1 This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, end-of-chapter problems, and end-of-chapter solutions, as well as PowerPoint slides for Chapter 3. The complete instructor resources consist of 39 pages of instructor notes; chapter models, end-of chapter problems, end-of-chapter solutions; and 744 PowerPoint slides. If you adopt this text you will be given access to complete materials. To obtain access, your request to and include the following information in your message: Book title Your name and institution name Title of the course for which the book was adopted and season course is taught Course level (graduate, undergraduate, or continuing education) and expected enrollment The use of the text (primary, supplemental, or recommended reading) A contact name and phone number/ address we can use to verify your employment as an instructor You will receive an containing access information after we have verified your instructor status. Thank you for your interest in this text and the accompanying instructor resources.
2 A B C D E F G H Chapter 3 UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed Time Value Analysis This spreadsheet model performs many of the calculations contained in Chapter 3. We recommend that you use the model in the following manner: 1. First, recognize that you do not have to use this model at all to understand time value analysis concepts. However, using the model will increase your understanding of the relevant concepts, and it will surely help when you use spreadsheet models for other purposes, especially any problem sets or cases assigned for this course. 2. Start by reading the chapter in its entirety. 3. Now place the text alongside your computer with this model on the screen. When you come to an explanation of a calculation in the text, see if the model has a matching calculation. 4. We assume that you know the basics of Excel, but you have not encountered some of its features or you may need a refresher or two. So we have built in explanations of how to do some of the functions in the model. As a result, you will learn more about Excel at the same time you learn about time value analysis. 5. Throughout this model, page numbers of the matching text calculations are provided in pink. Input data are in red on a yellow background, and output data are in green on a beige background. You are encouraged to change the input data to learn more about the calculations in the model. FUTURE VALUE OF A LUMP SUM (COMPOUNDING) (PAGE 81) 33 Find the future value (FV) of $100 after five years at an interest rate of 5% Interest rate 5.0% Note that input values are always Make some changes to the input values Lump sum 100 in red on a yellow background. to see the effect on future value. Time period Note that an FV at year end in green on This problem was solved using the formula, FV = PV x (1+I) N. However, there are a number of ways this problem could have been solved. One of the most valuable features in Excel is the "Function Wizard." To begin, first move the cursor to the cell where the answer is to appear. In this case, H90. Next, select the Function Wizard icon found in the toolbar at the top of the screen. It looks like this This button allows you to enter the Function Wizard. Upon clicking on it, you will see a dialog box entitled "Paste Function." On the left side of the dialog box is a menu entitled "Function Category," and on the right is a menu called "Function Name."
3 A B C D E F G H We will be selecting the "FV" function from the "Financial" category, and we will be using the following dialog box to input our data Notice that we entered a cell reference as the input for the problem instead of the actual value. We do this so that our spreadsheet can automatically reflect any changes to the input data. This is one of the features that make the spreadsheet such a valuable tool. Also note that the FV function can use up to five inputs. To find the future value of a lump sum only three are required, so the resulting formula has double commas, which means that the third input is zero. The final input (Type) is not required. The wizard enters =FV(B35,G38,,-B36) in Cell G90. FV = $ GRAPHIC VIEW OF THE COMPOUNDING (GROWTH) PROCESS (PAGE 85) With a spreadsheet, calculating FVs is a simple operation, and we can use them to graph the relationship between future value, growth, interest rates, and time. A similar graph can be found in the textbook in Figure 3.1. Period (n) 0% 5% 10% 15%
