Chapter 07 - R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. R. 7....

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Unformatted text preview: R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. R. 7. CHAPTER 7 REVIEW QUESTIONS The competitive nature of the market will determine whether positive net present value (NPV) projects can be found. In general, the greater the market’s competition, the less of an opportunity to find positive NPV projects. Most, if not all financial assets trade in highly competitive markets such that few positive NPV opportunities are available. In contrast, real asset markets are less competitive, providing more opportunities to uncover positive NPV projects. Corporate investments usually require outlays in the current period (negative cash flows or costs) and promise inflows in the future (positive cash flows or benefits). The concept of the time value of money requires that all cash flows be evaluated in the same time period. Discounting future cash flows back to the present allows the investment decision to be made by comparing the present value of costs with the present value of benefits. The net present value (NPV) method of evaluating projects compares the present value of all relevant cash outflows with the present value of all relevant cash inflows. Acceptable projects, called positive net present value projects, are those whose present value of inflows exceed the present value of outflows. The profitability index is NPV in ratio form; the present value of all relevant cash inflows divided by the present value of all relevant cash outflows. Acceptable projects are those whose profitability index is greater than one. The internal rate of return (IRR) is the discount rate that equates the present value of the initial cash outlay with the present value of the future cash benefits of the project. The IRR is also the discount rate that makes NPV equal to zero. Acceptable projects are those whose IRR is greater than the project’s required rate of return. ‘ The NPV profile is a graph that depicts the project’s NPV (on the vertical axis) against various discount rates (on the horizontal axis). The point where the NPV profile crosses the horizontal axis defines the project’s IRR. A standard project is a project whose cash flow stream begins with one cash outflow and is followed only by cash inflows. There are two kinds of non—standard projects; borrowing projects and multiple sign change projects. A borrowing project begins with a cash inflow and are followed by cash outflows. For borrowing projects, the IRR acceptance criterion changes; acceptable projects are those whose IRR is less than the project’s required rate of return. A multiple sign change project is a project whose cash flows switch from inflows 39 R. 8. R. 9. to outflows or outflows to inflows more than once. A different IRR can exist for every sign change switch such that two changes in sign can result in two IRRs, three changes in sign can result in three IRRs, on so on. An accept or reject project is one that can be evaluated on its own merits, while ranking projects must be evaluated in relation to other projects. There are no conflicts between the NPV and IRR methods in the case of accept or reject projects However, for ranking projects, shortcomings of the IRR method are exposed that may cause the IRR method to rank projects incorrectly. The IRR method correctly measures a rate of return, but is biased toward short term, small investment projects. Capital rationing is a shortage of investment capital caused either by an unwillingness of external entities to provide additional capital, or by an internal decision that a firm must limit growth. Capital rationing will likely lead to a ranking of projects. As described in question 8 above, we can expect conflicts in rank between the NPV and the IRR methods if the time patterns of cash flows from the projects differ greatly or if the amounts of the capital investments are significantly different. ’R. 10.The payback method does not incorporate the time value of money nor does the rule incorporate cash flows that occur beyond the payback period. Also, the payback acceptance criterion relies on an arbitrary cutoff period. The principal advantage of the payback method is its simplicity. R. 11.The accounting rate of return method requires the use of an arbitrary decision rule, does not discount future cash flows, and depends on accounting rules such as depreciation that can distort accounting income. The advantage of the accounting rate of return method over NPV or the IRR is the fact that the accounting rate of return may help a financial manager manipulate the firm’s accounting profitability. R. 12.The weighted average cost of capital is a measure of the average cost of capital to the firm. It is a measure of project risk for one—project firms and for firms whose projects have identical risk. Using the WACC as an estimate of the required rate of project return is inappropriate when the project under consideration has a different level of risk than the average risk in the firm’s existing assets. 