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Finance 301 Exam 1 Study Guide

by: Chris Amato

Finance 301 Exam 1 Study Guide Fin 301

Marketplace > Miami University > Finance > Fin 301 > Finance 301 Exam 1 Study Guide
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These notes cover any topic that will be on the exam
Intro to Finance
Dr. David S. Chappell
Study Guide
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This 7 page Study Guide was uploaded by Chris Amato on Tuesday September 13, 2016. The Study Guide belongs to Fin 301 at Miami University taught by Dr. David S. Chappell in Fall 2016. Since its upload, it has received 684 views. For similar materials see Intro to Finance in Finance at Miami University.


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Date Created: 09/13/16
Chapter 5 5.1 - First step in attempting any time value analysis is to set up a time line. The number of periods are listed at the top. Time 0 refers to today, and each number is both the beginning and end of the period. For example, the number 1 is both the end of the first period, and the beginning of the second period. The cash flows are listed at the bottom. The value at time 0 is the present value, which is negative because it is a cash outflow. The interest rate is typically constant for the entire period, but there are times where the interest rate may fluctuate. If it does change, the different rates will be listed in the periods on the time line. Future Values/Present values - A dollar today is worth more than a dollar in the future because if you had it now, you could invest it, earn interest, and own more than a dollar in the future. - The process of going from Present Value to Future Value is called Compounding - Cash flows (CF) can be negative or positive. At time 0, Cash Flows (CF)= Present Value THERE ARE 4 METHODS WE CAN USE TO SOLVE TIME VALUE PROBLEMS: But we will mainly use just 2 1) Formula approach ALL LUMP SUM TVM CALCULATIONS CAN BE SOLVED WITH THIS EQUATION: FV= PV(1+i)^N FV= Future value PV= Present value i= Interest rate N= number of periods 2) Financial Calculator -It is a good idea to check your answers on the exam with math, but all the problems can be solved with a financial calculator. -It is important to note that when plugging in the interest rate in the financial calculator, it will be a whole number. EX. If the interest rate is 5%, plug in 5 not .05. - When the problem is dealing with a deposit of money, the present value should always be entered in as a negative number. - When dealing with the repayment of a loan of any type, the future value should be entered in as 0 unless otherwise stated. Future Value Example: You are given the option of taking $125 today, or $188.00 exactly five years from today.  If the implied interest rate on this financial instrument is 8.5%, compounded semi­ annually, which option would you accept?  Remember, you are a rational financial investor and every penny counts. - First, realize that you will need to compute the future value of $125 in 5 years to see how it  compares to $188. - Next, figure out what all of the values in the problem mean: 10=          N $125=      PV (8.5%)/2= i 0=             PMT FIND FV  Notice the problem states that the 8.5% interest rate is compounded on a semi annual  basis. When plugging the rate into your calculator, IT ALWAYS HAS TO BE THE  PERIODIC RATE. So since there are two payments each year, the periodic rate will be  8.5 divided by 2.  When you plug in all these numbers and compute for future value, you get that $125 is  worth $189.53, and is more than $188.00. Therefore you would take the $125 today. Annuities and Uneven Cash flows - An annuity is a series of payments made all of which are the same value over N periods. - There may or may not be a present value depending on the problem.  - Payments should always be entered in as a negative number in a financial calculator. Annuity Example: Your girlfriend just won the Florida lottery. She has the option of $15,000,000 today or a 20 year annuity of $1,050,000 with the first payment occurring one year from today. What rate of return has Florida built into the annuity? - First take a look at the problem and realize what is given: N= 20 years I = X PV= 15,000,000 because this is what the lottery winnings are worth today. PMT= $1,050,000 FV= 0 because after 20 years, the state will have payed off the full amount owed to your gf.  Note­ IF THE PV, PMT, and FV ARE ALL THE SAME SIGN, YOU WILL GET AN  ERROR MESSAGE.  After plugging this into your calculator, you should get 3.44%  Uneven Cash flow example:  An uneven cash flow question will either be in the form of an annuity with a lump sum  added in the last period, or an irregular cash flow where not every payment is equal.  