4 A B C D E F G H Future Value of $1 $5.00 $4.00 $3.00 $2.00 $1.00 $0.00 Relationships Among Future Value, Growth, Interest Rate, and Time Periods To create a graph in Excel, you first must access the "Chart Wizard" found in the toolbar near the top of the screen denoted by. Upon selecting the Chart Wizard, the first input dialog box will appear, and it will ask for the "Chart Type." In this case, we want a line graph, so we select "Line," and then we click one of the subtypes, in this case the first one After clicking "Next," we are presented with the "Source Data" box. We first enter the "Data Range" for the chart. These are the 159 data that will comprise the lines in our line graph. For our example, this information can be found in the above table. To select the 160 data range, use the cursor to highlight the cells range from B99 to E104. Note that the data are contained in columns
5 A B C D E F G H Now we must select the "Series" for our graph. Essentially, this is the set of data that will comprise each line in the graph. In this 191 graph, you can name each individual series by selecting it in the Series section and typing a label into the Name box. When an 192 individual series is highlighted, the Values section will let you know what data from the data range make up that particular line. To 193 place appropriate labels on the X axis, you must go to the Category (X) axis labels box and highlight from A99 to A
6 A B C D E F G H At this point, all of the necessary data for the chart have been inserted. From here, the chart just needs to be formatted according to your preferences (e.g., show or hide gridlines, change the numbers on the axes). PRESENT VALUE OF A LUMP SUM (DISCOUNTING) (PAGE 87) Find the present value (PV) of $ discounted back five years at an interest rate of 5%. Interest rate Lump sum 5.0% Make some changes to the input values to see the effect on present value. Time period PV at year end This problem can also be solved using the function wizard using a procedure similar to that for the FV function. Begin by putting the pointer on the cell in which you want to display the result, in this case Cell C264. Then, after selecting the "PV" function from the "Paste Function" box, the input data for the problem must be entered. Then click OK to get the result, $ PV = $ SOLVING FOR INTEREST RATE (I) (PAGE 92) What is the interest rate of a security priced at $78.35 that pays $100 after five years? N 5 Make some changes to the input values 272 PV to see how the variables affect I (Cell C298). 273 FV Once again, Excel has a special function for this calculation. We suggest using either a financial calculator or the Function Wizard 276 to solve this type of problem, because of its complexity. The procedure can be carried out using the Function Wizard, by selecting the 277 "Rate" function from the list of financial functions in the "Paste Function" dialog box. Upon entering the time, present value, and 278 future value, the interest rate can be found. Note that you can either type the data in or activate the menu slot and then click on
7 A B C D E F G H the appropriate cell. I = 5.00% We noted above the difficulty of solving this problem mathematically. This is because it involves taking the n th root of a value (an operation that generally requires either a calculator or a computer). However, if you would like to know how to solve the problem mathematically, the formula is: (FV N / PV) 1/N - 1, which is derived from the FV formula. N 5 I = 5.00% PV FV 100 SOLVING FOR TIME (N) (PAGE 93) A security yields 5%, costs $78.35 today, and will return $100 at some future date. What is the security's term to maturity? I 5.0% Make some changes to see the impact 316 PV on N (Cell C338). 317 FV The Function Wizard can be used to solve for time, or N. This operation can be performed by selecting the "Nper" option from the li 320 of financial functions, and then entering the input data into the dialog box
8 A B C D E F G H N = 5.00 Solving for N mathematically is very complicated. The formula for finding N involves using natural logarithms, which is a complex operation. For this reason, we highly suggest the use of the Function Wizard or financial calculator to solve this type of problem. However, here is the formula needed to solve for N: N = (ln (FV N / PV ) / (ln (1+ I)). This formula is applied in Cell C345. N = 5.00 ORDINARY ANNUITIES (PAGE 94) (Future Value Calculation Only, See Row 427 for Present Value) If the interest rate is 5%, what is the future value of an ordinary annuity that pays $100 at the end of each of the next three years? As explained below, one way to solve this problem is to find the future value of each of the annuity payments. However, this is somewhat tedious, especially if a lot of years are involved. In the following example, we use the input data of the interest rate and time to calculate the future value in time period 3 of each individual cash flow. Lastly, we take the sum of all the future