Managerial Finance I
Managerial Finance I FRL 300
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This 23 page Class Notes was uploaded by Edmond Bergstrom on Saturday October 3, 2015. The Class Notes belongs to FRL 300 at California State Polytechnic University taught by Wei Yu in Fall. Since its upload, it has received 17 views. For similar materials see /class/218410/frl-300-california-state-polytechnic-university in Finance, Real Estate & Law at California State Polytechnic University.
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Date Created: 10/03/15
Chapter 5 Introduction to Valuation The Time Value of Money Future Value and Compounding Present Value and Discounting More on Present and Future Values Basic De nitions Time value of money a dollar in hand today is worth more than a dollar promised at some time in the future Future Value the amount an investment is worth after one or more periods later money on a tIme line Present Value the current value of future cash flows discounted at the appropriate discount rate earlier money on a time line Interest rate exchange rate between earlier money and later money Future Value Example 1 Suppose you invest 1000 for one year at 5 per year What is the future value in one year Interest 100005 50 Value in one year principal interest 1000 50 1050 Future Value FV 10001 05 1050 Suppose you leave the money in for another year How much will you have two years from now FV 100010510510001052 110250 Future Values General Formula FV PV1 rt FV future value PV present value r period interest rate expressed as a decimal t number of periods Future value interest factor 1 rt or FVFr t 1 rt Effects of Compounding Simple interest Compound interest Consider the previous example FV with simple interest FV with compound interest What does the difference stands for Calculator Keys Texas Instruments BA ll Plus 4 l I fill i i lit N number of periods IN period interest rate PY must equal 1 for the IN to be the period rate Interest is entered as number of percent not a decimal PMT annuity cash flow FV future value PV present value Remember to clear the registers CLR TVM after each problem Other calculators are similar in format Future Values Example 2 Suppose you invest the 1000 from the previous example for 5 years at 5 interest rate How much would you have at the end of year 5 Formula FV1000155 Calculator 5 N 5 IN 1000 PV CPT FV 127628 What is the effect of compounding The effect of compounding is small for a small number of periods but increases as the number of periods increases compare the difference between simple interest and compound interest for example 1 and 2 Future Values Example 3 Suppose you had a relative deposit 10 at 55 interest 200 years ago How much would the investment be worth today Formula Calculator What is the effect of compounding Present Values How much do I have to invest today to have some amount in the future FV PV1 rt Rearrange to solve for PV FV 1 rt Present value interest factor 1 1 rt or PVFr t 1 1 rt When we talk about discounting we mean finding the present value of some future amount Present Value Example 1 Suppose you need 10000 in one year for the down payment on a new car If you can earn 7 annually how much do you need to invest today Formula PV 10000 1071 934579 Calculator 1 N 7 IN 10000 FV CPT PV 934579 Present Values Example 2 You want to begin saving for your daughter s college education and you estimate that she will need 150000 in 17 years If you feel confident that you can earn 8 per year how much do you need to invest today Formula Calculator Present Values Example 3 Your parents set up a trust fund for you 10 years ago that is now worth 1967151 Ifthe fund earned 7 per year how much did your parents invest Formula Calculator Present Value Important Relationship I For a given interest rate the longer the time period the lower the present value What is the present value of 500 to be received in 5 years 10 years The discount rate is 10 5 years N 5 IN 10 FV 500 CPT PV 31046 10 years N 10 Y 10 FV 500 CPT PV 49277 Present Value Important Relationship 11 For a given time period the higher the interest rate the smaller the present value What is the present value of 500 received in 5 years if the interest rate is 10 15 Rate 10 N 5 W 10 FV 500 CPT PV 31046 Rate 15 N 5 W 15 FV 500 CPT PV 24859 The Basic PV Equation Refresher PV FV1 rt There are four parts to this equation PV FV r andt If we know any three we can solve for the fourth If you are using a financial calculator be sure and remember the sign convention put negative sign before PV or you will receive an error or a nonsense answer when solving for r or t Discount Rate Often we will want to know what the implied interest rate is on an investment Rearrange the basic PV equation and solve for r FV PV1 rt r FV PV1t 1 If you are using formulas you will want to make use of both the yX and the 1x keys Discount Rate Example 1 You are looking at an investment that will pay 1200 in 5 years if you invest 1000 today What is the implied rate of interest Formula r 12001OOO15 1 03714 3714 Calculator the sign convention matters N 5 PV 1000 you pay 1000 today FV 1200 you receive 1200 in 5 years CPT W 3714 Discount Rate Example 2 Suppose you are offered an investment that will allow you to double your money in 6 years You have 10000 to invest What is the implied rate of interest Formula Calculator Discount Rate Example 3 Suppose you have a 1year old son and you want to provide 75000 in 17 years towards his college education You currently have 5000 to invest What interest rate must you earn to have the 75000 when you need it Formula Calculator Finding the Number of Periods Start with basic equation and solve fort FV PV1 rt t nFV PV n1 r You can use the financial keys on the calculator as well just remember the sign convention Number of Periods Example 1 You want to purchase a new car and you are willing to pay 20000 If you can invest at 10 per year and you currently have 15000 how long will it be before you have enough money to pay cash for the car Formula Calculator Number of Periods Example 2 Suppose you want to buy a new house You currently have 15000 and you figure you need to have a 10 down payment plus an additional 5 of the loan amount for closing costs Assume the type of house you want will cost about 150000 and you can earn 75 per year How long will it be before you have enough money for the down payment and closing costs Table 54 PV Present value whai future cash ows are worth today m qum valu what cash laws are warm in the futura r Intareal rate rate of return m discount rate per period typically but nm always one year t Number 01 Mods typically but not always the number 91 years 0 Gash amount Emails E cxn f me term 1 isqalled39 rp39 mm w iua fhcron m E mmmm Bmazmrm PV 2 cm r39 The arm 1 m n is called the present value factor quot M r avmggm39 22