Chapter 4 The Time Value of Money (Part 2)


 Kevin Wesley Burke
 1 years ago
 Views:
Transcription
1 Chapter 4 The Time Value of Money (Part 2) LEARNING OBJECTIVES 1. Compute the future value of multiple cash flows. 2. Determine the future value of an annuity. 3. Determine the present value of an annuity. (Slide 42) 4. Adjust the annuity formula for present value and future value for an annuity due and understand the concept of a perpetuity. 5. Distinguish between the different types of loan repayments: discount loans, interestonly loans, and amortized loans. 6. Build and analyze amortization schedules. 7. Calculate waiting time and interest rates for an annuity. 8. Apply the time value of money concepts to evaluate the lottery cash flow choice. 9. Summarize the ten essential points about the time value of money. IN A NUTSHELL In Part two of this 2part unit on the time value of money topic, the author discusses and illustrates how the time value of money equation can be modified and used for calculations involving the compounding and discounting of interest in cash flow streams that are more complex that mere lump sums. Real life situations seldom involve single outflow/inflow types of cash flow streams. More often, we are faced with periodic outflows such as loan, rent, or lease payments and/or periodic inflows such as retirement annuities. In this chapter, we learn how to calculate the present and future values of more complex cash flow streams such as those involving unequal cash flows, ordinary annuities and annuities due. In addition, the different methods by which loans can be paid off; and the method of setting up and analyzing amortization schedules associated with mortgages and other installment loans are also covered. LECTURE OUTLINE 4.1 Future Value of Multiple Payment Streams (Slides 43 to 47) In the case of investments involving unequal periodic cash flows, we can calculate the future value of the cash flows by treating each of the cash flows as a lump sum and calculate its future value over the relevant number of periods. The individual future values are then summed up to get the future value of the multiple payment streams. 76
2 Chapter 4 n The Time Value of Money (Part 2) 77 It is best to use a time line, as shown in Figure 41 in the text, which clearly shows each cash flow, the respective number of periods over which interest is to be compounded, and the interest rate that will apply. There is a shorter alternative way to solve the future value of a stream of unequal periodic cash flows, which involves using the Net Present Value (NPV) function of a financial calculator or a spreadsheet. We can first compute the net present value (at t = 0) of the stream of uneven cash flows at the given rate of interest, and then using the NPV as the present value, we find the future value of a lump sum at the end point of the cash flow stream. This method is shown in Example 1 below. Example 1: Future Value of an Uneven Cash Flow Stream Jim deposits $3,000 today into an account that pays 10% per year, and follows it up with 3 more deposits at the end of each of the next three years. Each subsequent deposit is $2,000 higher than the previous one. How much money will Jim have accumulated in his account by the end of three years? T 0 T 1 T 2 T 3 $3,000 $5,000 $7,000 $9,000 $3,000 (1.10) 3 $5,000 (1.10) 2 $7,000 (1.10) 1 $7, $6, $3, We use the Future Value of a Single Sum formula and compound each cash $26, flow for the relevant number of years over which interest will be earned. Then we sum up the compounded values to get the accumulated value of Jim s deposits at the end of three years as shown below: FV = PV (1 + r) n FV of Cash Flow at T 0 = $3,000 (1.10) 3 = $3, = $3, FV of Cash Flow at T 1 = $5,000 (1.10) 2 = $5, = $6, FV of Cash Flow at T 2 = $7,000 (1.10) 1 = $7, = $7, FV of Cash Flow at T 3 = $9,000 (1.10) 0 = $9, = $9, Total = $26, Note: Students should be reminded that cash flows can only be added up if they occur at the same point in time as at the end of Year 3.
3 78 Brooks n Financial Management: Core Concepts, 2e ALTERNATIVE METHOD: Using the Cash Flow (CF) key of the calculator, enter the respective cash flows. That is, CF0 = $3000; CF1 = $5000; CF2 = $7000; CF3 = $9000; Next calculate the NPV using I = 10%; NPV = $20,092.41; Finally, using PV = $20,092.41; n = 3; i = 10%; PMT = 0; CPT FV = $26, Future Value of an Annuity Stream (Slides 48 to 413) Often, we are faced with financial situations which involve equal, periodic outflows/inflows. Such payment streams are known as annuities. Examples of an annuity stream include rent, lease, mortgage, car loan, and retirement annuity payments. An annuity stream can begin at the start of each period as is true of rent and insurance payments or at the end of each period, as in the case of mortgage and loan payments. The former type is called an annuity due while the latter is known as an ordinary annuity stream. This section covers ordinary annuities. Annuities due will be covered in a later section. Although the future value of an ordinary annuity stream can be calculated by using the same process that was explained in section 4.1 above, there is a simplified formula which makes the process much easier. The formula for calculating the future value of an annuity stream is as follows: ( r) + = 1 n FV PMT 1 r where PMT is the term used for the equal periodic cash flow, r is the rate of interest, and n is the number of periods involved. The item that PMT is multiplied by is known as the Future Value Interest Factor of an Annuity (FVIFA). It can be either calculated using the equation or got from a table provided in Appendix A3. Of course, table values are only available for discrete interest rates and time periods. Note: The length of the period can be a day, week, quarter, month, or any other equal unit of time, not just a year as is often misunderstood by students. The rate of interest, however, is often given on an annual basis and must be accordingly adjusted and used in the problem. Example 2: Future Value of an Ordinary Annuity Stream Jill has been faithfully depositing $2,000 at the end of each year since the past 10 years into an account that pays 8% per year. How much money will she have accumulated in the account? This problem could be solved by first calculating the FV of each of the year end deposits for the respective number of years involved, and then summing them all up at the end of year 10 as shown below: Future Value of Payment One = $2, = $3, Future Value of Payment Two = $2, = $3,701.86