values, which gives us the future value of the entire annuity. N 3 Change the I and PMT inputs to see their I 5.0% effect on FV. Note that N cannot be changed. PMT 100 Time period Annuity pmt Annuity FV FV = $ An easier procedure is to use the Function Wizard to solve for the future value of an annuity. This procedure is similar to that of a lump sum future value. Whereas before we left the "Pmt" field blank, now we insert the annuity payment ($100 in this case). First, we access the "FV" function box from the list of financial functions. Then, we input our new data. A key 369 thing to watch is the "Type" input box. Previously, we left this box alone. A "0" or no entry in the box indicates an ordinary annuity, and a "1" indicates an annuity due. Though we can leave the box blank, it is a good habit to enter a "0" in the field. FV = $ ANNUITIES DUE (PAGE 96) (Future Value Calculation Only, See Row 463 for Present Value) If the interest rate is 5%, what is the future value of an annuity due that pays $100 at the beginning of each of the next three years? The procedure for solving this problem follows the previous example with one notable exception. Because the payments occur at the
9 A B C D E F G H beginning of each year, the first annuity payment occurs in time period 0, and the last occurs in time period 2. N 3 Change the I and PMT inputs to see their I 5.0% effect on FV. Note that N cannot be changed. PMT 100 Time period Annuity pmt Annuity FV FV = $ Additionally, using the Function Wizard for this problem is exactly like above, but we enter a "1" instead of a "0" into the "Type" field. FV = $ ORDINARY ANNUITIES (PAGE 94) N 436 I 437 PMT (Present Value) If you were given the option of receiving a lump sum of money today or an annuity that pays $100 at the end of each of the next three years, at what price should you be indifferent to the two options, if the interest rate is 5%? The way to solve this problem is to find the PV of the annuity and then compare it with the lump sum. First, we consider each payment separately. 3 Change the I and PMT inputs to see their 5.0% effect on PV. Note that N cannot be changed. Time period Annuity pmt Annuity PV PV = $ Or, you could use the Function Wizard for this ordinary annuity.
10 A B C D E F G H PV = $ ANNUITIES DUE (PRESENT VALUE) (PAGE 96) (Present Value) What if the payments occurred at the beginning of each year? This problem is solved just like the previous problem, except that the payments occur in periods 0 through 2. N 3 Change the I and PMT inputs to see their I 5.0% effect on PV. Note that N cannot be changed. PMT 100 Time period Annuity pmt Annuity PV PV = $ Using the Function Wizard, we follow the same procedure as above, except remember to enter a "1" to tell Excel that this problem ha payments occurring at the beginning of the periods PV = $ PERPETUITIES (PAGE 99) What is a perpetuity worth if it pays $100 every year and the discount rate is 5%? PMT 100 Change the payment and discount rate 503 I 5.0% to see their impact on present value PV = $2, UNEVEN CASH FLOW STREAMS
11 A B C D E F G H Present Value (Page 100) Calculate the present value of the following cash flow stream, discounted at 10%. I 10.0% Change the discount rate (I) to examine its effect on PV Change the cash flows to examine their impact on PV PV of Stream NPV = $ As we show above, the first way to solve for the present value of this uneven cash flow stream is to use the timeline to find the present value of each of the cash flows in the periods in which they occur, then sum all the present values. This procedure will yield the correct present value. This problem could also be set up in a column format; it is a matter of personal preference as to which format is easier to interpret and use. Once we have placed the data into columns, we can solve for the present value of each of the cash flows (like we did previously) and add all of the present values together to get the final answer. I 10.0% N CF PV Try entering a $500 outflow at Year NPV = $ With, the financial calculator, we could enter each of these cash flows and the discount rate, and simply press NPV for the present value of the cash flow stream. In Excel, we can perform a similar calculation by using the "NPV" function. While this function is very similar, there is a key distinction. In the cash flow register of your calculator, the first entry you make would be the cash flow to occur in time period zero. However, the "NPV" function interprets the first data entry as being the cash flow in time period one. Therefore, the initial cash flow must be added separately. In this particular example, the initial cash flow is zero. Data from either the timeline or the columns could be entered here.