40 CHAPTER 7 PROBLEMS 1. Project NPV P1 IRR Payback Notes $ 8.94 1.0894 13.19% 3 Years Do as lump sum. > B $ 4.55 1.0455 15.00% 1 Year Do as lump sum. C $ 9.92 1.0992 +50%,—20% 1 Year See below D $ 4.74 1.1053 15.89% 3 Years Do as annuity. E $19.68 1.1968 18.90% 3 Years Do as bond w/FV=$60. Project C should be treated as an uneven cashflow problem with the IRR being found by a trial and error search while mapping out an NPV profile. There are two IRR’s: +50% and —20%. Project C (and project E) can be solved on many financial calculators much as bond problems were solved in Chapter 5. For Project E, set the payment amount to $30, the number of periods to 3 and the future value to 60. Note that the future value of $60 sums with the payment of $30 in the third period to form the full $90 cashflow. For Project C, some calculators can handle the problem with the payment set equal to $230 and the future value set equal to —$350 so that the combined payment and future value will for the correct final cashflow of —$120. 2. NPV=$22,727.27. Initial investment is $500,000 and cashflow received is $575,000 in one year. The $575,000 cash flow is found by multiplying 10,000 sets times $57.50 per set. The NPV is found by formula or financial calculator by taking the one year present value of the cashflow using the lump sum approach and a discount rate of 10%. NPV = ~$500,000 + $575,000/1.10 = —$500,000 + 522,727.27 = $22,727.27. 3. NPV=$66,689.54. The initial investment is $50,000 and the cash flows received are $30,000 each year for five consecutive years in years one through five. The NPV can be found using either the annuity function of a financial calculator or the annuity formula with n = 5, I: 9% and A: $30,000. The present value of the annuity is $1 16,689.54. The NPV is found by netting out the $50,000 initial cost and is equal to $66,689.54. 4. NPV=$220,645; Accept The cashflows of the project are shown below: Year Cashflow Present Value 0 ($500,000) ($500,000) 1 $150,000 $138,889 2 $165,000 $141,461 The NPV is the sum of the present values 3 $181,500 $144,081 $220,645 4 ‘ $199,650 $146,749 5 $219,615 $149,466 41 5. PI=0.95695. The initial investment is $700,000 and the cash flows received are $200,000 each year for four consecutive years in years one through four. The PI can be found using either the annuity function of a financial calculator or the annuity formula with n=4, r=7.5% and A=$200,000. The present value of the annuity is $669,865.26. The PI is found by dividing this present value of future cash inflows by the absolute value of the initial cost ($700,000) and is equal to 0.95695. 6. PI=1.02637. The initial investment is $600,000. The cash flows received are $100,000 each year for five consecutive years in years one through five and an additional $450,000 in year five.. The PI can be found using both the annuity approach to present value the $100,000 annual cash flow and the lump sum approach to present value the $450,000 cash flow in year 5. The results are then summed together to form the present value of future cash inflows. Some financial calculators will allow the user to perform both present values simulataneously by placing $100,000 in as the payment and $450,000 as the future value (as well as n and r) and computing PV. The present value of the annuity is $360,477.62. The present value of the lump sum is $255,342.09. Together, the present value of the cash inflows is $615,819.71. The PI is found by dividing this present value of future cash inflows by the absolute value of the initial cost ($600,000) and is equal to 1.02637. 7. Yes, because the IRR: 16%. The initial investment is $1,399,100 and produces cash inflows of $500,000 per year in years one through four. Most financial calculators will find the IRR by entering $1,399,100 as the present value, n=4 and A=$500,000, and then computing r. The answer of 16% can also be found by a trial and error search. 8. No, because the IRR: 10% and the NPV is negative: —$318,928 The intial investment is $7,272,727. The first year cash inflow is $2,000,000 and is found by multiplying the first year sales of 100,000 units times the $20 per unit cash flow figure. Second year sales are expected to be ten percent higher and therefore the second year cash inflow is also expected to be ten percent higher , or $2,200,000. The third and fourth year cash inflows also grow by ten percent and (with compounding assumed) grow to $2,420,000 and $2,662,000, respectively. The NPV with r=0% is $2,009,000. The NPV with r=10% is 0. So, the IRR is 10% (since the NPV is $0). Advanced students may wish to try a shortcut: present value the first year cash inflow of $2,000,000 at ten percent for one year to $1,818,181 and enter it as an annuity ($a). Enter n=4 and $7,272,727.27 as the present value and compute r. Adding ten percent to the result (0.00%) will generate the correct answer of 10.00%. The reason is that each of the cash inflows can be expressed as $1,818,181 future valued at ten percent. 