Principles of Finance

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[...] It is the solution of the equation: NPVA=NPVB NPVA-NPVB=0NPVA-B=0 Payback method: Indicates the time it takes for an investment to generate an amount of income or cash equal to the cost of the investment. Drawbacks: time value of money, bias for long-term investments. Profitability index PIPV=PVCFcost of the investment PINPV=NPVCFcost of the investment If PIPV [...]

[...] Investments of unequal lives: EAC=asset pricexdiscount rate1-1+discount rate-n +annual cost EAC=NPVArn+annual cost where Arn=1-11+rnr The Modigliani-Miller model: Prop. I (with no taxes): valuelevered=valueunlevered Prop. II (with no taxes): Rlevered equity= Runlevered equity + (vdebt /vlevered equity)(Runlevered equity - rdebt) Prop. I (with no taxes): vlevered=vunlevered+TCxdebt Prop. II (with no taxes): Rlevered equity= Runlevered equity + (vdebt /vlevered equity)(Runlevered equity - rdebt)(1-TC) The trade-off model: Thesis: there is an optimal level of debt for a company. The objective of each firm is to maximize firm value Vf such that: Vf=S+B+G+L. [...]

[...] Enterprise value: EV=market value of equity+debt-cash Total value of equity=EV-debt+cash Price of share=EV-debt+cashnumber of shares Capital Asset Price Model (CAPM): E(r p,n)=w1xE(r1)+w2xE(r2)+ . +wnxE(rn) σp,22=w12xσ12+w22xσ22+2w1w2Cova1,a2 Corrr r2=Covr1, r2V[r1] x V[r2] Σ=Covr1, r1Covr1, r2Covr1, r3Covr2, r1Covr2, r2Covr2, r3Covr3, r1Covr3, r2Covr3, r3 Ri=RF+βiRM-RF where Ri= cost of equity βi/m=Covrm, riVrm βp=w1β1+w2β2+ . +wnβn Security market line If = 0.5: stock is only half as volatile, or risky, as the average stock (or market). If = 1.0: stock has average risk (same as the market) If = 2.0: stock is twice as risky as the average stock (or market). [...]

[...] For the PINPV, the threshold value is not 1. All-equity financed companies: An all-equity firm should accept a project whose IRR exceeds the cost of equity capital and reject projects whose IRRs fall short of the cost of capital. requity=D1P0+g Operation leverage DOL: Operating leverage=FCFC + change in EBIT% change in sales DOL=sales-variables costsprofits βAsset=debtdebt+equityxβdebt+equitydebt+equityxβequity rWACC=equityequity+debtxrequity+debtequity+debtxrdebtx1-TC where rdebt=YTM (Expected total return). foverall =equityequity+debtxfequity+debtequity+debtxfdebt Making capital investment decisions: Incremental cash flows: After tax salvage value ATSV=SV-tax rate x(SV-book value) Operating cash flow=operating profit EBIT-taxes-depreciation Top-down approach: OCF=Sales-costs-EBITxtaxe rat Bottom-up approach (only works when no interest expenses): OCF=net income+depreciation Tax shield approach: OCF=sales-expensesx1-tax rate+depreciation xtax rate Nominal cash flows must be discounted at the nominal rate. [...]

[...] x1+returnn returnannualized=n(1+holding period return-1 Geometric average return: what was your average compound return per year over a particular period? Arithmetic average return: what was your return in an average year over a particular period? Stocks have outperformed bonds over most of the 20th century, although stocks have also exhibited more risk. Internal rate of return NPV=0 (-CF0)+i=1nECFi1+IRRi=0 If two investments are independent, the company can choose both if IRR is higher than the required rate of return. However, if those projects are mutually exclusive projects, it should choose the project that yields the highest NPV. [...]