Capital Budgeting OVERVIEW


 Nathaniel Robertson
 1 years ago
 Views:
Transcription
1 WSG12 7/7/03 4:25 PM Page Capital Budgeting OVERVIEW This chapter concentrates on the longterm, strategic considerations and focuses primarily on the firm s investment opportunities. The discussions in the preceding chapters dealt almost entirely with per period profit maximization. That analysis was fundamentally static in nature. By contrast, investment is fundamentally dynamic since it involves streams of expenditures and revenues over time. An essential element of any investment decision is the proper evaluation of alternative investment opportunities involving alternative initial outlays, expected net returns, and time horizons. Capital budgeting is the application of the principle of profit maximization to multiperiod projects. Capital budgeting involves investment decisions in which expenditures and receipts continue over a significant period of time. In general, capital budgeting projects may be classified into one of several major categories, including capital expansion, replacement, new product lines, mandated investments, and miscellaneous investments. Since every investment opportunity involves expenditures (cash outflows) and revenues (cash inflows) that are spread out over a number of time periods, capital budgeting is an especially critical element of effective management decision making. Capital budgeting techniques are used to evaluate the potential profitability of possible new product lines, to plan for the replacement of damaged or worn out (depreciated) plant and equipment, to expand existing production capacity, to engage in research and development, to institute or expand existing worker and management training programs, or evaluate the effectiveness of a major advertising campaign. Managerial Economics: Theory and Practice 191 Copyright 2003 by Academic Press. All rights of reproduction in any form reserved.
2 WSG12 7/7/03 4:25 PM Page Capital Budgeting Capital budgeting involves the subtraction of cash outflows from cash inflows with adjustments for differences in their values over time. Differences in the values of the flows are based on the time value of money, which says that a dollar today is worth more than a dollar tomorrow. There are five standard methods used to evaluate the value of alternative investment projects including payback period, discounted payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR). The payback period is the number of periods required to recover an original investment. In general, risk averse managers prefer investments with shorter payback periods. The net present value of a project is calculated by subtracting the discounted present value of all outflows from the discounted present value of all inflows. The discount rate is the interest rate used to evaluate the project, and is sometimes referred to as the cost of capital, hurdle rate, cut off rate and required rate of return. If the net present value of an investment is positive (negative), then the project is accepted (rejected). If the net present value of an investment is zero, the manager is indifferent to the project. The internal rate of return is the interest rate that equates the present values of inflows to the present value of outflows, i.e., the rate that causes the net present value of the project to equal zero. If the internal rate of return is greater than the cost of capital, the project is accepted. There are a number of problems associated with using the IRR method for evaluating capital investment projects. One problem is the possibility of multiple internal rates of return. Multiple internal rates of return occur when a project that has two or more internal rates of return. For independent projects both the NPV and the IRR methods will yield the same accept/reject decision rules. For mutually exclusive capital investment projects the NPV and the IRR methods could result in conflicting accept/reject decision rules. This is because the NPV method implicitly assumes that net cash inflows are reinvested at the cost of capital, whereas the IRR method assumes that net cash inflows are reinvested at the internal rate of return. The modified internal rate of return (MIRR) method for evaluating capital investment projects is similar to the IRR method in that it generates accept/reject decision rules based upon interest rate comparisons. But unlike the IRR method, the MIRR method assumes that cash flows are reinvested at the cost of capital, and avoids some of the problems associated with multiple internal rates of return. There are several categories of cost of capital, including the cost of debt, cost of equity, and the weighted cost of capital. The cost of debt is the interest rate that must be paid on aftertax debt. The weighed cost of capital is a measure of the overall cost of capital. It is obtained by weighting the various costs by the relative proportion of each component s value in the total capital structure.
3 WSG12 7/7/03 4:25 PM Page 193 Multiple Choice Questions 193 MULTIPLE CHOICE QUESTIONS 12.1 The process of selecting from alternative longterm investment projects is called: A. Net cash inflow maximization. B. Capital budgeting. C. Discounting cash inflows. D. Cash flow management. E. Capital rationing The time value of money refers to: A. The earning power of an investment or stream of investments over time. B. The opportunity cost of capital. C. The interest rate earned on an investment. D. The discount rate used to calculate the present value of an investment The future value of a lump sum payment is worth $10,000 at the end of 6 years. Suppose that the interest rate is 8 percent compounded semiannually. I. The present value of the $10,000 is greater if the interest rate is compounded monthly instead of semiannually. II. The effective annual rate of return is greater an 8 percent. III. The semiannual interest rate is 4 percent. Which of the following is correct? A. I only. B. II only. C. III only. D. I and II only. E. II and III are correct Future value may be defined as: A. The discounted value of future cash flows. B. The interest rate earned on future cash flows. C. The compounded value of future cash flows. D. The opportunity costs of future cash flows. E. The per period maximization of future cash flows Present value may be defined as: A. The discounted value of future cash flows. B. The interest rate earned on future cash flows. C. The compounded value of future cash flows. D. The opportunity costs of future cash flows. E. The per period maximization of future cash flows.