4 Chapter 4 n The Time Value of Money (Part 2) 79 Future Value of Payment Three = $2, = $3, Future Value of Payment Four = $2, = $3, Future Value of Payment Five = $2, = $2, Future Value of Payment Six = $2, = $2, Future Value of Payment Seven = $2, = $2, Future Value of Payment Eight = $2, = $2, Future Value of Payment Nine = $2, = $2, Future Value of Payment Ten = $2, = $2, Total Value of Account at the end of 10 years $28, FORMULA METHOD It is much quicker to solve this problem using the following formula: ( r) + = 1 n FV PMT 1 r where, PMT = $2,000; r = 8%; and n=10 i.e. the number of deposits involved. The FVIFA would equal [((1.08) 101)/.08] = , and the FV = $ = $28, USING A FINANCIAL CALCULATOR N= 10; PMT = 2,000; I = 8; PV=0; CPT FV = 28, USING AN EXCEL SPREADSHEET Enter =FV(8%, 10, 2000, 0, 0); Output = $28, Rate, Nper, Pmt, PV,Type Type is 0 for ordinary annuities and 1 for annuities due USING FVIFA TABLE A 3 Find the FVIFA in the 8% column and the 10 period row; FVIFA = FV = = $ Present Value of an Annuity (Slides 414 to 419) If we are interested in finding out the value of a series of equal periodic cash flows at the current point in time, we can either sum up the discounted values of each periodic cash flow (PMT) for the related number of periods or use the following simplified formula: 1 PV = PMT 1 ( 1+ r) r n
5 80 Brooks n Financial Management: Core Concepts, 2e The last portion of the equation, 1 1 ( 1+ r) n, is the Present Value Interest Factor of r an Annuity (PVIFA). The values of various PVIFAs are displayed in Appendix A4 for different combinations of discrete interest or discount rates (r) and the number of payments (n). A practical application of such a calculation would be in calculating how much to have saved up in an account prior to a child attending college or prior to retirement so as to be able to withdraw equal annual amounts each year over a required number of years. Example 3: Present Value of an Annuity John wants to make sure that he has saved up enough money prior to the year before which his daughter begins college. Based on current estimates, he figures that college expenses will amount to $40,000 per year for 4 years (ignoring any inflation or tuition increases during the 4 years of college). How much money will John need to have accumulated in an account that earns 7% per year, just prior to the year that his daughter starts college? Here the known variables are: n=4; PMT=$40,000; and r = 7%. What we have to solve for is the PV of the annuity series, which can be done by any one of 4 methods, i.e. formula, financial calculator, spreadsheet, or PVIFA factor using Table A4. FORMULA METHOD: Using the following equation: 1 PV = PMT 1 ( 1+ r) r n 1. Calculate the PVIFA value for n=4 and r=7%. 1 1 ( ) = [ 1 ( ) ] 0.07 = Then, multiply the annuity payment by this factor to get the PV, PV = $40, = $135, FINANCIAL CALCULATOR METHOD: It is important to remind students that the calculator must be in END mode so that the payments are treated as an ordinary annuity. Set the calculator for an ordinary annuity (END mode) and then enter: N= 4; PMT = 40,000; I = 7; FV=0; CPT PV = 135, SPREADSHEET METHOD: Enter =PV(7%, 4, 40,000, 0, 0); Output = $135,488.45
6 Chapter 4 n The Time Value of Money (Part 2) 81 Rate, Nper, Pmt, FV,Type PVIFA TABLE (APPENDIX A 4) METHOD Since the rate of interest (7%) and the number of withdrawals (4) are both discrete values, we could easily solve this problem by obtaining the PVIFA value from the table in Appendix A4 i.e and multiplying it by the PMT ($40,000) to get a PV of $ Notice the slight rounding error! 4.4 Annuity Due and Perpetuity (Slides 420 to 425) Annuity due: Certain types of financial transactions such as rent, lease, and insurance payments involve equal periodic cash flows that begin right away or at the beginning of each time interval. This type of annuity is known as an annuity due. Figure 4.5 in the text shows both types of annuities on a time line. An annuity due stream is scaled back for one period as shown by the arrows. Note that when calculating the PV of an annuity due stream one less period of interest would be required for each payment, since the first cash flow begins right away. Likewise, when calculating the FV of the cash flow stream at the end of 4 periods, an additional period of interest would apply to each periodic cash flow, since the 4 th payment occurs at the beginning of the 4 th year. Figure 4.5 Ordinary Annuity versus Annuity Due T 0 T 1 T 2 T 3 T 4 #1 $100 $100 $100 $100 Ordinary Annuity For problems involving an annuity due, the equations used to calculate the PV and FV of an ordinary annuity can simply be adjusted by multiplying them by the term (1+r). That is, 1 1 n ( + ) 1 r PV = PMT + r r Or ( 1 ) PV annuity due = PV ordinary annuity (1+r) AND #2 $100 $100 $100 $100 Annuity Due
