FBF- Formula- Sheet PDF

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Formula sheet for Business Finance...

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FBF FORMULA SHEET.

Time Value of Money  PV = present value, or principal  i = interest rate, later we use ‘r’  n = number of periods, later we use ‘t’  FV

= future value

Future value with simple interest FV = PV(1 + i ×n)

Future Value with compound interest FV = PV(1 + i)^n PV = FV ÷(1 + i)^n

Future Value of an Annuity FV = PMT [ ((1+i)^n – 1)/i ]

 PMT = annuity payment  n = number of payments  i = interest rate (per period)

Present Value of an Annuity PV = PMT [ (1-(1+i)^-n)/i ]

The present value of a perpetuity  PV = PMT / i

Effective Annual Rates (EAR) EAR = (1 + i)^m –1  m = number of compounding periods per year  i = interest rate per period

The “Rule of 72” divide 72 by the interest rate.

Valuing Bills  PV = FV ÷(1 + rt)  PV = present value, or price  FV = future value, or face value  r = interest rate  t = time to maturity

Bond Valuation PV = PMT [ (1-(1+i)^-n)/i ] + FV(1+i)^-n  If coupon rate < Yield, then Price < Face value Discount Bond  If coupon rate = Yield, then Price = Face Value  Par Value Bond  If coupon rate > Yield, then Price > Face Value  Premium Bond

Equity Valuation Current value of a share is present value of all future dividend payments  P0= D1/(1 + r) + D2/(1 + r)^2+ D3/(1 + r)^3+ D4/(1 + r)^4+ ...  Where  P0= the value of the share at time zero (PV)  Dt= the expected dividend payment at time t  r = the required return (i)

Constant Dividend Model  When cash flows are constant forever PV = PMT / i  In the case of shares, if dividends are constant P0= D / r Where:  P0= the value of the share at time zero (PV)  D = the constant dividend amount (PMT)  r = the required return (i)

Constant Growth Model If dividends are expected to change at the same (constant) rate then the share price is given by P0 = D1/ (r - g) Where;  g is the growth rate  D1 is the dividend at time 1  (next year’s dividend) D1= D0(1 + g)

Operating cash flow (after-tax cash flow) = Pre-tax cash flow x (1 – company tax rate) + (depreciation x company tax rate)

Depreciation tax savings = Depreciation × company tax rate (tc) Where dep. Is straight line method

Book value of asset (WDV)  = Initial Cost - Accumulated Depreciation

Tax effect on asset sale  Tax on sale = (WDV –salvage value) × company tax rate

Net Present Value formula NPV = the sum of …CF1/(1+r) + CF2/(1+r)^2… - CF0  r is the required rate of return  CFt is the cash flow for time period t

Reject projects that have a NPV < 0

Payback Period  Payback period is determined by adding expected cash flows for each year until the total is equal to original outlay Investment cost/yearly cash flows = number of years.

Accounting Rate of Return (Average net profit) / [ (initial cost + salvage)/2 ]

Profitability Index PI = (NPV + initial cost) / initial cost  PI = 1 – Indifferent  PI > 1 – Accept  PI < 1 – Reject

Capital gains yield  (Ending Price – Starting Price)/Starting Price Add dividend payment here^

The average return on an investment  R = (r1+ r2+ r3+ ......+ rn) / n  n = the number of observations  ri = return for period i

Calculating Historical Risk

Measuring expected return  Expected Return = the sum of ( Probability of Return × Return)

Measuring future risk

Expected rate of return for a portfolio E(RP) = (the sum of) Wi x E(Ri)  Wi is the % of asset i held in the portfolio  E(Ri) is the expected return of asset i

Capital Asset Pricing Model (CAPM) E(r) = Rf + (beta)(Rm-Rf)  Rf = risk-free rate  [ (RM) - Rf] = the market risk premium

 beta = amount of systematic risk

Portfolio Risk  βP= (the sum of) Wi × βi  Wi is % of asset i held in the portfolio  βi is the beta of asset i

Calculating WACC -

Cost: Determine the market’s required rate of return (cost of capital) on each form of financing

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Weight: Determine the market value of each form of financing. From this calculate the proportions (weights) of the firm financed by each form of financing.

Cost of Debt -

YTM

Cost of Preference Shares  P0= D / Rp  P0 = current preference share price  D = dividend payment  Rp= required rate of return  Reorganise equation to determine return:  Rp= D / P0

WACC WACC = Rd(1–tc)(D/V) + Re(E/V) + Rp(P/V) (Cost of debt)(1 – company tax rate) x weight of debt + (cost of equity)(weight of equity)

 Costs  Rd= market return on debt finance  tc= company tax rate  Re= market return on equity (cost of equity)  Rp= market return on preference shares  Weight  D = market value of debt  E = market value of ordinary shares  P = market value of preference shares  V =D+E+P

market value of equity  current share price * number of shares issued

Earnings per share EPS = [(EBIT – 1)X(1 – company tax rate)]/number of shares...