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Introduction to Valuation:
The Time Value of Money
Chapter 5
Setting the TI BA II Calculator: Set your interest rate for 1 pay period per year
- Hit 2 nd , I /Y , which is the 3rd^ row from the top, second from the left, hit 1, enter, CE/C.
- Set the calculator to properly compute annuities.
- Hit the 2 nd^ key
- Hit the PMT key, which is on the 3rd row from the top and it is the second key from the right.
- If your screen reads BGN , hit the 2nd key again and hit the enter key. Your screen should now read END. This is the correct setting. Future Values Suppose you invest $1000 for one year at 5% annual interest. What will your $1000 grow to at the end of one year? This is a _______future_______ value of a _______lump______ sum problem. We are given what the value is at the _______beginning_______ of the period. Our task is to find the value at the ____end____ of the period. There is one amount involved. We call this amount a lump sum.
Future Values A common sense illustration. To find the value of $1000 that earns 5% interest for 1 year: First, Find the $ amount of interest that will be earned = principal * interest ______rate______ = $1000(.05) = $50Then, ____add____ the principal and the $ interest = $1000 + $50 = $ Suppose you leave the money in for another year. How much will you have two years from _____now_____? Start with the balance as of the ____end____ of the first year and find the interest on it = $1050(.05) = $52.50. Then, add in the principal = $1050 + $52.5 = $1102. Future Values: General Formula FV = PV(1 + r)t FV = ______future______ value PV = ________present________ value r = period interest _____rate_____, expressed as a decimal; some books use the letter i. T = ___________number__________ of periods; some use the letter n. (1 + r)t^ is the future value interest factor The order of operations is critical. You are raising (1+r) to the t, not PV(1+r) In the previous examples:* FV of $1000 invested @ 5% for 1 year = PV (1+r) t $1000(1.05) = $1050. For 2 years = PV (1+r) t $1000(1.05)^2 = $1102. Note: 1.05^2 = 1.1025. Multiply this # by $1000 to get the answer.
Using the ___________Financial_____________ Keys: We can use the financial keys to solve these problems: The financial keys are on the 3rd row from the top of your calculator. N = # of pay periods I = interest rate or discount rate or rate of return PV = present value PMT = payment FV = future value CPT= compute. It is at the top left corner. Instead of using the formulas, use the financial keys: Remember to clear the registers, 2nd^ CLR TVM, 2nd^ CE/C, and CE/C, after each problem. We must input each key variable (i.e. PV, I/Y, N, PMT, FV). The order in which we enter the information does not matter except that the last 2 keystrokes will be CPT and the variable for which we are solving (i.e. PV, FV, I/Y, N or PMT). Note 2 weird things about the TI Business Analyst II calculator. 1- When you input a PV and CPT for FV, the calculator will give you a negative FV as an answer if you enter the PV as a positive #. To resolve this, you must change the sign of either the PV or the FV. You change the sign by hitting the +/- key. It is on the far right of the bottom row. To determine whether to change the sign of the PV or of the FV, consider which direction cash is moving, into or out of your pocket.
For example : say you start a savings account with $100. Cash will flow _____out______ of your pocket and into the account. It is a cash outflow. You input the PV as a negative #. At the end of the period you will have a larger amount that flows back to you. This FV is a positive #. If you do not input either PV or FV with a -, when you try to solve for I/Y or for N, your calculator will give you an error 5 message. 2-The other issue is that when you are inputting me /Y, which is a rate of return, an interest rate or a growth rate, you must multiply the rate by 100. For example : if the interest rate is 5%, you enter .05 * 100= 5 into I/Y. Solving our original example of $1000 invested for 2 years at 5% interest: 1000; +/- key = -1000 ; PV key; This # is input as a ________negative_________ because it involves an _________outflow________ of cash from an investor; 5; I/Y (period interest rate) key; 2; N (number of periods) key CPT (Compute) key; FV (Future Value) key = $1102.
If you are a borrower, you will be __________worse_________ off if you have more than 1 compounding period over a specified time frame because the rate you have to pay will be _______higher________- than if simple interest was being used. The Effect of Compounding The effect of compounding _______grows______ along with the # of pay periods. The chart shows the value of $10,000 earning 5% compounded annually for 5 (blue bar), 15 (red bar) and 30 (gold bar) years. The interest earned ___per year____ after 5 years is ($12763- $10000)/5 = $553. After 15 years it is ($20,789- $10,000)/15 = $719. After 30 years it is ($43,219- $10,000)/30 = $1107. Future Values – Example 3 Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today? FV = PV (1+r) t^ = $10(1.055) (^200) = $447,189. What is the effect of compounding? Simple interest = $10 + 200($10) (.055) = $ Compounding added $447,069.84 to the value of the investment.
Ending Value
$ $5, $10, $15, $20, $25, $30, $35, $40, $45, $50,
Future Value as a General Growth Formula You can use the FV formula to calculate units of measure other than $’s. Suppose your company expects to increase ________unit_______ sales by 15% per year for the next 5 years. If you currently sell 3 million units in one year, how many units do you expect to sell in year 5? FV = PV (1+r) t^ = 3,000,000(1.15)^5 = 6,034,072 units Quick Quiz: Part 1 Suppose you have $500 to invest and you believe that you can earn 8% per year over the next 15 years. How much would you have at the end of 15 years using compound interest? FV = PV (1+r) t^ = $500(1.08)^15 = $ How much would you have using simple interest? $500 + [($500 * .08) * 15] = $500 + $600 = $ FV Important Relationships I. There is a __________direct___________ or _______positive______ relationship between FV and I/Y. This means if I/Y goes up, FV goes up. For example, if I/Y went up, then, all else being the same, your FV would be _______higher________. Similarly, if I/Y went up, you could ______start______ with a _________smaller________ amount to get the FV you had in mind before I/Y went up. If I/Y goes down, FV goes ________down_______. So, if I/Y goes down, you either have to ______start_____ with a ________larger_________ amount to get the desired FV or your FV will be ___________lower____________. There is a _________direct__________ or ___________positive____________ relationship between time and FV. This means if your time period ________increases_________, all else being the same, your FV will increase.