7 82 Brooks n Financial Management: Core Concepts, 2e Or ( r) n 1+ 1 FV = PMT + r r ( 1 ) FV annuity due = FV ordinary annuity (1+r) When using a financial calculator we must set the mode to BGN for an annuity due or END for an ordinary annuity and proceed just as we would any other PV or FV problem. In the case of a spreadsheet, the Type of the cash flow, within the =PV or =FV functions is set to 0 or omitted for an ordinary annuity and 1 for an annuity due. Example 4: Annuity Due versus Ordinary Annuity Let s say that you are saving up for retirement and decide to deposit $3,000 each year for the next 20 years into an account which pays a rate of interest of 8% per year. By how much will your accumulated nest egg vary if you make each of the 20 deposits at the beginning of the year, starting right away, rather than at the end of each of the next twenty years? Given information: PMT = $3,000; n=20; i= 8%; PV=0; Future value of an ordinary annuity = Future value of an annuity due = FV = PMT ( r) 1+ n 1 r = $3,000 [((1.08) 201)/.08] = $3, = $137, ( r) n 1+ 1 FV = PMT + r r = $137, (1.08) = $148, Note: If we set the mode in the calculator to END; and enter: ( 1 ) PMT = $3,000; n=20; i= 8%; PV=0; and CPT FV; we get FV =$137, Likewise, if we set the mode to BGN; we get FV = $148, Similarly, using a spreadsheet and setting the Type to 0 we get FV= $137, i.e. the PV of an ordinary annuity and if we set the Type to 1; we get FV = 148, i.e. FV of an annuity due 4.6
8 Chapter 4 n The Time Value of Money (Part 2) 83 Perpetuity A Perpetuity is an equal periodic cash flow stream that will never cease. One example of such a stream is a British consol, which is a bond issued by the British government which promised to pay a specified rate of interest forever, without ever repaying the principal. The PV of a perpetuity is calculated by using the following equation: PMT PV = r Example 5: PV of a Perpetuity If you are considering the purchase of a consol that pays $60 per year forever, and the rate of interest you want to earn is 10% per year, how much money should you pay for the consol? Here, r=10%, PMT = $60; and PV = ($60/.1) = $600 is the most you should pay for the consol. Remind students that r should be in decimals. 4.5 Three Loan Payment Methods (Slides 426 to 430) Depending on the terms agreed upon at the time of issue, borrowers can typically pay off a loan in one of 3 ways: 1. They can pay off the principal (the original loan amount that you borrowed) and all the interest (the amount the lender charges you for borrowing the money) at one time at the maturity date of the loan. This is called a discount loan. 2. They can make periodic interest payments and then pay the principal and final interest payment at the maturity date. This is called an interestonly loan. 3. They can pay both principal and interest as they go by making equal payments each period. This is called an amortized loan. Example 6: Discount versus Interest only versus Amortized loans Roseanne wants to borrow $40,000 for a period of 5 years. The lenders offers her a choice of three payment structures: 1. Pay all of the interest (10% per year) and principal in one lump sum at the end of 5 years; 2. Pay interest at the rate of 10% per year for 4 years and then a final payment of interest and principal at the end of the 5 th year; 3. Pay 5 equal payments at the end of each year inclusive of interest and part of the principal. Under which of the three options will Roseanne pay the least interest and why? Calculate the total amount of the payments and the amount of interest paid under each alternative.
9 84 Brooks n Financial Management: Core Concepts, 2e Method 1: Discount Loan Since all the interest and the principal is paid at the end of 5 years we can use the FV of a lump sum equation to calculate the payment required, i.e. FV = PV (1 + r) n FV 5 = $40,000 (1+0.10) 5 = $40, = $64, Interest paid = Total payment  Loan amount Interest paid = $64, $40,000 = $24, Method 2: Interest Only Loan Method 3: Amortized Loan Annual Interest Payment (Years 14) = $40, = $4,000 Year 5 payment = Annual interest payment + Principal payment = $4,000 + $40,000 = $44,000 Total payment = $16,000 + $44,000 = $60,000 Interest paid = $20,000 To calculate the annual payment of principal an interest we can use the PV of an ordinary annuity equation and solve for the PMT value using n = 5; I = 10%; PV = $40,000, and FV = 0. That is: or PV PMT = 1 1 r ( 1+ r) $40,000 PMT = n ( ) 5 $40,000 PMT = = $10, Total payments = 5 $10,551.8 = $52, Interest paid = Total Payments  Loan Amount = $52, $40,000 Interest paid = $12, Comparison of Total payments and interest paid under each method Loan Type Total Payment Interest Paid Discount Loan $64, $24, Interestonly Loan $60, $20, Amortized Loan $52, $12, So, the amortized loan is the one with the lowest interest expense, since it requires a higher annual payment, part of which reduces the unpaid balance on the loan and thus results in less interest being charged over the 5year term. 4.9
10 Chapter 4 n The Time Value of Money (Part 2) Amortization Schedules (Slides 431 to 433) An amortization schedule is a tabular listing of the allocation of each loan payment towards interest and principal reduction, which can help borrowers and lenders figure out the payoff balance on an outstanding loan. To prepare an amortization schedule, we must first compute the amount of each equal periodic payment (PMT) using the PVIFA equation or the appropriate financial calculator keys. Next, we calculate the amount of interest that would be charged on the unpaid balance at the end of each period, minus it from the PMT, reduce the loan balance by the remaining amount, and continue the process for each payment period, until we get a zero loan balance. Example 7: Loan amortization schedule Prepare a loan amortization schedule for the amortized loan option given in Example 6 above. What is the loan payoff amount at the end of 2 years? PV = $40,000; n=5; i=10%; FV=0; CPT PMT = $10, Year Beg. Bal. Payment Interest Prin. Red. End Bal. 1 40, , , , , , , , , , , , , , , , , , , , , , , The loan payoff amount at the end of 2 years is $26, Waiting Time and Interest Rates for Annuities (Slides 