FNCE 100 FINAL CHEAT SHEETChapter 17 – Cost of Debt and Optimal Capital StructureFormulasVl = Vu + PVTS – PVCFDCFD = Costs of Financial DistressNotes Stockholders bear reduction in stock price costs from bankruptcy CFD high when:assets lost during bankrupt, assets generate volatile earnings, much of value depends on

future investment ie R&D Risk is a function of: Business risk(risk from all equity going broke) and Financial leverage(risk form

leveraging). Companies with high business risk have low leverage Agency Costs – self interested managers, exec perks, reduced effort

o Free Cash Flow Theory – lots of money to squander LBO’s – managers buy out stockholders with lots of debt at premium

o up tax shield, down agency costs, up CFD(b/c more debt)o Ideal for companies with stable cf’s tangible assets

Modern Portfolio Theory – Ch 10, 13Formulas

Return =R= ¿P0

+ P1−P0P0

= Div Yield + Capital Gain

Fisher Eq = (1+R) = (1+r)(1+h), r = real return, h = inf rate, R = nom returnAvg Risk Premium = AvgReturn - AvgRiskFreeRateVariance = Sum(x-xbar)2/n-1SD Yearly = sqrt(12)*SD[monthly]Cov(Ra,Rb) = corr(ra,rb)*SD(a)*SD(b), corr(Ra,Rb) =cov(ra,rb)/SD(ra)*SD(rb)

Rp=Xa∗Ra+Xb∗Rb, X = proportion in port, R =

expected return on assetVar(Rp) =

Xa2σ2+Xb2σ 2+2 XaXb∗cov (Ra ,Rb) = σ2 , if p = 1 = XaXb + a bσ σ σ

= responsiveness of the fund to movements in the market = βCov(Ra , Rm)

σ2mkt= ρ∗σ

σmExpected Market Return = E(Rm) = Rf + Historical Risk PremiumForecasted Stock Return = Rf + *[E(Rm)-Rf]βNotes SML – Line from Rf to Rm, B = 1. Security above SML is underpriced, below SML is overpriced. E(Rp)<E(Rc), c

below SML and is underpriced SD for individual securities: higher than those for mkt Systematic risk – market risk that you cant avoid Idiosyncratic risk – can be eliminated by diversification Expected return with any number of securities is same, only variance decreases as n increases. Expected

return graph will be horizontal, adding securities lowers risk while maintaining returnReturn and Risk – Ch 11FormulasNotes-Opportunity Set – curved line depicting possible achievable points of combinations of two securities – determined by rate return on each stock, Backward bending on left side indicates that SD decreases as return increases –due to diversification, Efficient Frontier – from min port var to highest point on ,Normal curve case is of 0 correlation, line is 100% corr, kinked < looking line is 100% negative corr-Best point on a efficient frontier curve to combine with cash is where it and the individual asset line are tangent-Beta is a measure of fund responsiveness to mkt, portfolio beta is the weighted avg of betas of individual stocks. Beta mkt = 1-Beta of a Project: Scale Enhancing Project – project has firm’s beta, Non Scale Enhancing Project – project should be discounted at beta related to project and to its leverage-Determining a project’s cost of capital:1)find industry that mirrors project 2) find re for each firm in industry 3) find ra for each firm in industry 4) find avg ra 5) rind re and rwacc for projectOptions – Ch. 22FormulasPut Call Parity: Price Underlying Stock = Price Call – Price Put + PV StrikeCovered Call: Price Underlying Stock – Price Call = -Price Put + PV StrikeBlack Scholes Model: C = S*N(d1) – Ee-Rt*N(d2)d1=[ln(S/E) + (R+ σ2/2)t]√ ( σ2t)d2 = d1-√ ( σ2t)Notes Option – contract giving owner right to by or sell an asset at a fixed price on or before a given date

o Exercising Option – buying or selling the actual stocko Strike Price – Fixed price at which holder can buy or sello Expiration Date – Maturity date, on or before it is dead

Call Option – gives owner right to buy asset at fixed price Pricing a Call Option – Exercise Price, Expiration Date, Stock Price, Variability of Underlying Asset, Interest

Rate Put Option – gives holder the right to sell 100 shares of a security at fixed price within a fixed time period Option Strategies: Straddle – Both a put and a call on the same security at the same striking price, Strangle –