In an irregular cash flow, we can use the cash flow register on a financial calculator to  find the Net Present value of the cash flow stream, the future value, or any one of the  payments if it is missing. What’s the present value of a 4­year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 11%? - This problem is an example of an uneven cash flow and not a straight annuity because there is a lump sum added at the end of the past period. - N= 4 years - I= 11% - PV= X - PMT= $2,250 per year - FV= $3,000. The additional lump sum can be entered as the future value of the annuity. Notice that the cash flow registry is not needed here, and this problem can be done with time value  of money keys only. - Once you plug in the numbers and compute for PV, you should get $8,956.67. Test­ Level Problems: 20 year event 8% annually compounded Deposit $1500 today You need a future value of exactly $8069.05 at the end of 20 years However, you only earn the 8% annually for the first ten years, after which you go to semi­annual  compounding and are forced to add a deposit of $50 each period for the last 10 years.  To get to the  FV of $8069.05, what is the EAR you must earn? - First thing to notice is that even though the problem is over 20 years, we need to compute it  as if it were separate problems because there is an event after 10 years. - For the first 10 years, we can calculate a straight compounding lump sum where: N= 10 years I= 8% PV= ($1,500) PMT= 0 FV= X - After solving this for future value, we get an amount of 3,238.3875. But now, the rules have  changed, and there is semi­annual compounding where we don’t know the interest rate  where: N= 20 periods (10 years X 2) I= X PV= (3,238.3875) PMT= (50) FV= 8069.05  NOTE­ your PV and PMT must have the same sign or you will get an error. - After plugging this in, you should get 3.65%  NOTE­ this number is the periodic rate i.e. the rate per each of the 20 periods.  - In order to get the EAR like the problem asks, we have to use the formula: [(1+0.0365)^2]­1 - The effective annual rate is 7.43%. You want to have $35,000 in a savings account at the end of 20 years.  You can earn 8%,  compounded annually on the money.  You determine that you must deposit $ ­­­­­ into the account  today in order to have the desired amount at the end of year 20.  However, you can only deposit  $7,000 today.  If so, how much additional deposit must you make at the end of year 5 in order to  reach your goal of $35,000? - At first glance, this problem can seem confusing, but it is way easier once you realize that it  only involves lump sum compounding and discounting. - The first step is to find how much you would need to deposit to have 35,000 and 20 years at  an 8% interest rate: N= 20 years I = 8% PV= X PMT= 0 FV= 35000 - After plugging this in, you should get that you need to deposit $7,509.19 into you account to  achieve your goal. - Since we can only deposit $7,000, the largest future value possible is $32,627.70. This is  obviously less than the 35,000 that we were hoping for. - If we take the difference between the two amounts, we get 2,373.30. This is what we would  have to pay at future value to equal the total we want, but the question asks what we would  th have had to pay after the 5  period in order to rectify the amounts. - To find this, we simply have to discount the 2,373.30 15 periods where: N= 15 I= 8% PV= X PMT= 0 FV= 2,373.30 After plugging this in, we get $748.16 as the amount we need to enter after year 5 to get a future  value of 35,000. Consider the following timeline. What is the missing payment if the future value is $14,121.77 - The first thing to recognize is that this is an irregular cash flow question where we are trying  to find an individual period. We do not know the present value, but we can calculate the  present value by discounting the future value. This is just one of a couple ways to do this  problem. - So discount $14,121.77 4 periods where: N= 4 I = 15% PV= X PMT= 0 FV= 14,121.77 After plugging this in, we find that the present value is equal to (8,074.17) - We can now use this present value and the cash flow register to solve for the missing value: C0= (8074.17) C1= 3,807 C2= 0 C3= 2,757 C4= 1,855 - We then compute for the net present value at an interest rate of 15% (using the NPV key on  your calculator) and find that the NPV is 1,890.36.  - But we don’t want this value at present. Since the question asks for the missing value at the  second period, we have to compound this value 2 periods where: N= 2 I= 15% PV= (1,890.36) PMT=0 FV=X After plugging all this in, we find that the missing value is equal to $2,500 IF YOU CAN DO AND UNDERSTAND ALL OF THESE, YOU WILL DO JUST FINE ON THE  EXAM.  


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