434 to 436) Problems involving annuities typically have four variables, i.e. the present (PV)or future value (FV)of the annuity stream, the amount of the annuity (PMT), the interest rate (r), and the number of annuities (n). If any three of the four variables are given, we can easily solve for the fourth one. This section deals with the procedure of solving problems where either n or r is not given. Examples of such problems include: finding out how many deposits it would take to reach a retirement or investment goal; figuring out the rate of return required to reach a retirement goal given fixed monthly deposits, etc. The problems can be solved easily by using a financial calculator or a spreadsheet. Use of an equation to solve the problem can be tedious. Example 8: Solving for the number of annuities involved Martha wants to save up $100,000 as soon as possible so that she can use it as a down payment on her dream house. She figures that she can easily set aside $8,000 per year and earn 8% annually on her deposits. How many years will Martha have to wait before she can buy that dream house? Method 1: Using a financial calculator INPUT? TVM KEYS N I/Y PV PMT FV
11 86 Brooks n Financial Management: Core Concepts, 2e Compute Method 2: Using an Excel spreadsheet Using the =NPER function we enter the following values Rate = 8%; Pmt = 8000; PV = 0; FV = ; Type = 0 or omitted; i.e. =NPER(8%,8000,0,100000,0) The cell displays So, Martha will have to wait approximately 9 years to accumulate $100, Solving a Lottery Problem (Slides 437 to 439) In this section, the author uses the example of lottery winnings to illustrate the use of time value functions to calculate the implied interest rate given an annuity stream (annual lottery payment) versus a lump sum lottery payout. The point is that the winner can make an informed judgment regarding the 2 choices once he or she has an idea of what rate of interest is being used by the lottery authorities to calculate the annuity that is being paid over the given number of years. If the winner feels that he or she can earn a higher aftertax rate of return on the lump sum payout than the implied rate used by the authorities, the lump sum choice would be better. Of course, as pointed out by the author, other factors are being ignored here. Example 9: Calculating an implied rate of return given an annuity Let s say that you have just won the state lottery. The authorities have given you a choice of either taking a lump sum of $26,000,000 or a 30year annuity of $1,500,000. Both payments are assumed to be aftertax. What will you do? Calculate the implied interest rate given the lump sum and the 30year annuity Using the TVM keys of a financial calculator, enter: PV = 26,000,000; FV=0; N=30; PMT = 1,625,000; CPT I = % OR Using the =RATE(nper,pmt,pv,fv,type,guess) function of Excel enter; =RATE(30, , ,0,0); the cell will display %, which is the rate of interest which is implicitly being used by the lottery authorities to determine the 30year annuity of $1,625,000 per year versus the $26,000,000 lump sum pay out. Choice: If you can earn an annual aftertax rate of return higher than 4.65% over the next 30 years, go with the lump sum. Otherwise, take the annuity option.
12 Chapter 4 n The Time Value of Money (Part 2) Ten Important Points about the TVM Equation (Slides 440 to 442) After covering the various topics dealing with the discounting and compounding of lump sums and annuity streams in this 2part series, the author identifies 10 key points that students must remember going forward. It is important to advise students that a proper grasp of these 10 points is paramount to their success in dealing with more complex financial problems that lie ahead. Ten Key Points about Time Value of Money 1. Amounts of money can be added or subtracted only if they are at the same point in time. 2. The timing and the amount of the cash flow are what matters. 3. It is very helpful to lay out the timing and amount of the cash flow with a timeline. 4. Present value calculations discount all future cash flow back to current time. 5. Future value calculations value cash flows at a single point in time in the future. 6. An annuity is a series of equal cash payments at regular intervals across time. 7. The time value of money equation has four variables but only one basic equation, and so you must know three of the four variables before you can solve for the missing or unknown variable. 8. There are three basic methods to solve for an unknown time value of money variable: Method 1, using equations and calculating the answer; Method 2, using the TVM keys on a calculator; and Method 3, using financial functions from a spreadsheet. All three give the same answer because they all use the same time value of money equation. 9. There are three basic ways to repay a loan: (1) principal and interest at maturity, or discount loans, (2) interest as you go and principal at maturity, or interestonly loans, and (3) principal and interest as you go with equal and regular payments, or amortized loans. 10. Despite the seemingly accurate answers from the time value of money equation, in many situations not all the important data can be classified into the variables of present value, i.e., time, interest rate, payment, or future value. Questions 1. What is the difference between a series of payments and an annuity? What are the two specific characteristics of a series of payments that make them an annuity? An annuity is a series of payments of equal size at equal intervals. Uniform payments and equal time intervals such as months, quarters or years, are the two characteristics that make a series of payments an annuity. So, a series of payments can be an annuity but not all series of payments are annuities. If the series of payments is of different values or at different intervals, it is not an annuity.