12 A B C D E F G H NPV = $ Both methods will yield the same result, so use the one that you are most comfortable with. In the event that you have a problem consisting of a cash flow at time period zero, you will have to manually add this value to the NPV of the remaining cash flows. Also note that when using the Function Wizard, we used the cash flow data from columns. However, we could have just as easily used the timeline data that we initially presented. Future Value (Page 101) Calculate the future value of the cash flow stream illustrated above in the previous question. First, we will solve this problem by adding the future values of all the cash flows in time period 7. I 10.0% Change the discount rate (I) to examine its effect on FV. N # compoundings CF FV FV = $ Excel does not have a net future value function, but the above procedure works for this type of problem. 601 An alternative is to calculate the NPV and then compound that value out to the end of the cash flow 602 stream, but that procedure is not as easy conceptually as that used above USING TIME VALUE ANALYSIS TO MEASURE FINANCIAL RETURNS Dollar Return (Page 103) Calculate the net present value (NPV) of the following cash flow stream, discounted at 10% I 10.0% Change the discount rate (I) to 611 examine its effect on PV Change the cash flows to 616 examine their impact on PV 617 PV of Stream NPV = $ As we show above, the first way to solve for the NPV of this investment is to use 623 the timeline to find the present value of each of the cash flows in the periods in which they occur, then 624 sum all the present values. This procedure will yield the correct present value This problem could also be set up in a column format; it is a matter of personal preference as to which format is easier to
13 A B C D E F G H interpret and use. Once we have placed the data into columns, we can solve for the present value of each of the cash flows (like we did previously) and add all of the present values together to get the final answer. I 10.0% N CF PV NPV = $80.95 With, the financial calculator, we could enter each of these cash flows and the discount rate, and simply press NPV for the present value of the cash flow stream. In Excel, we can perform a similar calculation by using the "NPV" function. While this function is very similar, there is a key distinction. In the cash flow register of your calculator, the first entry you make would be the cash flow to occur in time period zero. However, the "NPV" function interprets the first data entry as being the cash flow in time period one. Therefore, the initial cash flow must be added separately. In this particular example, the initial cash flow is Rate of Return (Page 104) NPV = $80.95 Calculate the internal rate of return (IRR) of the cash flow stream illustrated above in the previous question. Here we use the IRR function: IRR = 15.3% Note that the IRR function has this format: IRR(range, starting guess). The starting guess is required to "begin" the iterative calculation procedure used by Excel. We used the discount rate as the guess, but any reasonable value could have been entered. SEMIANNUAL AND OTHER COMPOUNDING PERIODS (PAGE 105) If $100 is invested in an account at an interest rate of 6%, annual compounding, for three years, what is the FV? N 3 FV = $ I 6.0% PV 100 What is the FV with semiannual compounding? N (years x 2) 6 FV = $ I (I per year/2) 3.0% PV 100 $0.30 is the difference. What is the PV of an ordinary annuity of $100 per year for three years when the interest rate is 8%, compounded annually? N 3 PV = $ I 8.0%