Both a put and a call on the same security at different striking prices Put Call Parity – two ways of buying a protective put(buying a put then buying the underlying stock

[protective measure if you have an unrealized gain and don’t want to lose it])o Buy a put and buy the underlying stock simultaneously. Cost = price of underlying stock +

price of puto Buy the call and buy a zero coupon bond. Cost = price call + price of zero coupon bond =

price call + PV exercise price Covered Call: Buying a stock and writing the call on the stock simultaneously. == selling a put and buying a

zero coupon bondFuture and Present ValueNotes APR compounded annually = EAY APR = annual percentage rate, EAY = Effective Annual Yield APR to EAY = APR = x%, x%/12 = monthly rate, (1+monthlyrate)^12 -1 = EAY EAY to APY=EAY^12-1=monthly rate, monthly rate*12=APR= Annuity Valued at period before first period is due Annuity in advance same as annuity in arrears plus initial payment

Capital BudgetingFormulas

lRR: 0= -OF + C11+ i

, i = x then accept if I >R

CF =

(REV−CashCost ) (1−TaxRate )+TaxRate∗DepreciationCF = AT Income + Depreciation-Add in after tax salvage value discounted by T at the end of the CF line for IRR calculation [and any other one time incidental cost or revenue])-Initial investments for project are subtracted at beginning and added back discounted at the end and adjusted for taxes

EAC = PVAnn

x ART

Equivalent Annual Cost lets you compare NPV’s of different times, compare the cash flows,

pick the higherCash from Asset Sale = MV – Tax(MV-BV)Net Working Capital = Diff Current Assets – Current Liabilities, increase in NWC is an outflow, decrease is an inflowNotes-NPV Approach – Find total NPV of projected cash flows, accept if NPV >0Payback –p is the number of years before the sum of cash flows exceeds the initial outlay, P* is the amount of maximum years willing for payback, Accept if p < or equal to p*, reject if not-IRR – Internal Rate of Return -Defined as the discount rate that makes the NPV of discounted CF’s equal 0, Accept if IRR > r, reject if not-Mutually Exclusive Projects -Differing decisions between projects, one has higher NPV, one has higher IRR, Use an “Incremental Cash Flow approach to reconcile IRR ranking with that of NPV” then investment of B-A, then tells whether to follow NPV or IRR, B = A + (B-A), See if IRR of incremental investment (B-A) > r, if it is, then invest in B, At NPV A = NPV B indifferent between both, If r >= IRR (B-A), accept project A, <= accept B

-Project Interactions - Matching Cycles - Find least common denominator and compare projects over that life span, A one cycle = 10 + 5A3, 1% and B one cycle = 20 + 10A4, 1% THEN A for 4 cycles = PV A4 = A one cycle+ A/(1+R)^3,6,9 AND B for 4 cycles = PV B4 = B one cycle + B/(1+R)^4,8 - EAC = PV/xAT

R - compare the C’s of each project and choose the higher one, use generally if investments go on for a while.-Determining Cash Flow -- Cash Flow = AT Income + Depreciation, CF = (Rev – CC)(1-T) + T(Depr)-Depreciation = Tax Shield = T (Depr)Valuing StocksPROBLEMSHow to equate NPV’s through Tax rate AdjustmentEx Set tax rate so annuity of project to change is also the annuity rate of the other project. IE if you find that the NPV

of a project of cash flows is x, the annuity would be x = C * ATR, and C is the annuity rate. Set the new tax projects

annuity rate to C from the other project and find the new NPV of new project. Solve for T.Delayed Annuity – Annuity formula yields an annuity whose first payment is one year after the annuity.-Beginning Annuity – Do C0 + CAT-1

R

Infrequent Annuity – Find interest rate over the period of intermittent cash flows ie 2 yrs. (1+r)*(1+r) -1 = new rate. Find the annuity over T/intermittent years at int rate new rate.Equate PV’s of Annuities – 1)Calculate PV of Annuities, discounted to date 0 2) Calculate annual C’s that would yield a PV of PV Annuity year 0 by C x AT

r = PV, find C 3) This finds the necessary CF’s. Get Monthly or Quarterly or SemiAnnual Rate - if is 12% compounded monthly, then monthly rate = .12/12 and semiannual rate = (.12/12)6-1. If it is x% compounded annually, then quarterly rate = (1+r)1/4-1Get Nominal Cashflows – increase each item in the income statement by the inflation rate, except for depreciation or recovery of networking capital. Find nominal cash flow for each year individually, increasing each value each year by inflation. NPV and IRR for Replacement Machine – The same as two competing projects: purchase new vs keep old. Initial cost of new machine is cost of machine plus increase in net working capital. Initial cash outlay for old machine is MV of old machine plus any tax consequence. Depreciation is generally only CF considerationWhen to abandon a CF Project – abandon if the cash flow from selling the equipment is greater than the present value of the future cash flows. We need to find the sale quantity where the two are equal. Set cf from sale = NET CF per sale * Q * AN-1