13 88 Brooks n Financial Management: Core Concepts, 2e 2. What effect on the future value of an annuity does increasing the interest rate have? Does a change from 4% to 6% have the same dollar impact as a change from 6% to 8%? The greater the interest rate the greater the future value of an annuity everything else held constant. Changing the interest rate from 4% to 6% will increase the annuity but with a smaller dollar increase when compared to the 6% to 8% change. For example: Annuity of $100 for five years at 4%: Future Value is $ Annuity of $100 for five years at 6%: Future Value is $ Annuity of $100 for five years at 8%: Future Value is $ Increase from 4% to 6% is $22.08 Increase from 6% to 8% is $22.95.which is higher 3. What effect on the present value of an annuity does increasing the interest rate have? Does a decrease from 7% to 5% have the same dollar impact as a decrease from 5% to 3%? Decreasing the interest rate (discount rate) increases the present value of an annuity. The impact is different as the discount rates get smaller. For example: Annuity of $100 for five years at 7%: Present Value is $ Annuity of $100 for five years at 5%: Present Value is $ Annuity of $100 for five years at 3%: Present Value is $ Decrease from 7% to 5% increases PV by $22.93 Decrease from 5% to 3% increases PV by $ What is the difference between an ordinary annuity and an annuity due? An ordinary annuity has the payments at the end of the period and an annuity due has the payment due at the start of the period. 5. What is an iterative process? An iterative process is a repetitive process where the replication of the operation produces an approximation of the desired result more and more closely. 6. What does the amortization schedule tell you about a loan repayment? An amortization schedule tells you the amount of each payment that is applied against the interest expense, the amount applied against the principal and the principal balance after the payment at each scheduled payment. 7. What does it mean that the current principal balance of a loan being repaid as an amortized loan is the present value of the future payment stream? The outstanding balance or remaining unpaid principal after the application of a scheduled payment reflects the current amount needed to pay off the loan. The remaining scheduled payment stream is another way to pay off the loan. Because both the principal and the remaining scheduled payments are sufficient to pay off the loan the current principal is therefore the present value of the remaining payments.
14 Chapter 4 n The Time Value of Money (Part 2) If you increase the number of payments on an amortized loan, does the payment increase or decrease? Why or why not? Increasing the number of payments (all else held constant) decreases the size of each payment. Reverse logic provides the rationale for the answer. If the payment was increased with the same interest payment, the loan would be paid off sooner with the higher payments. Therefore increasing the time to pay off the loan means the payments have been lowered. As the amount applied to the interest is the same but the amount applied to the principal is lower so it takes more payments to eliminate the principal. 9. If you increase the interest rate on an amortized loan, does the payment increase or decrease? Why or why not? The payment increases with a rise in interest rates all else held constant. The reason is that more of the payment is applied to the interest and so to reduce the principal at the same pace as before a higher payment is needed. 10. If you won the lottery and had the choice of the lumpsum payoff or the annuity payoff, what factors would you consider besides the implied interest rate (indifference interest rate) in selecting the payoff style? Factors such as your current wealth or debts could influence your decision. If you have a large amount of debt and want to be debt free you might elect the lumpsum option. If you are terrible at budgeting money and know you would probably squander the money you might elect a slower payment method, i.e. the annuity. If you wanted to be philanthropic you might want to take the lump sum to give more money away to important causes. These are just a few of the potential non financial impacts that could influence your decision on the pay out style. Prepping for Exams 1. b. 2. b. 3. d. 4. a. 5. b. 6. a. 7. d. 8. c. 9. a. 10. b. Problems 1. Different Cash Flow. Given the following cash inflow at the end of each year, what is the future value of this cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year?