14 A B C D E F G H PMT 100 What is the PV of an ordinary annuity of $100 per year for three years when the interest rate is 8%, compounded semiannually? N 6 FV = $ I 4.0% PMT 50 Remember that in cases of non-annual compounding, all input variables (N, I, PMT) must reflect the number of compounding period AMORTIZED LOANS (PAGE 108) What would the required payment be on a $1,000 loan that is to be repaid in three equal installments at the end of each of the next three years if the interest rate is 6%? N I PV PMT = $374,110 3 Change the inputs to see the impact 6.0% on the payment amount and the amortization table. Now, construct an amortization table for the loan described above. N Loan amount Payment Interest Principal Balance 1 $1,000,000 $374,110 $60,000 $314,110 $685, , ,110 41, , , , ,110 21, ,934 0 Totals $1,122,329 $122,329 $1,000,000
15 UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed Chapter 3 -- Time Value Analysis PROBLEM 1 Find the following values for a lump sum assuming annual compounding a. The future value of $500 invested at 8 percent for one year b. The future value of $500 invested at 8 percent for five years c. The present value of $500 to be received in one year when the opportunity cost rate is 8 percent d. The present value of $500 to be received in five years when the opportunity cost rate is 8 percent
16 A B C D E F G H I UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed Chapter 3 -- Time Value Analysis PROBLEM 1 Find the following values for a lump sum assuming annual compounding: a. The future value of $500 invested at 8 percent for one year b. The future value of $500 invested at 8 percent for five years c. The present value of $500 to be received in one year when the opportunity cost rate is 8 percent d. The present value of $500 to be received in five years when the opportunity cost rate is 8 percent ANSWER Spreadsheet solution: a. FV = $500 x (1.08)1 = $ ($540.00) =FV(0.08,1,,500) b. FV = $500 x (1.08)5 = $ ($734.66) =FV(0.08,5,,500) c. PV = $500 / (1.08)1 = $ ($462.96) =PV(0.08,1,,500) d. PV = $500 / (1.08)5 = $ ($340.29) =PV(0.08,5,,500)
17 3-1 CHAPTER 3 Time Value Analysis Future F t and present values Solving g for I and N Investment returns Opportunity cost Amortization 8/22/06
18 3-2 Time Value of Money Time value analysis is necessary because money has time value. A dollar in hand today is worth ot more oethan 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 constitutes the techniques that are used to account for the time value of money.
19 3-3 Time Lines I% CF 0 CF 1 CF 2 CF 3 Tick marks designate ends of periods. Time 0 is the starting gp point (the beginning g of Period 1); Time 1 is the end of Period 1 (the beginning of Period 2); and so on.
20 3-4 What is the FV after three years of a $100 lump sum invested at 10%? % -$100 FV =? Finding g future values (moving to the right along the time line) is called compounding. For now, assume interest is paid annually.
21 3-5 After 1 year: FV 1 = PV + INT 1 = PV + (PV x I) = PV x (1 + I) = $100 x 1.10 = $ After 2 years: FV 2 = FV 1 + INT 2 = FV 1 +(FV 1 xi)= FV 1 x(1+i) = PV x (1 + I) x (1 + I) = PV x (1 + I) 2 = $100 x (1.10) 10) 2 = $121.00
22 3-6 After 3 years: FV 3 = FV 2 +I 3 = PV x (1 + I) 3 = 100 x (1.10) 10) 3 = $ In general, FV N = PV x (1 + I) N
23 3-7 Three Primary Methods to Find FVs Solve l the FV equation using a regular calculator. Use a financial calculator that is, one with financial functions. Use a computer with a spreadsheet program such as Microsoft Excel.
24 3-8 Regular Calculator l Solution % -$100 $ $ $ $100 x 1.10 x 1.10 x 1.10 = $133.10
25 3-9 Spreadsheet Solution Function = FV(rate,nper,pmt,pv,type) pmt pv type) Cell formula = FV(0.1,3,,100) Cell display = (133.10) 10)
26 3-10 Spreadsheet Solution (Cont.) rate = interest rate per period nper = total number of payment periods in an annuity pmt = payment made each period; cannot change over the life of the annuity pv = present value or lump sum amount that a series of future payments is worth now; if omitted, pv=0 type = payment at beginning of period = 1; payment at end of period = 0 or omitted
27 3-11 What is the PV of $100 due in three years if I = 10%? % PV =? $100 Finding present values (moving to the left along the time line) is called discounting.