4 WSG12 7/7/03 4:25 PM Page Capital Budgeting 12.6 If the interest (discount) rate is positive, then: A. The present value of a series of cash flows will be greater than its future value. B. The future value of a series of cash flows will be greater than its present value. C. The present value of a series of cash flows will equal its future value. D. The present value is only greater than the future value for an annuity Suppose that Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded annually. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50, Suppose the Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded quarterly. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50, Suppose the Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded monthly. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50, Suppose the Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded continuously. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50,
5 WSG12 7/7/03 4:25 PM Page 195 Multiple Choice Questions A series of fixed payments that are made fixed intervals for a specified period of time is called: A. An annuity. B. A cash flow. C. A mutually exclusive payments. D. A payback period. E. Compounding A series of fixed payments that are made fixed intervals at the end of each period is called: A. An annuity due. B. An ordinary annuity. C. A payback annuity. D. Discounting. E. Compounding A series of fixed payments that are made fixed intervals at the beginning of each period is called: A. An annuity due. B. An ordinary annuity. C. A payback annuity. D. Discounting. E. Compounding Cletus invests $2,000 annually in an ordinary annuity that pays 9 percent interest compounded annually. The future value of this annuity in 10 years is: A. $28, B. $29, C. $30, D. $32, E. $33, Cletus invests $2,000 annually in an annuity due that pays 9 percent interest compounded annually. The future value of this annuity in 10 years is: A. $28, B. $29, C. $30, D. $33, E. $33,
6 WSG12 7/7/03 4:25 PM Page Capital Budgeting Cletus invests $2,000 annually in an annuity due that pays 9 percent interest compounded quarterly. The future value of this annuity in 10 years is: A. $28, B. $29, C. $30, D. $33, E. $33, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded annually, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded semiannually, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded quarterly, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13,
7 WSG12 7/7/03 4:25 PM Page 197 Multiple Choice Questions Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded monthly, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded continuously, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus decides to invest $4,000 per year into a 25 year annuity due that earns an interest rate of 8.5 percent compounded annually. Calculate the present value of Cletus investment plan? A. $40, B. $41, C. $42, D. $42, E. $44, Suppose that Cletus decides to invest $4,000 per year into a 25 year ordinary annuity that earns an interest rate of 8.5 percent compounded annually. Calculate the present value of Cletus investment plan? A. $40, B. $41, C. $42, D. $42, E. $44,
8 WSG12 7/7/03 4:25 PM Page Capital Budgeting Suppose that Cletus has decided to invest in a retirement annuity. Cletus goal is to have $1,000,000 in his annuity by the time that he is 65 years old. Cletus is confident of earning a 6 percent interest rate compounded annually. Cletus is currently 30 years old and plans to make his first investment today. How much will Cletus have to invest annually to reach is goal? A. $8, B. $8, C. $8, D. $9, E. None of the above Suppose that Chloe borrows $300,000 from the First National State Bank at 2.5 percent interest compounded annually to purchase a new home. Chloe agrees to repay the loan in 30 equal annual installments, with the first payment due at the end of the first year. How much are Chloe s annual payments? A. $14, B. $15, C. $16, D. $17, E. None of the above The payback period is: A. The number cashflow periods of an capital investment project. B. The number of years that it takes to earn a profit of a capital investment project. C. The number of periods required to pay for the original investment. D. The number of periods required to calculate the net present value of an investment project An advantage of the payback period method of evaluating a capital investment project is that it: A. Does not consider the time value of money. B. Ignores cash flows beyond the payback period. C. Provides a rough approximation of a projects liquidity and risk. D. Provides a rough approximation of the present value of net cash flows. E. None of the above.
9 WSG12 7/7/03 4:25 PM Page 199 Multiple Choice Questions An advantage of the discounted payback period method of evaluating a capital investment project is that it: A. Considers the time value of money. B. Ignores cash flows beyond the payback period. C. Provides a rough approximation of a projects liquidity and risk. D. Provides a rough approximation of the present value of net cash flows. E. Both A and C are correct Suppose that the payback period for a particular project is 5 years and 6 months. If the annual cash inflows are $5,000, then the initial investment was: A. $22,500. B. $24,000. C. $27,500. D. $29,000. E. None of the above Two project are independent if: A. Acceptance of one project means rejection of the other. B. Their cash flows are unrelated. C. They have different hurdle rates. D. They have different discounted payback periods The cost of capital is: A. The cost of acquiring funds to finance a capital investment project. B. The minimum rate of return that must be earned to justify a capital investment. C. The same thing as the required rate of return. D. Also referred to as the hurdle rate. E. All of the above statements are true Suppose that a project with an initial investment of $50,000 is expected to generate an annual cash flow of $4,000 for each of the next 7 years. This project should not be accepted if the cost of capital is: A. 8 percent. B. 9 percent. C. 10 percent. D. 11 percent. E. Both C and D are correct.