R, find QBreakeven Analysis – Breakeven point is the after tax sum of the FC and the depreciation charge divided by the (selling price – VC) = Q* ----- Then to find the financial break even of an initial investment ie liscensing do EAC = investment/Annuity FactorStock Valuation – For stock valuations with a stream of changes, start at the latest div or rate change chunk, then calculate the Price at that date start date, not the date of first dividends because stocks are valued at the date before dividends. With this Px, sub it into the last value of the next earlier chunk that you evaluate, and so on.

Finding Number of Shares – Divide amount invested by the stock price. The share price is the presnt value of the cash flows, so to find the price of the stock, we need to find the cash flows. CF’s include dividends and sale price. Remember Tax.Calculating P/E Ration – Always use the current earnings under the stock price, the stock price includes future cash flows, while the current earnings do not include future earningsFinding Rate for Discounting – (1+APR/n)n = 1+EAY…. What if given APR x% that’s compounded semiannually, but want the quarterly rate?? THEN, take (1+ semiannual rate).5 -1 = quarterly rate. X% APR compounded semiannualy yields a x/5% semi annual rate. EAC Budgeting Comparison – Use EAC, matching cycles, or salvage method only when projects flows continue in perpetuity, yet if projects for some reason have a clearly established cash flow just compare the total NPV’s. Back to EAC method, after finding the NPV’s of each project, do NPV = C AT

T where C is the unknown and solve for the equivalent cash flow of each project, choose the higher cash flow. Interest Rate and Bonds – CH 8FormulasYield to Maturity = Current Yield + Appreciation to Maturity R = c*Par/P + (Par-P)/P, c = coupon rate, C*Par = interest receivedGrowth Rate in Div = Expected %age capital gain or loss on stockClean Price = Dirty Price – Accrued Interest Accrued Interest = Coupon Pmnt for period x (Fraction of Period elapsed since payment)Current Yield = Coupon Amnt/Price of Bond

P = c∗Par1+r 1

+ c∗Par+1000

(1+r 2)2

P = c∗Par1+ y

+ c∗Par+Par(1+ y)2

YTM = y = here is average of spot rates

F2 = (1+r2 )2

1+r 1−1

Expectations Hypothesis = f2 = E(1r2) Liquidity Hypothesis = f2> or < E(1r2). Buy a two year zero coupon bond or two one year zero coupon bonds. Under Expectation, those are equal when f2 = r2. Liquidity says they will only be equal when spot rate > forward rate because of risk. OR invest in 1 year bond or two year bond but sell after one year. Then forward has to be greater than the spot spot rate r2 to make them equal because of risk.1r2 = return on a bond issued one year from now maturing in two yearsNotes Assume Semiannual Compounding for Bonds If rates fall (YTM<coupon rate) bond price > P so is Premium If rates rise (YTM > coupon rate) bond price < P so is Discount Dirty Price is Invoice Price At T >1, we need 2 discount rates: r1 and r2 are spot rates. R2 likely > R1 bc of risk F2 = rate you lock in for the second year when you buy a two year bond. One year rate one year from now

implicit in the two year spot rate ie forward rateEfficient Capital Markets and Structures – CH 14Ptoday = Pyesterday + Trend+ RandomErrorArbitrage – Generating profit from simultaneous purchase and sale of substitute securities, Representativeness – deviation from rationality drawing conclusions insufficient data, conservatism – too slow to adjust new infoForms of Market Efficiency: Weak Form – Ptoday = Pyesterday + Trend+ RandomError: Market prices reflect information containted in historical prices. Investors are unable to earn abnormal returns using historical prices to predict future price movements. Semi Strong Form – In addition to historical data, market prices reflect all publicly available information. Investors with insider or pricate information are able to earn abnormal returns. Strong Form – Market prices reflect all information public or private. Investors are unable to earn abnormal returns using insider information or historical prices to predict future price movements. Abnormal Returns – investors on average merely earn what the market offers, all trades have NPV =0. Capital Structure– CH 16FormulasNotes If D/V = x, D=x*VL using VL not V! Although D+E=V, after leverage, E and V will have diff values with taxes because with taxes leverage increases