15 90 Brooks n Financial Management: Core Concepts, 2e Year 1 $15,000 Year 2 $20,000 Year 3 $30,000 Years 4 through 6 $0 Year 7 $150,000 FV at 6% = $15, = $15, = $21, $20, = $20, = $26, $30, = $30, = $37, $150, = $15, = $150, FV = $21, $26, $37, $150, = $235, FV at 9% = $15, = $15, = $25, $20, = $20, = $30, $30, = $30, = $42, $150, = $15, = $150, FV = $25, $30, $42, $150, = $248, FV at 15% = $15, = $15, = $34, $20, = $20, = $40, $30, = $30, = $52, $150, = $15, = $150, FV = $34, $40, $52, $150, = $277, Future value of an ordinary annuity. Fill in the missing future values in the following table for an ordinary annuity. PMT = $250; n= 10; PV = 0; I% = 6; CPT FV = $ PMT =$ ;n=20; PV=0; I%=12; CPT FV = $100, PMT =$600; n=25; PV=0; I%=4; CPT FV = $24, PMT =$572.25; n=360; PV=0; I%=1; CPT FV = $1,999, Future value. A speculator has purchased land along the southern Oregon coast. He has taken out a tenyear loan with annual payments of $7,200. The loan rate is 6%. At the
16 Chapter 4 n The Time Value of Money (Part 2) 91 end of ten years, he believes that he can sell the land for $100,000. If he is right on the future price, did he make a wise investment? To solve this problem, we must calculate the rate of return earned on an annual investment of $7,200 over a 10year period, with a future value of $100,000 and compare it with the interest rate paid on the loan. If the rate earned is higher, then the investment would be worth it. FV = $100,000; PMT = $7,200; n = 10; PV = 0; CPT I% = 7.11% > 6%; Good Investment 4. Future value. Jack and Jill are saving for a rainy day and decide to put $50 away in their local bank every year for the next twentyfive years. The local UptheHill Bank will pay them 7% on their account. a. If Jack and Jill put the money in the account faithfully at the end of every year, how much will they have in it at the end of twentyfive years? b. Unfortunately, Jack had an accident in which he sustained head injuries after only 10 years of savings. The medical bill has come to $700. Is there enough in the rainy day fund to cover it? Part a. FV = $50 ( )/0.07 = $ = $3, Part b. FV = $50 ( )/0.07 = $ = $ so the rainy day fund is $9.18 short of being able to cover the medical bill. 5. Future value: You are a new employee with the Metropolis Daily Planet. The Planet offers three different retirement plans for you to choose from. Plan 1 starts the first day of work and puts $1,000 away in your retirement account at the end of every year for forty years. Plan 2 starts after ten years and puts away $2,000 every year for thirty years. Plan 3 starts after twenty years and puts away $4,000 every year for the last twenty years of employment. All three plans guarantee an annual growth rate of 8%. a. Which plan should you choose if you plan to work at the Planet for forty years? b. Which plan should you choose if you only plan to work at the Planet for the next thirty years? c. Which plan should you choose if you only plan to work at the Planet for the next twenty years? d. Which plan should you choose if you only plan to work at the Planet for the next ten years? e. What do the answers in parts (a) through (d) imply about savings?
17 92 Brooks n Financial Management: Core Concepts, 2e Part a: Plan One FV = $1,000 ( )/0.08 = $1, = $259, Part a: Plan Two FV = $2,000 ( )/0.08 = $2, = $226, Part a: Plan Three FV = $4,000 ( )/0.08 = $4, = $183, Chose Plan One Part b: Plan One FV = $1,000 ( )/0.08 = $1, = $113, Part b: Plan Two FV = $2,000 ( )/0.08 = $2, = $91, Part b: Plan Three FV = $4,000 ( )/0.08 = $4, = $57, Chose Plan One Part c: Plan One FV = $1,000 ( )/0.08 = $1, = $45, Part c: Plan Two FV = $2,000 ( )/0.08 = $2, = $28, Part c: Plan Three FV = $4,000 ( )/0.08 = $4, = $0.00 Chose Plan One Part d: Plan One FV = $1,000 ( )/0.08 = $1, = $14, Part d: Plan Two FV = $2,000 ( )/0.08 = $2, = $0.00 Part d: Plan Three FV = $4,000 ( )/0.08 = $4, = $0.00 Chose Plan One Part e: The sooner you begin to save the better and that increasing the amount of savings in later years may not be sufficient to catch up to an early savings program. 6. Different cash flow. Given the following cash inflow, what is the present value of this cash flow at 5%, 10%, and 25% discount rates? Year 1: $3,000 Year 2: $5,000 Years 3 through 7: $0 Year 8: $25,000 PV at 5% = $3,000 1/ = $3, = $2, $5,000 1/ = $5, = $4, $25,000 1/ = $25, = $16, PV at 5% = $2, $4, $16, = $24, PV at 10% = $3,000 1/ = $3, = $2, $5,000 1/ = $5, = $4, $25,000 1/ = $25, = $11, PV at 10% = $2, $4, $11, = $18, PV at 25% = $3,000 1/ = $3, = $2, $5,000 1/ = $5, = $3,200.00
18 Chapter 4 n The Time Value of Money (Part 2) 93 + $25,000 1/ = $25, = $4, PV at 25% = $2, $3, $4, = $9, Present value of an ordinary annuity. Fill in the missing present values in the following table for an ordinary annuity. Number of Payments or Years Annual Interest Rate Future Value Annuity Present Value 10 6% 0 $ % 0 $3, % 0 $ % 0 $2, Formula Answer (Rounded final answer to two decimal places) PV = $ [11/( ) 10 ] / 0.06 = $ = $1, PV = $3, [11/( ) 20 ] / 0.12 = $3, = $25, PV = $ [11/( ) 25 ] / 0.04 = $ = $9, PV = $2, [11/( ) 360 ] / 0.01 = $2, = $249, Ordinary annuity payment. Fill in the missing annuity in the following table for an ordinary annuity stream. Number of Payments or Years Annual Interest Rate Future Value Annuity Present Value 5 9% 0 $25, % $25, % 0 $200, % $96, Formula Answer (Rounded final answer to two decimal places) PMT = $25, / ([11/( ) 5 ] / 0.09) = $25, / = $6, PMT = $25, / ([( ) 201] / 0.08) = $25, / = $546.31