10 WSG12 7/7/03 4:25 PM Page Capital Budgeting Suppose that a project with an initial investment of $30,000 has the following annual cash inflows: Year Cash inflow $4,000 $3,500 $8,000 $12,000 $8,000 If the cost of capital is 8 percent, then the net present value of the project: A. $3, the project should be rejected. B. $4, the project should be rejected. C. $3, the project should be accepted. D. $4, the project should be accepted. E. None of the above statements are true The internal rate of return (IRR) is: A. The same thing as the discount rate. B. The same thing as the cost of capital. C. The discount rate that equates the present values of inflows and outflows. D. The same thing as the net present value. E. The ratio of average annual profits to average investments Project A and Project B are mutually exclusive. Project A has an IRR of 10 percent. Project B has an IRR of 12 percent. If the marginal cost of capital is 11 percent, then: A. Project A should be accepted and Project B rejected. B. Project B should be accepted and Project A rejected. C. Both projects should be accepted since the decision is not based on the IRR but the NPV. D. Both projects should be rejected since the decision is not based on the IRR but the NPV Project A and Project B are independent. Project A has an IRR of 12 percent. Project B has an IRR of 14 percent. If the marginal cost of capital is 10 percent, then: A. Project A must have a higher NPV than Project B. B. Project B must have a higher NPV than Project A. C. The NPV of both projects must be negative. D. The NPV of both projects is positive.
11 WSG12 7/7/03 4:25 PM Page 201 Multiple Choice Questions Suppose that a firm is considering several mutually exclusive projects. The firm should choose: A. The project with the highest NPV. B. The project with the lowest NPV. C. All projects with a positive NPV. D. The project with the lowest IRR. E. The project with the lowest cost of capital Suppose that a project with an initial investment of $30,000 has the following annual cash inflows: Year Cash inflow $4,000 $3,500 $8,000 $12,000 $8,000 Using a financial calculator, the IRR for this project is: A percent. B percent. C percent. D percent. E. None of the above Suppose that a firm is considering to independent projects. The crossover rate is: A. The IRR at which the NPV of the two projects are equal. B. The cost of capital at which the NPV of the two projects are equal. C. Is the discount rate at which the NPV of the two projects are equal. D. Is the discount rate at which the discounted payback period of the two projects are equal. TABLE 1 Net Cash Flows for Projects Amber and Jade Year (t) Project Amber Project Jade 0 $3,000 $4, ,000 1, ,000 1, ,500 2, Consider the information presented in Table 1. If the discount rate is 9 percent, the NPV of Project Amber is: A. $ B. $ C. $ D. $ E. None of the above.
12 WSG12 7/7/03 4:25 PM Page Capital Budgeting Consider the information presented in Table 1. If the discount rate is 9 percent, the NPV of Project Jade is: A. $ B. $ C. $ D. $ E. None of the above Consider the information presented in Table 1. Suppose that Projects Amber and Jade are mutually exclusive. If the discount rate is 9 percent, then: A. Project Jade is preferred to Project Amber. B. Project Amber is preferred to Project Jade. C. Project Amber is equivalent to Project Jade. D. Both projects will be chosen since the NPV is positive. E. Neither projects will be chosen since they are mutually exclusive Consider the information in Table 1. The IRR for Project Amber is: A percent. B percent. C percent. D percent. E. None of the above Consider the information in Table 1. The IRR for Project Jade is: A percent. B percent. C percent. D percent. E. None of the above When the cost of capital is less than IRR for two mutually exclusive projects, then: A. The NPV and IRR methods will always result in the same accept and reject decisions. B. The NPV method will lead to an accept decision while the IRR method will lead to a reject decision. C. The IRR method will lead to an accept decision while the NPV method will lead to a reject decision. D. The project with the highest IRR should be chosen. E. Both A and E are correct.
13 WSG12 7/7/03 4:25 PM Page 203 Multiple Choice Questions Cyborg Electronics is considering two mutually exclusive capital investment projects. Project A has an IRR of 10 percent. Project B has an IRR of 12 percent. The crossover rate is 8 percent. Cyborg should: I. Invest in both projects if the cost of capital is less than 10 percent. II. Invest in Project A if the cost of capital is less than 8 percent. III. Invest in Project B if the cost of capital is greater than 8 percent but less than 12 percent. IV. Invest in Project A if the cost of capital is greater than 8 percent but less than 10 percent. Which of the following is correct? A. I only. B. II only. C. III only. D. II and III only. E. II and IV only Cyborg Electronics is considering two independent capital investment projects. Project A has an IRR of 10 percent. Project B has an IRR of 12 percent. The crossover rate is 8 percent. Cyborg should: I. Invest in both projects if the cost of capital is less than 10 percent. II. Invest in Project A if the cost of capital is less than 8 percent. III. Invest in Project B if the cost of capital is greater than 8 percent but less than12 percent. IV. Invest in Project A if the cost of capital is greater than 8 percent but less than 10 percent. Which of the following is correct? A. I only. B. II only. C. III only. D. I and III only. E. I, II, III and IV Which of the following statements about the modified internal rate of return (MIRR) is correct? A. The assumption regarding reinvestment underlying the MIRR method is more reasonable than that underlying the IRR method. B. The selection of a capital investment project using the MIRR method is always consistent with that of the IRR method.
