its wacc. Find equal dividend value (pmt calc): investor wants1 vs investor gets2: i. e. (121,14 x 1000 = ((cid:883)+)+ (cid:884) (cid:4666)(cid:883)+(cid:4667)(cid:884) Extra (use to buy more shares: 3.