19 94 Brooks n Financial Management: Core Concepts, 2e PMT = $200,000 / ([11/( ) 30 ] / 0.07) = $200,000 / = $16, PMT = $96, / ([( ) 101] / 0.04) = $96, / = $8, Present value. County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for twentyfive years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume that it is an ordinary annuity and that the price is the same as present value. Formula Answer (Rounded final answer to two decimal places) PV = $ ([11/( ) 25 ] / 0.06) = $ = $6, Present value. A smooth usedcar salesman who smiles considerably is offering you a great deal on a preowned car. He says, For only six annual payments of $2,500, this beautiful 1998 Honda Civic can be yours. If you can borrow money at 8%, what is the price of this car? Formula Answer (Rounded final answer to two decimal places) PV = $2, ([11/( ) 6 ] / 0.08) = $2, = $11, Payments. Cooley Landscaping Company needs to borrow $30,000 for a new frontend dirt loader. The bank is willing to loan the funds at 8.5% interest with annual payments at the end of the year for the next ten years. What is the annual payment on this loan for Cooley Landscaping? Payments = $30,000 / [(1 1/(1.085) 10 ) /.085] = $30,000 / = $4, Payments. Sam Hinds, a local dentist, is going to remodel the dental reception area and two new workstations. He has contacted ADec, and the new equipment and cabinetry will cost $18,000. ADec will finance the equipment purchase at 7.5% over a sixyear period of time. What will Hinds have to pay in annual payments for this equipment? Payments = $18,000 / [(1 1/(1.075) 6 ) /.075] = $18,000 / = $3, Annuity due. Reginald is about to lease an apartment for the year. The landlord wants the lease payments paid at the start of the month. The twelve monthly payments are
20 Chapter 4 n The Time Value of Money (Part 2) 95 $1,300 per month. The landlord says he will allow Reginald to prepay the rent for the entire year with a discount. The onetime annual payment due at the beginning of the lease is $14,778. What is the implied monthly discount rate for the rent? If Reginald is earning 1.5% on his savings monthly, should he pay by month or take the one annual payment? Using TVM Keys from a Texas Instrument BAII Plus Calculator and rounded to two decimal places for interest percent. The P/Y and C/Y variables are set to 12. Set the MODE to BGN as this is an annuity due problem. INPUT 1214,778 1,300 0 TVM KEYS N I/Y PV PMT FV OUTPUT This is an annual rate so with simple interest you get 12% / 12 = 1% per month. If he can get 1.5% interest per month...then his annual rate is 18% and he can generate $1, per month with the $14,778 it would take to pay off the rent. He is ahead $34.82 per month by not taking the one time payment. INPUT ,778 0 TVM KEYS N I/Y PV PMT FV OUTPUT 1, Timeline of cash flow and application of time value of money. Mauer Mining Company leases a special drilling press with annual payments of $150,000. The contract calls for rent payments at the beginning of each year for a minimum of six years. Mauer Mining can buy a similar drill for $750,000, but will need to borrow the funds at 8%. a. Show the two choices on a time line with the cash flow. b. Determine the present value of the lease payments at 8%. c. Should Mauer Mining lease or buy this drill? (Part A). Draw in a timeline with $750,000 at T 0 for the buy option and $150,000 annuity due stream for the lease option. (Part B). PV = $150,000 + $150,000 (1 1/ )/0.08 = $150,000 + $150, = $150,000 + $598, = 748,906.51
Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
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
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
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
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
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
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
More information1. 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%?
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
More informationCHAPTER 2. Time Value of Money 21
CHAPTER 2 Time Value of Money 21 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 22 Time lines 0 1 2 3
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, 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,
More informationDiscounted Cash Flow Valuation
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
More informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
More informationTIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;
In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time value.
More informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
More informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
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
More informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
More informationModule 5: Interest concepts of future and present value
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
More informationThis is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).
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 byncsa 3.0 (http://creativecommons.org/licenses/byncsa/
More informationREVIEW MATERIALS FOR REAL ESTATE ANALYSIS
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
More informationModule 5: Interest concepts of future and present value
file:///f /Courses/201011/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
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationChapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS
Chapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS 71 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 $10,000(1.10) 5 $10,000(FVIF 10%, 5 ) $10,000(1.6105) $16,105. Alternatively, with a financial calculator enter the
More informationOklahoma State University Spears School of Business. Time Value of Money
Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a signin bonus for your new job? 1. $15,000 cash upon signing the
More informationFuture Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.