14 WSG12 7/7/03 4:25 PM Page Capital Budgeting C. The MIRR method always overcomes the problems associated with multiple IRR. D. All of the above are correct. E. All of the above are incorrect The cost of debt capital is: A. The interest rate that must be paid on the debt. B. The aftertax interest rate that must be paid on the debt. C. The future value of the debt less principal. D. The equivalent rate of return on the company s equity. E. The required rate of return on a company s stock The optimal capital structure of a firm: A. Minimizes the firm s cost of debt capital. B. Is that combination of debt, preferred and common stock that maximizes the firm s share values. C. Is one in which the weighted cost of capital is less than the IRR. D. All of the above are correct. E. None of the above are correct. SHORTER PROBLEMS 12.1 Adam wants to borrow $15,000 at 7.5 percent interest compounded monthly from the Cedar Federal Credit Union to purchase a new car. If the loan principal is to be repaid in a lump sum, how much will Adam repay the bank in 3 years? 12.2 Andrew deposits $25,000 in a certificate of deposit that pays 6 percent interest compounded continuously. How much money will Andrew s certificate of deposit be worth at the end of 25 years? 12.3 Alex wants to invest $2,500 a year into an annuity that can reasonably expect to earn 7 percent compounded annually. If Alex makes his first $2,500 investment immediately, how much will his annuity be worth in 20 years? 12.4 Alex wants to invest $2,500 a year into an annuity that can reasonably expect to earn 7 percent compounded annually. Suppose that Alex is uncertain as to whether to open the annuity immediately, or wait until the end of the year to make his first deposit since he can earn $250 in interest the first year by lending
15 WSG12 7/7/03 4:25 PM Page 205 Longer Problems 205 $2,500 to his brother, Adam. Suppose that Alex plans to deposit the $2,750 into a certificate of deposit earning 6 percent interest compounded annually for 19 years. Should Alex loan $2,500 to Adam, or should he open the annuity immediately? 12.5 Suppose that Folderol Savings and Loan is offering 10year certificates of deposit earning a 7.5 interest rate compounded quarterly. How much would Nina have to deposit today in order for the certificate of deposit to be worth $250,000 at the end of 10 years? 12.6 Suppose that Zelda borrows $500,000 at 6.5 percent to purchase a luxury condominium in downtown Toledo, Ohio. Zelda will to repay the loan in 20 equal annual installments, with the first payment due at the end of the first year. A. What are Zelda s annual mortgage payments? B. How much interest will Zelda be paying? 12.7 Calculate the weighted average cost of capital of a project that is 35 percent debt and 65 percent equity. Assume that the firm pays 10 percent on debt and 15 percent on equity. Assume that the firm s marginal tax rate is 33 percent. LONGER PROBLEMS 12.1 The Finance & Economics Department of the Hobgoblin School of Business is considering purchasing a new photocopying machine for use by faculty and doctoral candidates. Dr. Windsock, the department chair, has asked Dr. Steadfast, a finance professor, to determine which of two models, the Galaxy 5000 or the Nova 2700, should be purchased. In addition to the cost of the photocopy machine itself, the manufacturer of each model offers 5year service contract. The cash outflows for each photocopy machine is summarized in the following table. Net Cash Flows (CF t ) for the Galaxy 5000 and Nova 2700 Year (t) Galaxy 5000 Nova $10,500 $11,
16 WSG12 7/7/03 4:25 PM Page Capital Budgeting If the cost of capital is 5.5 percent compounded annually, which photocopy machine should the department purchase if the estimated salvage values for the Galaxy 500 and Nova 2700 after five years are $1,000 and $2,000, respectively? 12.2 Samuel Adams of Niagra Company is a leading producer of natural gas. Adams is considering two mutually exclusive projects involving drilling operations Alaska. The projected net cash flows for each project are summarized in the following table. Net Cash Flows (CF t ) for Projects A and B ($millions) Year (t) Project A Project B 0 $4,000 $5, ,000 2, ,000 2, ,000 Determine which project should be accepted if the cost of capital is 9 percent Mandalay Enterprises is considering two mutually exclusive projects. The projected net cash flows for Projects A and B are summarized in the following table. Net Cash Flows (CF t ) for Projects A and B Year (t) Project A Project B 0 $27,000 $20, ,000 6, ,000 6, ,000 6, ,000 6, ,000 6,500 A. Calculate the NPV for both projects if the cost of capital is 15 percent. B. Based on your answer to part A, which project should be accepted? C. Calculate the IRR for both projects. D. Based on your answer to part C, which project should be accepted? E. If Projects A and B are independent and the cost of capital is 18.5 percent, then which project(s) should be accepted?
17 WSG12 7/7/03 4:25 PM Page 207 Answers to Multiple Choice Questions Consider, again, the net cash flows the two projects being considered by Mandalay Enterprises in the previous question. A. Illustrate the net present value profiles for Projects A and B. B. What is the crossover rate for the two projects? C. Assuming that Projects A and B are mutually exclusive, which project should be selected if the cost of capital is greater than the crossover rate? Which project should be selected if the cost of capital is less than the crossover rate? 12.5 Consider the following cash flows for a capital investment project: Net Cash Flows (CF t ) Year (t) CF t 0 $1, , ,000 A. Summarize the projects net present value profile for selected costs of capital? B. Does the project have multiple internal rates of return? What are they? C. What is the IRR that maximizes the projects NPV? D. Diagram your answer. ANSWERS TO MULTIPLE CHOICE QUESTIONS 12.1 B A D C A B B C D E A B A C D E E D C B A E A B A C C E C B E E A C B D A D B C A B D C A D E A B B.