28 3-12 Solve FV N = PV x (1 + I ) N for PV PV = FV /(1+I) N N PV = $100 / (1.10) 3 = $100(0.7513) = $75.13? If I offer you $75.13 today or $100 three years from now, which would you prefer?
29 3-13 Spreadsheet Solution Function = PV(rate,nper,pmt,fv,type) pmt type) Cell formula = PV(0.1,3,,100) Cell display = (75.13)
30 3-14 Solving for I Assume that a bank offers an account that will pay $200 after five years on each $75 invested. What is the implied interest rate? Function = RATE(nper,pmt,pv,fv,type) Cell formula = RATE(5,0,-75,200) 00) Cell display = 22%
31 3-15 Solving for N Assume an investment earns 20 percent per year. How long will it take for the investment to double? Function = NPER(rate,pmt,pv,fv,type) pv type) Cell formula = NPER(0.2,0,-1,2) Cell display = ? What is the Rule of 72?
32 3-16 Types of Annuities Three Year Ordinary Annuity I% PMT Three Year Annuity Due PMT PMT I% PMT PMT PMT
33 3-17 What is the FV of a three-year ordinary annuity of $100 invested at 10%? % $100 $100 $ FV = $331
42 3-26 Spreadsheet Solution Function = NPV(rate,value1,value2, ) value2 Cell formula =NPV(0.1,100,300,300,-50) Cell display =
43 3-27 Return on Investment t (ROI) The financial performance of an investment is measured by its return on investment. Time value analysis is used to calculate investment returns. Returns can be measured either in dollar terms or in rate of return terms. Assume that a hospital is evaluating a new MRI. The project s expected cash flows are given on the next slide.
44 3-28 MRI Investment t Expected Cash Flows (thousands) $1,500 $310 $400 $500 $750? Where do these numbers come from?
45 3-29 Simple Dollar Return $1,500 $310 $400 $500 $ $ 460 = Simple dollar return? Is this a good measure?
46 3-30 Discounted Cash Flow (DCF) Dollar Return -$1, % $310 $400 $500 $750 $ 78 = net present value (NPV)
47 3-31 Spreadsheet Solution A B C D % Interest rate 3 $ (1,500) Year 0 CF Year 1 CF Year 2 CF Year 3 CF Year 4 CF $ 78 =NPV(A2,A4:A7)+A3 (entered into Cell A10)
48 3-32 Opportunity Cost Rate To find an investment s dollar return (NPV), we need to apply a discount rate. Where does it come from? The discount rate is the opportunity cost rate. It is the rate that could be earned on alternative investments of similar risk. It does not depend on the source of the investment funds. We will apply this concept over and over in this course.
49 3-33 Opportunity Cost Rate (Cont.) The opportunity cost rate is found (at least in theory) as follows. Assess the riskiness of the cash flow(s) to be discounted. Identify alternative investments (usually securities) that have the same risk. Estimate t the expected return on the similar-risk il i alternative investment. When applied, the resulting PV provides a return equal to the opportunity cost rate. In most time value situations, s, benchmark opportunity cost rates are known.
50 3-34 Opportunity Cost Rate (Cont.) When calculating lating NPV, the discounting process automatically recognizes the opportunity cost of capital. Thus, A positive NPV means that the investment is expected to create value for the investor. A negative NPV means that the investment is expected to lose value for the investor.
51 3-35 -$1, Rate of f(percentage) )Return % $310 $400 $500 $750 $ 0.00 = NPV, so E(R) = 10.0%.
52 3-36 Spreadsheet Solution A B C D % Interest rate guess 3 $ (1,500) Year 0 CF Year 1 CF Year 2 CF Year 3 CF Year 4 CF % =IRR(A3:A7,A2) (entered into Cell A10)
53 3-37 Rate of Return (Cont.) In capital investment analyses, the rate of return often is called internal rate of return (IRR). In essence, it is the percentage return expected on the investment. To interpret the rate of return, it must be compared to the opportunity ty cost of capital. In this case, 10 percent versus 8 percent.
