FIN 311 1st Edition Lecture 7Outline of Last Lecture I. Price-Earnings P/E RatioII. DuPont Analysis III. Ethics IssuesIV. Time and Money Outline of Current LectureI. Time Value of MoneyII. Compute Present Value III. AssumptionsIV. Compute (Implied) Discount RateCurrent LectureI. Time Value of MoneyPV = 1,000 →PVr = 5% → I/Y [CMP] [FV] FV = ?? →FV FV = -1,050t = 1 year →N- Calculator Solves FV = PV(1+r)t FV - PV(1+r)t = 0- Inflows: Positive sign, Cash/payment Received - Outflows: Negative sign, Cash/payment Paid- PV = -1000 FV = +1050: Outflow investor, Inflow to bank- When solving PV or FV sign is less important 2 cash flows- When solving for r or t or PVA or FVA be more careful about signs - After almost every problem clear the TVM register  [2nd][FV] Clr TVM- FV = PV(1+r)t →Compounded Interest- Excel: = FV(rate, nper, PMT, PV, type) rate: Discount rate, r, I/Y (decimal form: .07 or percent form: 7%) nper: Number of periods, t, N PMT: Annuity, Payment, cash flows PV: PV Present Value type: When the cash flow is received (Options: 0 or 1, Default = 0 end of the year cash flows, set type = 1 beginning of the year cash flows)  For Homework: Use cell references PMT = 0 and type: leave blank)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.II. Compute Present Value - FV = PV(1+r)t Compounding- PV = FV Discounting (1+r)t- FV Greater than or equal to PVPV = ??FV = 10,000t = 1 r = 7%PMT = 0 PV= 9,345PV = 30,000FV = ??t =5r = 8%PMT = 0 FV = 44,079.84PV = ??FV = 75,000t = 17r = 8%PMT = 0 PV = 20,270.17III. Assumptions: How the TVM formulas are derived- Unless otherwise stated, future cash flows occur at the end of each period.- Positive value cash flows are inflows and negative value cash flows are outflows.- There is one single appropriate discount rate for each problem. If not we need to modify the formulas. FV = PV(1+r)t if interest rates change FV = PV(1+r1) (1+r2) (1+r3)…- Time 0 is today, time 1 is one period from today.0 1 2 3 4 Today One period from today End of Period 3 and Beg. of Period 4IV. Compute (Implied) Discount RateFV = PV(1+r)t Solve for r r = [(FV/PV)1/t ]FV = 15540PV = 12000t = 3r = ??PMT =0 r =