18 WSG12 7/7/03 4:25 PM Page Capital Budgeting SOLUTIONS TO SHORTER PROBLEMS 12.1 FV n = PV 0 (1 + i/m) mn FV 3 = $15,000( /12) 3 12 = $15,000( ) 36 = $15,000( ) = $18, FV n = PV 0 e in FV 25 = $25,000e = $25,000e 1.5 = $25,000(4.4817) = $112, This is an example of an annuity due. The future value of Alex s annuity will be FVAD n = A{[(1 + i) n  1]/i}(1 + i) = $2,500{[(1.07) 201]/0.07}(1.07) = $2,500[( )/0.07](1.07) = $2,500(40.995)(1.07) = $109, From the previous problem we saw that if Alex opens the annuity immediately, then its value in 20 years will be $109,663. If Alex waits for a year before making the first deposit then the future value of an ordinary annuity is FVOA n = A[(1 + i) n  1]/i = $2,500[( )/0.07] = $2,500( )/0.07 = $2,500( ) = $102, To this amount must be added the future value of $2,750 compounded annually for 19 years at an interest rate of 6 percent. This amount is given as FV n = PV 0 (1 + i) n = $2,500(1.06) 19 = $2,500(3.0256) = $7,564 Adding this amount to the future value of an ordinary annuity yields $102, $7,564 = $110, which is greater than the amount that Alex can earn by opening the annuity immediately. Thus, Alex should lend to his brother.
19 WSG12 7/7/03 4:25 PM Page 209 Solutions to Longer Problems PV 0 = FV n /(1 + i/m) nm = $250,000/( /4) 10 4 = $250,000/ = $118, A. A = PVOA n /S t=1æn [1/(1 + i)] t = $500,000/S t=1æ20 [1/(1.065)] t = $500,000/ = $45, B. Zelda will make total mortgage payments of 20(45,378.23) = $907, Thus, the total amount of interest paid will be $907, $500,000 = $407, WACC = w d k d (1  t) + w e k e = 0.35(0.1)(10.33) (0.15) = or percent SOLUTIONS TO LONGER PROBLEMS 12.1 The NPV for the Galaxy 5000 (NPV G ) and the Nova 2700 (NPV N ) are NPV G = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 5 /(1 + k) 5 =10,500/(1.055) 0320/(1.055) 1320/(1.055) 2320/(1.055) 3320/(1.055) 4320/(1.055) 5 + 1,000/(1.055) 5 =$11, NPV N =11,500/(1.055) 0230/(1.055) 1230/(1.055) 2230/(1.055) 3230/(1.055) 4230/(1.055) 5 + 2,000/(1.055) 5 =$10, Since /NPV N / < /NPV G /, Windsock will purchase the Nova Since the projects have different lives, they must be compared over the least common multiple of years, which in this case is 6 years. NPV A = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 6 /(1 + k) 6 =4,000/(1.09) 0 + 2,000/(1.09) 1 + 3,000/(1.09) 24,000/(1.09) 2 + 2,000/(1.09) 3 + 3,000/(1.09) 44,000/(1.09) 4 + 2,000/(1.09) 5 + 3,000/(1.09) 6 = $ NPV B =5,000/(1.09) 0 + 2,000/(1.09) 1 + 2,500/(1.09) 2 + 3,000/(1.09) 35,000/(1.09) 3 + 1,000/(1.09) 4 + 2,500/(1.09) 5 + 3,000/(1.09) 6 = $1, Since NPV B > NPV A, then Adams will choose Project B over Project A.
20 WSG12 7/7/03 4:25 PM Page Capital Budgeting 12.3 A. NPV A = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 5 /(1 + k) 5 =27,000/(1.15) 0 + 8,000/(1.15) 1 + 9,000/(1.15) ,000/(1.15) ,000/(1.15) 4 + 6,000/(1.15) 5 = $2, NPV B =20,000/(1.15) 0 + 6,500/(1.15) 1 + 6,500/(1.15) 2 + 6,500/(1.15) 3 + 6,500/(1.15) 4 + 6,500/(1.15) 5 = $1, B. Since NPV A > NPV B, then Project A should be accepted. C. To determine the internal rate of return for Projects A and B, substitute the isnformation provided in the table into the Equation (12.27) and solve for IRR. NPV A = CF 0 + CF 1 /(1 + IRR A ) 1 + CF 2 /(1 + IRR A ) CF 5 /(1 + IRR A ) 5 =$27,000 + $8,000/(1 + IRR A ) 1 + $9,000/(1 + IRR A ) 2 + $10,000/(1 + IRR A ) 3 + $10,000/(1 + IRR A ) 4 + $6,000/(1 + IRR A ) 5 = 0 NPV B =$20,000 + $6,500/(1 + IRR B ) 1 + $6,500/(1 + IRR B ) 2 + $6,500/(1 + IRR B ) 3 + $6,500/(1 + IRR B ) 4 + $6,500/(1 + IRR B ) 5 = 0 Since calculating IRR A and IRR B by trial and error is time consuming and tedious, the solution values were obtained by using a financial calculator. The internal rates of return for Projects A and B are IRR A = percent IRR B = percent D. Since IRR B > IRR A, then Project B should be accepted. E. The internal rate of return is greater than the hurdle rate for Project B and less than the hurdle rate for Project B. Thus, Project B should be accepted and Project A rejected A. With the use of a financial calculator, the net present values for Projects A and B for various interest rates are summarized in the following table.