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
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
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
More information1.21.3 Time Value of Money and Discounted Cash Flows
1.1.3 ime Value of Money and Discounted ash Flows ime Value of Money (VM)  the Intuition A cash flow today is worth more than a cash flow in the future since: Individuals prefer present consumption to
More informationImportant Financial Concepts
Part 2 Important Financial Concepts Chapter 4 Time Value of Money Chapter 5 Risk and Return Chapter 6 Interest Rates and Bond Valuation Chapter 7 Stock Valuation 130 LG1 LG2 LG3 LG4 LG5 LG6 Chapter 4 Time
More informationDeterminants of Valuation
2 Determinants of Valuation Part Two 4 Time Value of Money 5 FixedIncome Securities: Characteristics and Valuation 6 Common Shares: Characteristics and Valuation 7 Analysis of Risk and Return The primary
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
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
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationThe Time Value of Money
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
More informationThe Time Value of Money
C H A P T E R6 The Time Value of Money When plumbers or carpenters tackle a job, they begin by opening their toolboxes, which hold a variety of specialized tools to help them perform their jobs. The financial
More informationKey Concepts and Skills
McGrawHill/Irwin Copyright 2014 by the McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash
More informationChapter 4. The Time Value of Money
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
More informationTexas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e
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,
More informationTime Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam
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
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation
More informationTopics. Chapter 5. Future Value. Future Value  Compounding. Time Value of Money. 0 r = 5% 1
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
More informationSolutions to Problems: Chapter 5
Solutions to Problems: Chapter 5 P51. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
More informationStatistical Models for Forecasting and Planning
Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
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
More informationCHAPTER 9 Time Value Analysis
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 91 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
More informationChapter 3 Present Value
Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationThe time value of money: Part II
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
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
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
More informationApplying Time Value Concepts
Applying Time Value Concepts C H A P T E R 3 based on the value of two packs of cigarettes per day and a modest rate of return? Let s assume that Lou will save an amount equivalent to the cost of two packs
More informationFinance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization
CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need
More informationCHAPTER 4. The Time Value of Money. Chapter Synopsis
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
More information5. Time value of money
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
More informationTimeValueofMoney and Amortization Worksheets
2 TimeValueofMoney and Amortization Worksheets The TimeValueofMoney and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More informationEXAM 2 OVERVIEW. Binay Adhikari
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
More informationCorporate Finance Fundamentals [FN1]
Page 1 of 32 Foundation review Introduction Throughout FN1, you encounter important techniques and concepts that you learned in previous courses in the CGA program of professional studies. The purpose
More informationTime Value of Money. Nature of Interest. appendix. study objectives
2918T_appC_C01C20.qxd 8/28/08 9:57 PM Page C1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationIntroduction. Turning the Calculator On and Off
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
More informationSolutions to Problems
Solutions to Problems P41. LG 1: Using a time line Basic a. b. and c. d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project,
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
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
More informationChapter 02 How to Calculate Present Values
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
More informationCalculations for Time Value of Money
KEATMX01_p001008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with
More informationSolutions Manual. Corporate Finance. Ross, Westerfield, and Jaffe 9 th edition
Solutions Manual Corporate Finance Ross, Westerfield, and Jaffe 9 th edition 1 CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concept Questions 1. In the corporate form of ownership, the shareholders
More informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
More informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
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.
More informationTIME VALUE OF MONEY (TVM)
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
More informationPresent Value and Annuities. Chapter 3 Cont d
Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects
More informationFNCE 301, Financial Management H Guy Williams, 2006
Review In the first class we looked at the value today of future payments (introduction), how to value projects and investments. Present Value = Future Payment * 1 Discount Factor. The discount factor
More informationContinue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.
Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two
More informationThe explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
More informationRegular Annuities: Determining Present Value
8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded
More informationCompounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.
Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has builtin preset assumptions
More informationCompounding Quarterly, Monthly, and Daily
126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationFinancial Management
Just Published! 206 Financial Management Principles & Practice 7e By Timothy Gallagher Colorado State University Changes to the new Seventh Edition: Updating of all time sensitive material and some new
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
More informationUNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis
This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, endofchapter problems, and endofchapter
More informationChapter 3 Present Value and Securities Valuation
Chapter 3 Present Value and Securities Valuation The objectives of this chapter are to enable you to:! Value cash flows to be paid in the future! Value series of cash flows, including annuities and perpetuities!
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
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
More informationHOW TO CALCULATE PRESENT VALUES
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGrawHill/Irwin Copyright 2014 by The McGrawHill Companies, Inc. All rights reserved.
More informationChapter 3 The Time Value of Money (Part 1)
Chapter 3 The Time Value of Money (Part 1) LEARNING OBJECTIVES 1. Calculate future values and understand compounding. 2. Calculate present values and understand discounting. (Slides 31 to 32) 3. Calculate
More informationIntroduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations
Introduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the HewlettPackard
More informationTime Value of Money (TVM)
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
More informationEhrhardt Chapter 8 Page 1
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,
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM0905. January 14, 2014: Questions and solutions 58 60 were
More informationApplications of Geometric Se to Financ Content Course 4.3 & 4.4
pplications of Geometric Se to Financ Content Course 4.3 & 4.4 Name: School: pplications of Geometric Series to Finance Question 1 ER before DIRT Using one of the brochures for NTM State Savings products,
More informationsubstantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus
for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society
More informationKey Concepts and Skills. Chapter Outline. Basic Definitions. Future Values. Future Values: General Formula 11. Chapter 4
Key Concepts and Skills Chapter 4 Introduction to Valuation: The Time Value of Money Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received
More informationTIME VALUE OF MONEY. HewlettPackard HP12C Calculator
SECTION 1, CHAPTER 6 TIME VALUE OF MONEY CHAPTER OUTLINE Clues, Hints, and Tips Present Value Future Value Texas Instruments BA II+ Calculator HewlettPackard HP12C Calculator CLUES, HINTS, AND TIPS Present
More information1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000
D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of
More informationActivity 3.1 Annuities & Installment Payments
Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.
More informationCompound Interest Formula
Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
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
More informationFinancial Math on Spreadsheet and Calculator Version 4.0
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
More informationrate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 $100.00 $112.00
In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs
More informationFoundation review. Introduction. Learning objectives
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
More information