value. When you recapitalize, you have a diff number of total shares than all equity While the expected return on equity rises with leverage, risk to stockholders rises After issuing shares, cash increases and equity increases. Shareholders equally well off with debt and equity financing in a world of no taxes!Adjusted Present Value, Flows to Equity and Weighted Average Cost of Capital – CH 18APV: Value = UCF/rA + TcDAPV = NPV(all equity) + NPV(financing side effects)

Value Levered = Vu + TcD = Value Unlevered = EBIT(1-Tc)/rA

MM Prop2 = rE=rA + D/E(rA-rD) re>ra>rdRa=rwacc=D/(D+E)*rD+E/(D+E)*rE BreakEven EBIT = When Capitalization plans result in same EPSEPS = (EBIT –RDD)/SharesOutstanding EBIT-RDD gives NI, set the EPS of two cap structs == to find EBIT Vu = EBIT/WACC (no taxes)!Vu = EBIT(1-Tc)/WACCWACC = Cost of Equity Capital = RaAnnual Tax Savings from Lever = TCrDD rD = interest rate, D = amnt borrowed, TC = tax rateMM Prop1: VL=VU + PVTS = VU+TCD

Value = Debt + Equity Vu = CF/rA rA = cost of capital unlevered firm = re re = cost of equity levered

rwacc = DV

rD(1−Tc)+ EVr E

be careful…Vl = CF/rwacc rD+rE = 1 rD = borrowing rateValue Max = min(rwacc) Share Price = Equity/Shares outstanding = (value of

Common Stock – Constant growth in divs, P = Div/(r-g)Preferred Stock – Constant dividends = P = Div/rg = ROE x PB, return on equity times plowback, plowback = retained earnings/earnings = retention ration, pay out ratio = 1- plowback ratioGrowth – P = EPS/r + NPVGOGrowth does not necessarily raise share valueOnly growth generated by earnings retained and invested in positive npv projects creates positivePrice to Earnings Ratio = P/E = (1-PB)/(r – PBxROE)Cash Cow – EPS = DIV, value of stock = EPS/R Growth – NPVGO , value = EPS/r + NPVGOP/EPS = 1/R + NPVGO/EPS

FormulasP0=

¿11+r

+ ¿2

(1+r)2+ ¿3

(1+r )3….

P0 = ¿1r

Constant Dividends (Preferred

Stock)

P0 = ¿1r−g

Constant growth Dividends

ß port = weight%a(ßa)+…ß risk free = 0ß market = 1Capital Market Line – efficient set of portoflios formed by risky and riskless asset each point on line is a portfolioCAPM: Ra = Rf + ßx(Rm-Rf) ∆ = swing call/swing stockValue Arbitrage = S = ∆ * C – PV(E)PutCallParity: P+S=PV(E)+C

Call Price = S – PV(E)Call Price Arbitrage: S = [StockPrice∆/(HighS –E)]*C+LowS/(1+r)Call Intrinsic Val = S-EPut Intrinsic Val = E-S

APV = (-Outflow + PV (1-Tc)(CF) + PV(Dep Tax Shield = Tc*outflow/yrs)) + (Proceeds(Net of Flotation totatl) – Aftertax PV Int Payments – PV Principal Payments + Flotation Cost Tax ShieldPVTS = TcD = Delta(Vu and Vl)FTE: PVflow to equity = LCF/rE

LCF = (EBIT –rDD)(1-Tc)LCF = UCF – AfterTaxInterest on DebtRE=rA +D/E (1-Tc)(rA-rD)Vfirm = Vdebt+VequityWacc: NPV = UCF/rWACC - Initial InvestmentD/V+E/V=1RWACC= rA(1-Tc(D/V))Cost of Debt = YTM company bondsProblems -Finding effect on stock price immediately after funding project on all equity. NPV of move = - project cost outflow + CF/re. Price = (this NPV + total firm equity original)/#shares originally. This causes total equity to increase by NPV. To find number of shares needed to fund this project, divide project cost by new share price. Share price after purchase is made = total equity(original equity + project cost shares issued + NPV project)/(original shares + new issued shares). Share price stayed the same before and after immediately after announcement and after deal was done.-Finding effect on stock price immediately after funding project on all debt. NPV of announcement = - project cost outflow + CF/re. Price = (this NPV + original firm equity ie value)/#original shares. Share price stays same immediately after announcement and after deal is done. Price of Share after deal finalized = Equity(original + NPV project)/original shares. In absence of taxes, shareholders are equally well off with debt and equity!!