21 WSG12 7/7/03 4:25 PM Page 211 Solutions to Longer Problems 211 Net Present Value Profiles for Projects A and B Cost of Capital Project A Project B 0.00 $16,000 $12, ,383 8, ,358 7, ,496 5, ,780 4, ,195 3, ,729 2, ,371 1, ,003 1, , B. To determine the crossover rate, equate the net present value of Project A with the net present value of Project B and solve for the cost of capital, k. NPV A = NPV B $27,000/(1 + k) 0 + $8,000/(1 + k) 1 + $9,000/(1 + k) 2 + $10,000/(1 + k) 3 + $10,000/(1 + k) 4 + $6,000/(1 + k) 5 =$20,000/(1 + k) 0 + $6,500/(1 + k) 1 + $6,500/(1 + k) 2 + $6,500/(1 + k) 3 + $6,500/(1 + k) 4 + $6,500/(1 + k) 5 Bringing all of the terms in this expression to the lefthand side of the equation we obtain $7,000/(1 + k) 0 + $1,500/(1 + k) 1 + $2,500/(1 + k) 2 + $3,500/(1 + k) 3 + $3,500/(1 + k) 4  $500/(1 + k) 5 = 0 The value for k in this expression may be found using the IRR function of a financial calculator. Solving for k we obtain Crossover rate = percent C. From the previous problem, the internal rates of return for the two projects is IRR A = percent IRR B = percent Finally, calculating the net present value of Projects A and B using the crossover rate yields NPV A = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 5 /(1 + k) 5 =27,000/(1.1657) 0 + 8,000/(1.1657) 1 + 9,000/(1.1657) ,000/(1.1657) ,000/(1.1657) 4 + 6,000/(1.1657) 5 = $1,003 NPV B =20,000/(1.1657) 0 + 6,500/(1.1657) 1 + 6,500/(1.1657) 2 + 6,500/(1.657) 3 + 6,500/(1.1657) 4 + 6,500/(1.1657) 5 = $1,003
22 WSG12 7/7/03 4:25 PM Page Capital Budgeting With this information, the net present value profiles for Project A and Project B may be illustrated in the following diagram. From the above diagram, if the cost of capital is greater than percent, but less than percent, then Project B is preferred to Project A since NPV B > NPV A. This choice of projects is consistent with the IRR method since IRR B > IRR A. On the other hand, if the cost of capital is less than percent, then Project A is preferred to Project B since NPV A > NPV B. This result, however, is in conflict with the choice of projects based on the IRR method A. Net Present Value Profile k NPV $2, ,
23 WSG12 7/7/03 4:25 PM Page 213 Solutions to Longer Problems 213 B. NPV = 1, ,000/(1 + IRR) 16,000/(1 + IRR) 2 = 06,000[1/(1 + IRR)] 2 + 5,000[1/(1 + IRR)]  1,000 = 0 a[1/(1 + IRR)] 2 + b[1/(1 + IRR)] + c = 0 [1/(1 + IRR)] 1,2 = {b [b 24ac]}/2a = {5,000 ± [(5,000) 24(6,000)(1,000)]}/2(6,000) = [5,000 ± (1,000,000)]/12,000 = (5,000 ± 1,000)/12,000 [1/(1 + IRR)] 1 = (5, ,000)/12,000 = (1 + IRR) 1 = 3.00 IRR 1 = 2.00 or 200 percent [1/(1 + IRR)] 2 = (5,0001,000)/12,000 = 0.5 (1 + IRR) 2 = 2.00 IRR 2 = 1.00 or 100 percent Thus, and this was illustrated NPV profile, the project has internal rates of return of 100 percent and 200 percent. C. NPV = 1, ,000(1 + IRR) 16,000/(1 + IRR) 2 dnpv/d(1 + IRR) = 5,000(1 + IRR) ,000/(1 + IRR) 3 = 0 5,000(1 + IRR) = 12, IRR = 12,000/5,000 IRR* = 1.40 or 140 percent The value of IRR that maximizes the NPV of the firm is 140 percent, which is highlighted in the NPV profile. D.
24 WSG12 7/7/03 4:25 PM Page 214
WHAT IS CAPITAL BUDGETING?
WHAT IS CAPITAL BUDGETING? Capital budgeting is a required managerial tool. One duty of a financial manager is to choose investments with satisfactory cash flows and rates of return. Therefore, a financial
More informationNet Present Value (NPV)
Investment Criteria 208 Net Present Value (NPV) What: NPV is a measure of how much value is created or added today by undertaking an investment (the difference between the investment s market value and
More information( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100
Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded
More informationChapter 10. What is capital budgeting? Topics. The Basics of Capital Budgeting: Evaluating Cash Flows
Chapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows 1 Topics Overview and vocabulary Methods NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life 2 What
More informationUnderstanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions
Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions Chapter 8 Capital Budgeting Concept Check 8.1 1. What is the difference between independent and mutually
More informationWhy Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of
1 Why Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of Return Problems with the IRR Approach The Profitability
More informatione C P M 1 0 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
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
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 information$1,300 + 1,500 + 1,900 = $4,700. in cash flows. The project still needs to create another: $5,500 4,700 = $800
1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project has created: $1,300 + 1,500 + 1,900 = $4,700 in cash flows.
More informationCapital Budgeting: Decision. Example. Net Present Value (NPV) FINC 3630 Yost
Capital Budgeting: Decision Criteria Example Consider a firm with two projects, A and B, each with the following cash flows and a 10 percent cost of capital: Project A Project B Year Cash Flows Cash Flows
More informationThe Time Value of Money
The Time Value of Money Future Value  Amount to which an investment will grow after earning interest. Compound Interest  Interest earned on interest. Simple Interest  Interest earned only on the original
More informationBank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later.
ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return
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 8 Capital Budgeting Process and Techniques
Chapter 8 Capital Budgeting Process and Techniques MULTIPLE CHOICE 1. The capital budgeting process involves a. identifying potential investments b. analyzing the set of investment opportunities, and identifying
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 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 informationChapter 13 The Basics of Capital Budgeting Evaluating Cash Flows
Chapter 13 The Basics of Capital Budgeting Evaluating Cash Flows ANSWERS TO SELECTED ENDOFCHAPTER QUESTIONS 131 a. The capital budget outlines the planned expenditures on fixed assets. Capital budgeting
More informationPlanning for Capital Investments
121 Planning for Capital Investments Managerial Accounting Fifth Edition Weygandt Kimmel Kieso 122 study objectives 1. Discuss capital budgeting evaluation, and explain inputs used in capital budgeting.
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 informationCapital Budgeting Tools. Chapter 11. Capital Budgeting. Types of Capital Budgeting Projects. The Basics of Capital Budgeting: Evaluating Cash Flows
Capital Budgeting Tools () Payback Period (a) Discounted Payback Period Chapter The Basics of Capital Budgeting: Evaluating s () Net Present Value (NPV) (a) Profitability Index (PI) () Internal Rate of
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 informationCHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA
CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Basic 1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After two years, the
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 information(Relevant to AAT Examination Paper 4 Business Economics and Financial Mathematics)
Capital Budgeting: Net Present Value vs Internal Rate of Return (Relevant to AAT Examination Paper 4 Business Economics and Financial Mathematics) Y O Lam Capital budgeting assists decision makers in a
More informationPrepared by: Dalia A. Marafi Version 2.0
Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version
More informationFinQuiz Notes 2 0 1 4
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.
More informationVol. 2, Chapter 4 Capital Budgeting
Vol. 2, Chapter 4 Capital Budgeting Problem 1: Solution Answers found using Excel formulas: 1. Amount invested = $10,000 $21,589.25 Compounding period = annually Number of years = 10 Annual interest rate
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 informationMHSA 8630  Healthcare Financial Management Time Value of Money Analysis
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
More informationCAPITAL BUDGETING. Net Present Value and Other Investment Criteria
CAPITAL BUDGETING Net Present Value and Other Investment Criteria Net Present Value (NPV) Net present value is the difference between an investment s market value (in today s dollars) and its cost (also
More informationPart 7. Capital Budgeting
Part 7. Capital Budgeting What is Capital Budgeting? Nancy Garcia and Digital Solutions Digital Solutions, a software development house, is considering a number of new projects, including a joint venture
More informationInvestment Appraisal
Investment Appraisal Article relevant to F1 Business Mathematics and Quantitative Methods Author: Pat McGillion, current Examiner. Questions 1 and 6 often relate to Investment Appraisal, which is underpinned
More informationExercise 6 8. Exercise 6 12 PVA = $5,000 x 4.35526* = $21,776
CHAPTER 6: EXERCISES Exercise 6 2 1. FV = $10,000 (2.65330 * ) = $26,533 * Future value of $1: n = 20, i = 5% (from Table 1) 2. FV = $10,000 (1.80611 * ) = $18,061 * Future value of $1: n = 20, i = 3%
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 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 informationCHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA
CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Answers to Concepts Review and Critical Thinking Questions 1. A payback period less than the project s life means that the NPV is positive for
More informationExercise 1 for Time Value of Money
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
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 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 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 informationCHAPTER 6 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA
CHAPTER 6 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Answers to Concepts Review and Critical Thinking Questions 1. Assuming conventional cash flows, a payback period less than the project s life means
More informationMODULE 2. Capital Budgeting
MODULE 2 Capital Budgeting Capital Budgeting is a project selection exercise performed by the business enterprise. Capital budgeting uses the concept of present value to select the projects. Capital budgeting
More informationBF 6701 : Financial Management Comprehensive Examination Guideline
BF 6701 : Financial Management Comprehensive Examination Guideline 1) There will be 5 essay questions and 5 calculation questions to be completed in 1hour exam. 2) The topics included in those essay and
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 informationAnswers to WarmUp Exercises
Answers to WarmUp Exercises E101. Answer: E102. Answer: Payback period The payback period for Project Hydrogen is 4.29 years. The payback period for Project Helium is 5.75 years. Both projects are acceptable
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationSolutions to Chapter 8. Net Present Value and Other Investment Criteria
Solutions to Chapter 8 Net Present Value and Other Investment Criteria. NPV A = $00 + [$80 annuity factor (%, periods)] = $00 $80 $8. 0 0. 0. (.) NPV B = $00 + [$00 annuity factor (%, periods)] = $00 $00
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 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 informationNPV calculation. Academic Resource Center
NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year
More informationCARNEGIE MELLON UNIVERSITY CIO INSTITUTE
CARNEGIE MELLON UNIVERSITY CIO INSTITUTE CAPITAL BUDGETING BASICS Contact Information: Lynne Pastor Email: lp23@andrew.cmu.edu RELATED LEARNGING OBJECTIVES 7.2 LO 3: Compare and contrast the implications
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 informationIng. Lenka Strýčková, Ph.D.
