Its an exam. Its around 50 questions, two hour time limit. You quoted me $100.
D 3:10 PM 3:14 PM 3:15 PM 3:17 PM 3:19 PM 3:21 PM 3:23 PM 3:25 PM 3:27 PM 3:28 PM 3:29 PM 3:30 PM 3:33 PM 3:34 PM 3:36 PM 3:39 PM 3:47 PM 3:49 PM 3:51 PM 3:53 PM 3:56 PM 3:59 PM 4:02 PM 57 mins 55 mins 53 mins 50 mins 45 mins 43 mins 41 mins 39 mins 37 mins 34 mins 26 mins 25 mins 23 mins 21 mins 19 mins 18 mins 9 mins 8 mins 5 mins 4 mins 3 mins 1 min Chapter 9 Time Value Analysis Chapter 9 Time Value Analysis Gapenski’s Healthcare Finance: 7th Edition 1 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. In this section of the course, we turn from financial and managerial accounting to financial management. We will be discussing a foundational topic in the area of financial management – time value analysis. In these chapter lectures, there will be slides that show the Excel functions and formulas to use. I won’t go into detail on these in the chapter lectures because I will have separate lectures that will provide demonstrations of these Excel calculations. What I want to do in these chapter lectures is to give you an understanding of the terms, what they mean, how to solve them using basic math, and then just show the Excel solutions without necessarily demonstrating them. So, be sure to follow up and watch the video lectures that will help you to understand how to use Excel formulas to do these calculations we will be learning about in this chapter. This is also discussed quite extensively in the textbook. 1 Time Value of Money Time value analysis is necessary because money has time value. A dollar in hand today is worth more than a dollar to be received in the future. Why? Because of time value, the values of future dollars must be adjusted before they can be compared to current dollars. Time value analysis, or discounted cash flow analysis, constitutes the techniques used to account for the time value of money. 2 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. The reason time value analysis is so important is because a dollar in hand today is generally worth more than a dollar to be received in the future. When we get a promise of money in the future, we try to determine what that money is worth in today’s dollars – something we call present value. And then we will also look at what an investment made today will be worth in a future period of time, which is called future value. The process of determining these is called time value analysis, or, discounted cash flow analysis. A dollar in the future will not buy as much as a dollar in the current period because of inflation. Think back to 1950. I know most, if not all of use were not around then. But you’ve probably seen things showing what you could buy for a dollar back then. A decent car could be purchased for a couple of thousand dollars, gas cost much less, groceries, houses, etc. So if you had a dollar back then, it was considered of much greater worth than a dollar in today’s time. So, using time value analysis using the process of discounted cash flow analysis, we can estimate inflationary factors to help us determine the future value of current dollars. Time value can also be used to determine what future dollars are worth today. For instance, if someone promises you a certain amount of money, you need to consider what that amount is worth in today’s dollars, or, its present value, in order to see if that future payment is worth what you think it is. 2 Time Lines Tick marks designate ends of periods. Time 0 is the starting point (the beginning of Period 1); Time 1 is the end of Period 1 (the beginning of Period 2); and so on. I% 0123 CF0CF1CF2CF3 3 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. So now let’s talk about how we do this thing called discounted cash flow analysis. On this time line, Point 0 represents the starting point, the current period, and, 1 represents one period in the future, 2 is two periods, etc. The tick marks represent the end of a period. 3 What is the future value (FV) after three years of a $100 lump sum invested at 10% 0123 10% $100FV =? Finding future values (moving to the right along the time line) is called compounding. For now, assume interest is paid annually. 4 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. So let’s look at the future value of $100 invested at 10% over three years. We have $100 in an investment now, at point 0, and, we want to know what it is worth at the end of period 3. Now, we are going to calculate the interest on this investment using compounding, which simply means that the interest is calculated on the investment plus the interest earned during a certain period. For instance, in this example, we are going to assume that interest is paid annually. So the interest earned at the end of period 1 will be added to the initial investment and then the interest that was earned in period 1 will be earning interest along with the initial investment. So, at the end of period two, both the initial investment and the interest payment earned in period 1 will earn interest. This is called compound interest. It should make more sense to you as we go through the example. 4 Future Value: After 1 and 2 years After 1 year: FV1=PV + INT1 = PV + (PV × I) =PV × (1 + I) =$100 × 1.10 = $110.00. After 2 years: FV2=FV1 + INT2 =FV1 + (FV1 × I) = FV1 × (1 + I) =PV × (1 + I) × (1 + I) = PV × (1 + I)2 =$100 × (1.10)2 = $121.00. 5 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. This is the formula that we use to calculate the FV. The formula for future value at the end of period 1, represented by FV1, is the present value plus the interest for period 1 equals the present value plus the present value times the interest rate. So it will be $100 times 1 plus the interest rate, which is 10%, or, .1. So that will be $100 times 1.1 equals $110. The formula for the future value at the end of period 2, represented by FV2, is the future value at the end of period 1 plus the future value times the interest rate. So this will be $110 times 1.1 equals $121. Or, another way to put it is the present value times 1 plus the interest rate times 1 plus the interest rate, which ends up being the present value times 1 plus the interest rate squared, which also equals $121. In this case, since we are looking at period 2, we are squaring 1 plus the interest rate. For periods beyond period 2, we would simply replace the 2 with the number of that period, which is the n of the formula. 5 Future value after 3 years and in general After 3 years: FV3=FV2 + I3 =PV × (1 + I)3 =100 × (1.10)3 =$133.10. In general, FVN=PV × (1 + I)N. 6 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. So, here, for period 3, we have a 3 as the n and then do the same calculation, taking the present value times 1.1 times 1.1 times 1.1, which equals $133.10. Or, you can take $121, the value at the end of period 2, times 1.1, to get $133.10. 6 Three Primary Methods to Find FVs Solve the FV equation using a regular (nonfinancial) calculator. Use a financial calculator; that is, one with financial functions. Use a computer with a spreadsheet program such as Excel. We will focus our examples on Methods 1 & 3. 7 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. Now, there are three methods for finding the FVs. One is just going through the calculations for each individual year, which we just did. Next, is using a financial calculator, which is not used that often anymore. And third, the method used most often now, a spreadsheet, such as Excel. This is how you will be expected to do these calculations in this course. You can see how cumbersome it can get if there are multiple periods, so, using Excel can alleviate having to do all those calculations. 7 Nonfinancial Calculator Solution 0123 10% $100$110.00$121.00$133.10 100 × 1.10 × 1.10 × 1.10 = $133.10. 8 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. So, here is the example we just worked through with $100 invested at 10% for three years. We worked through it for each year, taking the present value times 1 plus the interest rate, or 1.1, and multiplying that times each period to get the value at the end of year three. 8 Spreadsheet Solution 9 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. And, here is the spreadsheet solution, showing the Excel calculations and functions. Again, as I mentioned previously, I will have a separate lecture where I will demonstrate how to work through these calculations in Excel. 9 What is the PV of $100 due in three if I = 10% 10% 0123 PV = ?$100 Finding present values (moving to the left along the time line) is called discounting. 10 Gapenski’s Healthcare Finance Chapter 9: Time Value Analysis Copyright 2021 Foundation of the American College of Healthcare Executives. Not for sale. Now, we are going to