54 3-38 Intra-Year Compounding Thus far, all examples have assumed annual compounding. When compounding occurs intra-year, the following occurs: Interest t t is earned on interest t during the year (more frequently). The future value of an investment is larger than under annual compounding. The present value of an investment is smaller than under annual compounding.
55 % Annual: FV 10) 3 3 = 100 x (1.10) = % Semiannual: FV = x (1.05) =
56 3-40 Effective Annual Rate (EAR) EAR is the annual rate that causes the PV to grow to the same FV as under intra-year compounding. What is the EAR for 10 percent, semiannual compounding? Consider the FV of $1 invested for one year. FV = $1 x (1.05) 2 = $ EAR = 10.25%, because this rate would produce the same ending amount ($1.1025) 1025) under annual compounding.
57 3-41 The EAR Formula I Stated EAR = M M = = (1.05) = = 10.25%
58 3-42 EAR of 10% at Various Compounding EAR Annual = 10% EAR Q = ( /4) = 10.38% EAR M = ( /12) = 10.47% EAR D(360) = ( /360) = 10.52%
59 3-43 Spreadsheet Solution Function = EFFECT(nominal_rate,npery) nper Cell formula = EFFECT(0.10,4) Cell display = Function = EFFECT(nominal_rate,npery) Cell formula = EFFECT(0.10,12) 12) Cell display = Function = EFFECT(nominal_rate,npery) Cell formula = EFFECT(0.10,365) Cell display =
60 3-44 Spreadsheet Solution nominal_rate = nominal interest rate npery = number of compounding periods per year
61 3-45 Using the EAR month 5% periods $100 $100 $100 Here, payments occur annually, but compounding occurs semiannually, so we can not use normal annuity valuation techniques.
62 First Method: Compound Each CF % $100 $100 $ $331.80
63 3-47 Second Method: Treat as an Annuity Find the EAR for the stated rate: Function = EFFECT(nominal_rate,npery) Cell formula = EFFECT(0.10,2) Cell display = Then, use standard annuity techniques: Function = FV(rate,nper,pmt,pv,type) pmt pv type) Cell formula = FV(0.1025,3,100) Cell display = (331.80)
64 3-48 Amortization Construct an amortization schedule for a $1,000, 10% annual rate loan with three equal payments.
65 3-49 Step 1: Find the required payments % -$1,000 PMT PMT PMT Function = PMT(rate,nper,pv,fv,type),p,, Cell formula =PMT(0.1,3,1000) Cell display = (402.11)
66 3-50 Step 2: Find interest t charge for Year 1. INT t = Beginning balance x I. INT 1 = $1,000 x 0.10 = $100 Step 3: Find repayment of principal in Year 1. Repmt = PMT - INT = $ $100 = $302.11
67 3-51 Step 4: Find ending balance at end of Year 1. End bal = Beg balance - Repayment = $1,000 - $ = $ Repeat these steps for Years 2 and 3 to complete the amortization table
68 3-52 BEG PRIN END YR BAL PMT INT PMT BAL 1 $1,000 $402 $100 $302 $ TOTAL $1,206 $206 $1,000 Note that annual interest declines over time while the principal payment increases.
69 $ Interest Principal Payments Level payments. Interest declines because outstanding balance declines. Lender earns 10% on loan outstanding, t which h is falling.
70 3-54 Conclusion This concludes our discussion i of Chapter 3 (Time Value Analysis). Although not all concepts were discussed in class, you are responsible for all of the material in the text.? Do you have any questions?