Ing. Lenka Strýčková, Ph.D. 1. Introduction to Business Financial Management (introduction to the course, basic terminology) 2. Capital Budgeting: LongTerm Decisions (capital budgeting, shortterm and
More information6 Investment Decisions
6 Investment Decisions After studying this chapter you will be able to: Learning Objectives Define capital budgeting and explain the purpose and process of Capital Budgeting for any business. Explain the
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 informationFinance 3130 Corporate Finiance Sample Final Exam Spring 2012
Finance 3130 Corporate Finiance Sample Final Exam Spring 2012 True/False Indicate whether the statement is true or falsewith A for true and B for false. 1. Interest paid by a corporation is a tax deduction
More informationChapter 18. Web Extension: Percentage Cost Analysis, Leasing Feedback, and Leveraged Leases
Chapter 18 Web Extension: Percentage Cost Analysis, Leasing Feedback, and Leveraged Leases Percentage Cost Analysis Anderson s leaseversuspurchase decision from Chapter 18 could also be analyzed using
More informationExcel Financial Functions
Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money
More informationTIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!
TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on
More informationChapter 10. Capital Budgeting Techniques. Copyright 2012 Pearson Prentice Hall. All rights reserved.
Chapter 10 Capital Budgeting Techniques Copyright 2012 Pearson Prentice Hall. All rights reserved. Overview of Capital Budgeting Capital budgeting is the process of evaluating and selecting longterm investments
More informationFinQuiz Notes 2 0 1 5
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.
More informationCHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA
CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA 1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project
More informationKey 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 information6. FINANCIAL MANAGEMENT
6. FINANCIAL MANAGEMENT Syllabus Financial Management: Investmentneed, Appraisal and criteria, Financial analysis techniquessimple pay back period, Return on investment, Net present value, Internal rate
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 informationSolutions to Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
More informationInvestment Decision Analysis
Lecture: IV 1 Investment Decision Analysis The investment decision process: Generate cash flow forecasts for the projects, Determine the appropriate opportunity cost of capital, Use the cash flows and
More informationTime Value of Money Concepts
BASIC ANNUITIES There are many accounting transactions that require the payment of a specific amount each period. A payment for a auto loan or a mortgage payment are examples of this type of transaction.
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 informationMGT201 Lecture No. 07
MGT201 Lecture No. 07 Learning Objectives: After going through this lecture, you would be able to have an understanding of the following concepts. Discounted Cash Flows (DCF Analysis) Annuities Perpetuity
More informationProject Management Seminars. Financial Management of Projects
Project Management Seminars Financial Management of Projects.inproject managementandsystems engineering, is a deliverableoriented decomposition of a project into smaller components. (source: Wikipedia)
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
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 informationChapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows ANSWERS TO ENDOFCHAPTER QUESTIONS 101 a. Capital budgeting is the whole process of analyzing projects and deciding whether they should
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 informationCHAPTER 7: NPV AND CAPITAL BUDGETING
CHAPTER 7: NPV AND CAPITAL BUDGETING I. Introduction Assigned problems are 3, 7, 34, 36, and 41. Read Appendix A. The key to analyzing a new project is to think incrementally. We calculate the incremental
More informationHO23: METHODS OF INVESTMENT APPRAISAL
HO23: 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,
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 informationMBA Financial Management and Markets Exam 1 Spring 2009
MBA Financial Management and Markets Exam 1 Spring 2009 The following questions are designed to test your knowledge of the fundamental concepts of financial management structure [chapter 1], financial
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 informationWeek 1: Solutions to HW Problems
Week 1: Solutions to HW Problems 101 a. Payback A (cash flows in thousands): Annual Period Cash Flows Cumulative 0 ($5,000) ($5,000) 1 5,000 (0,000) 10,000 (10,000) 3 15,000 5,000 4 0,000 5,000 Payback
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationOklahoma State University Spears School of Business. NPV & Other Rules
Oklahoma State University Spears School of Business NPV & Other Rules Slide 2 Why Use Net Present Value? Accepting positive NPV projects benefits shareholders. NPV uses cash flows NPV uses all the cash
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 informationIng. Tomáš Rábek, PhD Department of finance
Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,
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 informationCapital Investment Analysis and Project Assessment
PURDUE EXTENSION EC731 Capital Investment Analysis and Project Assessment Michael Boehlje and Cole Ehmke Department of Agricultural Economics Capital investment decisions that involve the purchase of
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More informationAccounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money
Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate WynnWilliams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest
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 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 informationKENT FAMILY FINANCES
FACTS KENT FAMILY FINANCES Ken and Kendra Kent have been married twelve years and have twin 4yearold sons. Kendra earns $78,000 as a Walmart assistant manager and Ken is a stayathome dad. They give
More informationSpring 2012. True/False Indicate whether the statement is true or false.
Corporation Finance Spring 2012 Sample Exam 2B True/False Indicate whether the statement is true or false. 1. The total return on a share of stock refers to the dividend yield less any commissions paid
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 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 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 informationTime Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology
Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations
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 informationIntroduction to Discounted Cash Flow and Project Appraisal. Charles Ward
Introduction to Discounted Cash Flow and Project Appraisal Charles Ward Company investment decisions How firms makes investment decisions about real projects (not necessarily property) How to decide which
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 information