FINANC 300 1st Edition Lecture 5 Outline of Last Lecture I. Organizing Cash FlowsII. Different Types of InterestIII. Future ValueIV. The Power of CompoundingV. Present ValueOutline of Current Lecture I. Moving Cash FlowsII. Rule of 72III. Finding Interest RatesIV. Solving For TimeCurrent LectureMoving Cash Flows- Concepts: Discounting & Compoundingo Move cash flows around in time Use PV calculation when cash flow is moved to an earlier date Use FV calculation when cash flow is moved to a later date- Ex. of moving cash flowso Assumptions PV: Expected cash flow of $200 in 3 years Decision: change receipt of CF to 2 years (one year earlier) Discount rate= 6%o PV calculation to discount the cash flow for 1 year PV2 = FV3/(1+i)^1- = $200/(1.06)^1 = $188.68o Assumptions FV: Expected cash flow of $200 in 3 years Decision: change receipt of CF to year 5 Compound rate = 6%o FV calculation to compound the cash flow for 5 years FV5 = PV3 x (1+i)^2- = $200 x (1.06)^2These 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.o = $200 x 1.1236 = $224.72Rule of 72- Concept: Compound Interesto How much time for an amount to double? Approximate number of years to double an investment- = 72/Interest rateo Ex.  Assumptions:- Interest rate = 6% Rule of 72 calculation:- 72/6 = amount of time for investment to doubleo = 12 yearsFinding the Interest Rate- i = [(FV/PV)^(1/t)]-1- Ex. computing interest rateso Assumptions Bought gold coin for $350 Sold gold coin for $475 Timeframe: 3 yearso $475 = $350 x (1+i)^3 $475/$350 = (1+i)^3 or 1.357 = (1+i)^3- 1.107 = (1+i) or i = 0.107o 10.7%Return Assymetries- You bought a gold coin for $700 a year ago, now it’s worth $350. How much did you lose?o (700-350)/700 = 0.5 or 50%- How much do you need to earn to get back to $700?o (700-350)/350 = 1 or 100%Solving for Time- Assumptions/Known Data:o Present value/ starting cash flowo Interest rateo Future value/future cash flow- Complex calculation – use financial calculatoro FV = PV x (1+i)^N- Ex. solving for timeo When interest rates are 9%, how long will it take $5000 to double? 10,000 = 5000 x (1.09)^N- 2 = 1.09^No Log (2)/Log(1.09) = N 8.04 = No A loaf of bread sold for $0.05 in 1933. Now it sells for $2.50. If this annual growthrate continues, what will be the closest price of a loaf in another 80 years? $2.50 = 0.05 x (1+i)^80- I=5.01 FV = 2.50 x (1.0501)^80- FV =