Lecture 2 - Discounted Cash Flow Valuation and NVP Dividend payout ratio = cash dividends/net income We can now calculate the ratio of the addition to retained earnings to net income Addition to retained earnings/net income This ratio is called retention or plowback ratio and it is equal to 1 minus the dividend payout ratio because everything not paid out is retained EFN = External Financing Needed, and there are three possible financing sources; short term borrowing, long term borrowing and new equity. The choice of some combination among these three is up to the firm's management. Internal Growth Rate The maximum growth rate that can be achieved with no external financing of any kind is called internal growth rate. Internal growth rate = (Return on assets x retention ratio)/ (1 - ROA x b) Sustainable Growth Rate The sustainable growth rate is the maximum growth rate a firm can achieve with no external equity financing, while it maintains a constant debt-equity ratio i.e. without increasing its financial leverage. The value can be calculated as = (ROE x b) / (1 - ROE x b) This is identical to internal growth rate except that ROE is used instead of ROA. Net Present Value The NPV of an investment is the present value of the expected cash flows less the cost of the investment. An investment is deemed good is NPV is over 0 The formula for NPV can be written as: NPV = - Cost + PV (one period case) NPV = C0 / (1 + i)^t C0 is cash flow at date 0 i is the appropriate discount rate T is the number of periods over which the cash is invested
Compounding Periods Compounding an investment m times a year for T years provides for future value of wealth: mxT FV = C Ă— 1+- | m Effective Annual Interest Rates (EAR) The EAR is the annual rate that would give us the same end-of-investment wealth after 3 years. Continuous Compounding The general formula for the future value of an investment compounded continuously over many periods can be written as: FV = CoxerT C0 is the cash flow at date 0 e is a transcendental number approximately equal to 2.718 (use key on calculator) r is the stated annual interest rate T is the number of periods over which the cash is invested Perpetuity This is a constant stream of cash flows that lasts forever. The formula is; PV = C/r Growing Perpetuity This is a growing stream of cash flows that lasts forever. The formula is: PV = C/(r - g) Annuity This is a constant stream of cash flows with a fixed maturity. The formula is: PV =- 1- r 1 (1+r)â„¢
Growing Annuity This is a growing stream of cash flows with a fixed maturity. The formula is: 1+g T PV = C 1- (1+r) r - g Payback Period Advantages Easy to understand Biased towards liquidity Ignores cash flows after the payback period Average Accounting