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# Finance January 26-2016 FINA 3000

UGA

GPA 3.5

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This 10 page Class Notes was uploaded by Anna O'Neil on Wednesday January 20, 2016. The Class Notes belongs to FINA 3000 at University of Georgia taught by Pope in Spring 2016. Since its upload, it has received 30 views. For similar materials see Intro to Business Finance in Finance at University of Georgia.

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Date Created: 01/20/16

Current Event: McDonalds issues (prior to 2015)- CEO change -Stagnant menus -Did not respond to customers NOW: - out preforming market - -Announced that same store sales are up 5.7% WHY? - All day breakfast- response to customer demand - Mild weather - World growth is up Changes to business model: - Revamped the menu o Higher end, gourmet burger § Compete with 5 guys o Added more value items - Add “better quality” without losing core customers Challenges in the future: - Growing menu is a logistical challenge - - Changing customer tastes New Zaxby’s downtown: - Typical fast food business o 40-55% comes from drive through - Increase in carryout business TIME VALUE OF MONEY PART II OBJECTIVES: 1. Find PV of uneven cash flow streams. 2. Understand difference between simple and compound interest. 3. Find PV and FV with multiple compounding periods in a year. 4. Calculate Effective Annual Rate and compare to nominal rate. 5. Calculate PV and FV with ordinary annuities. A Review Problem From Last Time: Suppose you put $1000 in a bank account for one year. If the bank pays 9% interest compounded annually (compound frequency), what is the value of your account in one year? N I/YR PV PMT FV FV= PV* (1+r)= 1,000*(1.09)= $1,090 What if we compound more frequently than one year? What happens? Compounding more frequently means we are paid interest more frequently. How will this affect future value? – We can therefore reinvest interest sooner. This grows to an increasing future value. Typically, interest rates are expressed as a nominal or annual rate followed by the compound frequency. This stated annual rate is referred to as the APR or the Annual Percentage Rate. (Advertised rate, nominal rate), use APR to find periodic rate How do we approach a compounding problem? We need to adjust our period length (n) and our discount rate (i). Let’s add a definition. Let m = the number of times that interest is compounded (credited to your account each year) Compound Frequency m context Annual 1 Sami-Annual 2 Bonus Quarterly 4 Stocks Monthly 12 Mortgages, any loan Weekly 52 leases Daily 252 or 360 or 365 investment Using m, we can adjust the time period and the discount rate to match the compounding frequency. For example, if we have monthly compounding, we want a monthly discount rate and we want the number of periods to be in MONTHS. Take APR + M to find periodic values Defining a few terms: r’ = any sub-annual discount rate = APR/ M (Periodic rate) n’ = the # of sub-annual time periods = N*M (# of compounded periods) Example: If interest is calculated at 12% compounded monthly for 4 years, find r’ and n’. R’= APR/M = 12%/12 = 1% per month N’= N*M = 4*12 = 48 months How does this work? Interest is credited to your account every month. With compound interest, you earn interest on your interest each period…. Now, suppose we have the following. You invest the same $1000, but the bank pays 9% annual interest (compounded quarterly M=4 ) What is the value of your account in one year? N I/YR PV PMT FV 4 2.25 -1,000 0 ? R’= APR/M= 9%/4 = 2.25% per quarter * FV(4)= 1,000* (1.0225)^4 N’= N*M = 1*4 = 4 quarters FV= $1,093.08 Suppose the interest was 9% compounded monthly. What is the value in one year? N I/YR PV PMT FV 12 0.75 -1,000 0 ? R’= 9%/12 = 0.75% per month N’= 1*12 = 12 months FV= $1,000* (1.0075)^12 FV= 1,093 Let’s compare our three solutions after one year: Compound Future Value Frequency 9% APR After 1 Year Annual m=1 $1,090.00 Quarterly m=4 $1,093.08 Monthly m=12 $1,093.81 Two Comments: 1. Increase M, increased FV 2. Increase M, we increase FV at a decreasing rate We now introduce the idea of an effective annual interest rate or EAR. So we earn yearly > 9% The EAR (annual compounded return or rate – true return) is the rate of annually compounded interest that is equivalent to some nominal rate of compounded more frequently. (What???) Let’s see using our example: With quarterly compounding, we had a future value of $1,093.08 in one year. EAR does the following: It finds an annual interest rate (one compound period per year) that provides the identical future value ($1093.08 in this case). FV= PV* (1+r) 1093.08= 1000*(1+EAR) N I/YR PV PMT FV 1 ? -1,000 0 1093.08 I= EAR= 9.31% So, $1000 would grow to $1093.08 in one year using annual compounding if the interest rate was 9.31%. There is also a formula we can use to find EAR: R’= 2.25% per quarter N’= 4 quarters (1+r’)(1+r’)*….. (1.0225)(1.0225)(1.0225)……. For 4 quarters EAR= (1.0225)^4-1 = 0.0931 So to solve for EAR: (1+r’)^m -1 Or EAR= (1+ APR/m)^m - 1 Example: What is the EAR on a savings account with 12% APR and quarterly compounding? EAR= (1+0.12/4)^4 -1 = Why care? - allows us to compare any two accounts - “true” cost of opportunity CASH FLOW STREAMS WITH DCF PRESENT VALUE AND FUTURE VALUE WITH UNEVEN CASH FLOW STREAM: PV WITH UNEVEN CASH STREAM Example: Suppose you sign a contract that will pay $100,000 in the first year, $125,000 in year 2, and $150,000 for the third year. If your discount rate is 10%, what is the present value of your contract? We can add cashflows IF values at the same time PV of contract= sum of PV of each cash flow Year 1: FV= $100,000 PV= FVn/(1+r)^n = 100,000/1.10= 90,909.09 Year 2: FV= $125,000 PV= 125,000/1.10^2 = $103,305.79 Year 3: FV= 150,000 PV= 150,000/1.10^3 = $112,697.22 *PV of contract= 90909.09+103305.79+112697.22= $306912.10 In summary: PV= (sum of) (FV/(1+r)^t FV WITH UNEVEN CASH STREAM Example: Suppose you sign a contract that will pay $100,000 in the first year, $125,000 in year 2, and $150,000 for the third year. If your discount rate is 10%, what is the future value of your contract at the end of three years? Year 1: FV= 100,000 FV(year 3)= FV * (1+r)^2 = 100,000*(1.10)^2= 121,000 Year 2: FV= 125,000 FV (year 3)= FV*(1+r) = 125,000*(1.10)= 137,500 Year 3: FV GET NOTES ORDINARY ANNUITIES: § Annuity: series of equal payments § An ordinary annuity is a cash flow stream in which an equal flow (payment) occurs at the end of every period for n periods. Examples? Mortgages, salary, GET HOW TO CALCULATE PRESENT VALUE OF AN ORDINARY ANNUITY Let’s illustrate with one of the most questioned baseball contracts of the last 50 years. Alex Rodriquez (AROD) was signed to a 10-year contract with the Texas Rangers in 2001 for $25 million per year. If AROD had a 7% discount rate, what was the present value of his contract (PV in 2001…)? On a timeline, How do we solve? PMT Mathematically, we can write the present value of an ordinary annuity: GET ALL NOTES PV of an annuity= PMT/r * [1- (1/1+r)^n] Using the calculator: FV N I/YR PV PMT 10 7 ? 25 0 CMT PV =175.59 million FUTURE VALUE OF AN ORDINARY ANNUITY Now, let’s find the FV of an ordinary annuity. We can derive the formula using the basic lump sum formula. Example: A hard-working professor puts away $15,000 per year in his University’s 401k plan. The plan earns 8% per year. What will be the balance of the 401k plan after 30 years of contributions? Examples to Finish Class: EXAMPLE 1: Suppose after graduating from UGA, you decide to start investing in money market funds with some of your new income. You decide to invest $250 a month in a fund that pays 6% APR compounded monthly. a) If you invest for ten years, how much will you have after your last payment? b) Now, suppose you invest for ten years, and then you let the money sit in the money market fund for three more years. How much will you have at this time? EXAMPLE 2: After starting a new job, you go out to buy a new Explorer from Gailey Motors. The sticker price on the Explorer with the options you want is $28,000. Unfortunately, you don’t have the cash to pay for the car, and decide to completely finance your purchase. The dealer offers you a 10-year loan with monthly payments of $350. a) What is the monthly interest rate for this loan? b) What is the APR for the loan? c) What is the EAR for the loan? ANNUITY DUE So far, we have considered cases where annuity payments come at the end of the first period. An annuity due describes a payment stream where the first payment is TODAY. On the timeline, How do we solve for an annuity due? The easiest way is to compare with the ordinary annuity formula. EXAMPLE 3: You sign a one-year lease with a local apartment complex. The lease calls for 12 equal payments of $500 at the first of each month. If you can earn a return of 12% compounded monthly on your investments, how much would you be willing to pay today (a one time payment) to cover the full year’s rent?

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