Value Levered = Vu + TcD = Value Unlevered = EBIT(1-Tc)/rA

MM Prop2 = rE=rA + D/E(rA-rD) re>ra>rdRa=rwacc=D/(D+E)*rD+E/(D+E)*rE BreakEven EBIT = When Capitalization plans result in same EPSEPS = (EBIT –RDD)/SharesOutstanding EBIT-RDD gives NI, set the EPS of two cap structs == to find EBIT Vu = EBIT/WACC (no taxes)!Vu = EBIT(1-Tc)/WACCWACC = Cost of Equity Capital = RaAnnual Tax Savings from Lever = TCrDD rD = interest rate, D = amnt borrowed, TC = tax rateMM Prop1: VL=VU + PVTS = VU+TCD

Value = Debt + Equity Vu = CF/rA rA = cost of capital unlevered firm = re re = cost of equity levered

rwacc = DV

rD(1−Tc)+ EVr E

be careful…Vl = CF/rwacc rD+rE = 1 rD = borrowing rateValue Max = min(rwacc) Share Price = Equity/Shares outstanding = (value of

Midterm 2 APV (20 points) MomCorp is considering a two-year project that requires an investment of $1 million now. Under all-equity financing, the project would generate after-tax cash flows (after consideration of any depreciation) of $750,000 one year from now and $1,500,000 two years from now. The project has a zero salvage value at the end of two years. The appropriate cost of capital is 15% with all-equity financing.Suppose, however, that MomCorp will borrow $500,000 against the project and this debt will be repaid in two equal installments. The borrowing rate is 10%. The firm’s tax rate is 30%. Calculate the project’s Adjusted Present Value (APV).Solution:The net present value of the project for an all-equity firm would be NPVU=-1,000,000+750,000/1.15+1,500,000/1.15^2=786,389.414. If $500,000 of the project is financed with debt to be repaid in two equal installments of X, we must have 500,000=X/1.10+X/1.102 , which gives X=288,095.238. In the first year’s installment, interest repayment is 500,000∙0.10=50,000 which generates a tax shield of 0.3∙50,000=15,000. The rest is the principal repayment 288,095.238-50,000=238,095.238, reducing the debt outstanding in the second year to 500,000-238,095.238=261,904.762. Therefore, the interest payment in the end of second year is 261,904.762∙0.10=26,190.4762 which generates a tax shield of 0.3∙26,190.4762=7,857.14286. The present value of tax shields is PVtax shields=15,000/1.10+7,857.14286/1.10^2=20,129.8701 and the adjusted present value of the project is A𝑃V=NPVU+PVtax shields=786,389.414+20,129.8701=806,519.284.

Final Prac Issueance of Equity Ra = .12, E = 56 M, 4M shares, D = 70M r = .05 perp. Reorganization plan – buy back some debt thru issuance of 15M of new equity. T = .34, no depr or cfd, r = .05(a) Give: Stock Price at (i) now, (ii) at announcement, (iii) after announcement(b) After reorganization in (a), now want to acquire new company for 10M, generate EBIT of 3.5M perp annually. Re = .12, It will issue additional 10M of equity and use proceeds to buy company.(i) at announcement, what is D/E ratio? (ii) how many shares must be issued in order to get the 10M in new euqity?(a) (i) Stock Price Now = Total equity/number shares, price = 14 = 56M/4M (ii) Stock Price after announcement = (Current Equity Val – Lost Tax Shield)/# Shares = (56M-.34*15M)/4M = 12.725(iii) Stock Price after repurchase = New Val Equity / New # Shares = (Current Equity Val –Lost tax Shield + Val Repurchased Equity)/(Old#shares + New Equity/Price/Share) = (50.9M + 15M)/(4M + 15M/12.725) = 12.725(b)(i) NPV Project= initial investment + (1-T)(EBIT)/r = -10M + (.66*3.5M/.12) = 9.25MSo, Equity is worth New Val Equity from (a) + NPV project = 65.9M + 9.25M = 75.15M, D = 70M-15M = 55M, D/E ratio = 55M/75.15M = .732(ii) Stock Price after announcement = New Equity from (i) / new number of shares from (a)(iii) = 75.15M/5178781 = 14.511. Number of shares needed = money needed/new price = 10M/14.511 = 689132 Shares

