Needed to generate 1 in sales total assets sales

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needed to generate \$1 in sales = Total Assets / Sales External Financing Needed (EFN) The amount of financing required to balance both sides of the balance sheet External Financing and Growth Symbols S = Previous year’s sales A = Total Assets D = Total Debt E = Total equity p = Profit Margin R = Retention Ratio ROA = Return on Assets ROE = Return on Equity D/E = Debt/Equity Ratio g = Growth rate in sales
FIN 300 Blawal Aleem Increase in Total Assets = A x g Addition to retained earnings = p(S)R x (1+g) EFN = Increase in total assets Addition to retained earnings = A(g) p(S)R x (1+g) EFN = -p(S)R + [A-p(S)R] x g Internal Growth Rate The growth rate a firm can maintain with only internal financing = (ROA x R) / (1 ROA x R) Debt Capacity The ability to borrow to increase firm value Sustainable growth rate The growth rate a firm can maintain given its debt capacity, ROE, and retention ratio D/E = New borrowing / Addition to retained earnings New Borrowing = D/E[p(S)R(1+g)] EFN* = Increase in total assets Addition to retained earnings New borrowing = A(g) p(S)R x (1+g)[D/E] = 0 g* = ROE x R/[1 ROE x R] ROE = Profit Margin x Total Asset Turnover x Equity Multiplier = p(S/A)(1+D/E) Chapter 5 Future Value and Compounding Future Value (FV) The amount an investment is worth after one or more periods. Also compound value. = \$1 x (1+r) t Compounding The process of accumulating interest in an investment over time to earn more interest Interest on interest Interest earned on the reinvestment of previous interest payments Compound Interest Interest earned on both the initial principal and the interest reinvested from prior periods Simple interest Interest earned only on the original principal amount invested Present Value and Discounting
FIN 300 Blawal Aleem Present Value (PV) The current value of future cash flows discounted at the appropriate discount rate = \$1 x [1/(1+r) t ] = \$1/(1+r) t Discount Calculate the present value of some future amount Discount rate The rate used to calculate the present value of future cash flows More on Present and Future Values FV = PV x (1+r)^t PV = FV t / (1+r) t = FV t x [1/(1+r) t ] Symbols PV = Present Value FV t = Future Value r = Interest rate t = Number of periods C = Cash amount TIME VALUE CALCULATIONS FV t = C x (1+r) t PV = C / (1+r) t PV = FV t / (1+r) t Chapter 6 Valuing Level Cash Flows: Annuities and Perpetuities Annuity A level stream of cash flows for a fixed period of time Annuity present value = C x (1-Present Value Factor/r) = C x ((1-1/(1+r) t )/r) Annuity FV factor = (Future Value Factor 1)/r = ((1+r) t -1)/r Annuity Due An annuity doe which the cash flows occur at the beginning of the period Annuity due value = Ordinary annuity value x (1+r) Perpetuity An annuity in which the cash flows continue forever
FIN 300 Blawal Aleem Consol A time of perpetuity Cash flow = Perpetuity present value x Rate Perpetuity PV = C/r = C x (1/r) ANNUITY AND PERPETUITY CALCULATIONS FV t = C x {[1+r) t 1]/r} PV = C x {1-[1/(1+r) t ]}/r PV = C/r Growing Perpetuity A constant stream of cash flows without end that is expected to rise indefinitely = PV = C/r-g Growing Annuity A finite number of growing annual cash flows = PV = (C/r-g)(1-(1+g/1+r) t ) Comparing Rates: The effect of compounding Stated Interest Rate The interest rate expressed in terms of the interest payment made each period. Also, quoted interest rate Effective Annual Rate (EAR) The interest rate expressed as if it were compounded once per year = [1+(Quoted rate/m] m -1 (m=number of time interest is compounded during the year) Annual Percentage Rate (APR) The interest rate charged per period multiplied by the number of periods per year EAR = e q 1 (q=quoted rate) (continuous compounding) Loan Types and Loan Amortization Pure Discount Loans Interest-Only Loans Amortized Loans
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