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
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Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
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Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
Lease Analysis Tools 2009 ELFA Lease Accountants Conference Presenter: Bill Bosco, Pres. firstname.lastname@example.org Leasing 101 914-522-3233 Overview Math of Finance Theory Glossary of terms Common calculations
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flows--either payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash
6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
: Financial Calculations The Time Value of Money Growth of Money I Growth of Money II The FV Function Amortisation of a Loan Annuity Calculation Comparing Investments Worked examples Other Financial Functions
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
Chapter 2 - Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equal-sized
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities
This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
MHSA 8630 -- Healthcare Financial Management Time Value of Money Analysis ** One of the most fundamental tenets of financial management relates to the time value of money. The old adage that a dollar in
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
Time Value of Money 1 This topic introduces you to the analysis of trade-offs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
BUSI Financial Management Time Value of Money 1 Time Value of Money (TVM) Present value and future value how much is $1 now worth in the future? how much is $1 in the future worth now? Business planning
REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS
file:///f /Courses/2010-11/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present
UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT Calculator (Hewlett-Packard 10BII) Tutorial To begin, look at the face of the calculator. Most keys (except a few) have two functions: Each key s primary function
2 Determinants of Valuation Part Two 4 Time Value of Money 5 Fixed-Income Securities: Characteristics and Valuation 6 Common Shares: Characteristics and Valuation 7 Analysis of Risk and Return The primary
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
Chapter 3 Understanding The Time Value of Money Prentice-Hall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple
To begin, look at the face of the calculator. Almost every key on the BAII PLUS has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
Basic Pivot Tables Pivot tables summarize data in a quick and easy way. In your job, you could use pivot tables to summarize actual expenses by fund type by object or total amounts. Make sure you do not
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations
Using Technology to Assist in Financial Calculations Calculators: TI-83 and HP-12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI-83 / 84 Graphing Calculator Section 5.5 of textbook
CHAPTER 7 The Time Value of Money After studying this chapter, you should be able to: 1. Explain the concept of the time value of money. 2. Calculate the present value and future value of a stream of cash
Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing
File C5-96 June 2013 www.extension.iastate.edu/agdm Understanding the Time Value of Money If I offered to give you $100, you would probably say yes. Then, if I asked you if you wanted the $100 today or
Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-733A Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:
e C P M 1 5 : P o r t f o l i o M a n a g e m e n t f o r P r i m a v e r a P 6 W e b A c c e s s Capital Budgeting C o l l a b o r a t i v e P r o j e c t M a n a g e m e n t e C P M 1 5 C a p i t a l
SECTION 1, CHAPTER 6 TIME VALUE OF MONEY CHAPTER OUTLINE Clues, Hints, and Tips Present Value Future Value Texas Instruments BA II+ Calculator Hewlett-Packard HP-12C Calculator CLUES, HINTS, AND TIPS Present
Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
I Corporate Finance Models Basic Financial Calculations. Overview This chapter aims to give you some finance basics and their Excel implementation. If you have had a good introductory course in finance,
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
TVM Functions in EXCEL Order of Variables = (Rate, Nper, Pmt, Pv, Fv,Type, Guess) Future Value = FV(Rate,Nper,Pmt,PV,Type) Present Value = PV(rate,nper,pmt,fv,type) No. of Periods = NPER(rate, pmt, pv,
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
PMT Calculates the payment for a loan based on constant payments and a constant interest rate. PMT(rate,nper,pv,fv,type) For a more complete description of the arguments in PMT, see the PV function. Rate
Course FM / Exam 2 Introduction It wasn t very long ago that the square root key was the most advanced function of the only calculator approved by the SOA/CAS for use during an actuarial exam. Now students
HO-23: METHODS OF INVESTMENT APPRAISAL After completing this exercise you will be able to: Calculate and compare the different returns on an investment using the ROI, NPV, IRR functions. Investments: Discounting,
Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction
Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS
FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems - Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 3-1 a) Future Value = FV(n,i,PV,PMT)
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
Foundation review: Introduction Foundation review Introduction Throughout FN1, you will be expected to apply techniques and concepts that you learned in prerequisite courses. The purpose of this foundation