Share Recap Midterm 2 (20 points) Big Kahuna Burger (BKB), an all-equity firm, is valued at $39.5 million. BKB expects $5 million in earnings after taxes each year into perpetuity. The firm has 500,000 shares outstanding. The firm’s tax rate is 35%. Suppose that BKB announces that it will borrow $30 million of perpetual debt at an interest rate of 8% and simultaneously buy back $30 million worth of equity with the funds. Ignore personal taxes.How many shares outstanding will BKB have after it buys back the equity?What are the firm’s expected earnings per share before AND after BKB issues debt and buys back the equity?What would the interest rate on the debt have to be so that the share repurchase has no effect on expected earnings per share?Solution: After the announcement of the stock buyback, the value of the equity isEL=EU+tC∙D=$39,500,000+0.35∙$30,000,000=$50,000,000,and the per share price is $50,000,000/500,000=$100. The number of shares that the firm buys back is $30,000,000/$100=300,000, so the firm has 500,000-300,000=200,000 shares outstanding after it buys back the equity. For the unlevered firm, the earnings per share are EPSU=$5,000,000/500,000=$10. In order to calculate the earnings per share for the levered firm, we first calculate the total before-tax earnings, E=$5,000,000/(1-tc)=$5,000,000/(1-0.35)=$7,692,308. For the levered firm, the earnings per share are EPSL=(E-rD)(1-tC)/200,000=$7,692,308-0.08∙$30,000,000)*(1-0.35)/200,000=$17.20. The interest rate on debt must solve EPSU=EPSL, i.e., 10=7,692,308-rD∙30,000,0001-0.35200,000, which givesrD=7,692,308-10∙200,0001-0.3530,000,000=0.15385.The forward rate between the end of year 1 and the end of year 3 is(1+r3^3)/(1+r1)-1≈17.31%.

The forward rate between the end of year 1 and the end of year 3, expressed in annual terms is:Sqrt((1+r3)^3/(1+r1))-1≈8.31%. 

(10 points) Today is January 1. The stock of the NyanCat Corporation is currently trading at $40 per share. Analysts are expecting the NyanCat Corporation to have $5 of earnings per share in the coming year. The company will reinvest 60% of these earnings in projects that earn a 20% rate of return per year with the rest being paid out as dividends. Assume that earnings occur and dividends are paid at the end of the year. Assume that both the reinvestment rate of 60% and the rate of return of 20% will continue indefinitely.What would happen to NyanCat's stock price if, alternatively, the company were to cut its dividend payout ratio (i.e. the ratio of dividends to earnings) as of the end of this year to 25% every year with projects still earning 20% annually? Assume that the company's risk is unaffected by the change in payout ratio. (10 points) Again, today is January 1. The NyanDog Corporation paid a dividend of $1 per share yesterday. Analysts are forecasting that NyanDog will experience two years of growth of 10% per year in earnings and dividends, followed by three years of growth of 5% per year in earnings and dividends. Earnings and dividends are paid at the end of the year. Analysts are also estimating that, right after the dividends are paid at the end of year 5, NyanDog will have a ratio of price to year 5's earnings equal to the average P/E ratio in the relevant peer group, which is 22.4. Assuming that the discount rate for NyanDog is 17% and that NyanDog will pay 90% of its earnings in dividends every year from year 1 through year 5, calculate NyanDog's share price.Solution:

If we denote E=$5 ,k=0.6 and r¿=0.2, then the expected

dividend per share at the end of the year is

D (1−k )E=(1−0.6 )$5=$ 2 and the expected

growth rate in earnings and dividends is

g=k r¿=(0.6 ) (0.2 )=0.12 . From P= Dr−g

we calculate r=DP

+g= 240

+0.12=0.17 .

Therefore, if the company were to cut its dividend payout ratio to 25% every year, the

plowback ratio would increase to k '=0.75 and the new price would be