42 9. 11.005%. Yes, the IRR exceeds the required rate of return. The solution is found using trial and error. The cash inflows are a three year annuity from years four to 6 & must be discounted first as a 3 year annuity and then as a 3 year lump sum. 10. No, because the lRR=8%. The initial investment is $257,710 which is the sum of the three initial costs. The machine produces cash inflows of $100,000 per year in years one through three. Most financial calculators will find the IRR by entering $257,710 as the present value, n=3 and A=$100,000, and then computing r. The answer of 8% can also be found by a trial and error search. 11. IRR=13%. The initial investment is $215,330 which is the sum of the two initial costs. The machine produces one cash inflow of $275,000 in year two. Most financial calculators will find the IRR by entering $275,000 as the future value, n=2 and $215,330 as the present value and then computing r. The answer of 13% can also be found directly using the lump sum formula of Chapter 4. 12.a. 2 years. The payback is found by counting the number of years that it takes to receive back as cash inflows the amount of money spent on the initial investment. In this problem, $1,500 would be spent in order to receive incremental cash inflows of $750 per year. After one year, $750 would be received and $750 of the initial investment would remain “unreimbursed”. After the second year the full $1,500 would be "reimbursed". b. 4 years. Using the same concepts as in 12(a), the $3,000 wouldn’t be fully reimbursed until the end of the fourth year. 13. The payback is the number of years required in order to receive back as cash inflows the amount of money that was spent on the investment. Both types of trees require a $500,000 investment. Thus the payback is the number of years that it will take to receive $500,000 of cash inflows. a. 4 years. The $250,000 per year cash inflow starts in year three. b. 5 years. The $125,000 per year cash inflow starts in year two. 14. 26.56% or 25.5% The accounting rate of return is defined as average accounting profit divided by average accounting value. Thus, this problem is solved by computing profit and asset value in each year, averaging each value accross the years, and then forming the desired ratio. Although precise definitions can vary, a reasonable computation of the accounting rate of return follows: 43 15. 16. Year 1 Year 2 Year 3 Year 4 Year 5 Revenues $600,000 $800,000 $800,000 $800,000 $800,000 Cash expenses $150,000 $300,000 $300,000 $300,000 $300,000 Cash Profit $450,000 $500,000 $500,000 $500,000 $500,000 Depreciation $400,000 $400,000 $400,000 $400,000 $0 Accounting Profit $ 50,000 $100,000 $100,000 $100,000 $500,000 Average Profit = ($50,000 + $ 100,000+$ 100,000+ $ 100,000+ $500,000)/ 5 = $ 170,000 Year 1 Year 2 Year 3 Year 4 Year 5 Starting Book Value $1,600,000 $1,200,000 $800,000 $400,000 $0 Depreciation $ 400,000 $ 400,000 $400,000 $400,000 $0 Ending Book Value $1,200,000 33 800,000 $400,000 $ 0 $0 Mid—Year Book Value $1,400,000 $1,000,000 $600,000 $200,000 $0 The above table lists three definitions to book value: starting year, mid—year and ending year. There is no definitive answer as to which is best. Note that the Year 0 Ending Book Value is $1,600 and that the Year 6 Starting Book Value would be $0. The average book value is found by summing the figures from each of the appropriate years and dividing by the number of years. Average starting book value = $666,667 Average mid—year book value = $640,000 Average ending book value = $666,667 Uses years one through six. Uses years one through five. Uses years zero through five. Dividing the $170,000 average profit by the $640,000 average book value produces 26.56% average accounting rate of return. By selecting the appropriate years, the starting and ending year book values approaches produce the same accounting rates of return of 25.5%. The IRR of the project is 15.8%. Functionally speaking, projects can be ranked using either method. However, NPV usually gives the best ranking. In this problem, all three projects add value to the firm. NPV correctly recognizes that Poject C has the largest scale and therefore adds the most value to the firm even though it has the lowest IRR. Project NPV IRR Rank w/NPV Rank w/IRR A $1.065 mil 18.03% middle middle B $0.843 mil 25.41% worst best C $1.320 mil 14.59% best worst Proposal NPV IRR (better) #1 $3,021,147 12.5% #2 $ 623,835 21.7% 44 Proposal #1 has an initial investment of $15,000,000 and produces a five year annuity as the inflow which does not begin until year four. Using the annuity formula or the anuity function of a financial calculator, the five year $6 mil. stream can be discounted to year four as (using 9% as r) $23,337,908. This value is then discounted for three years using lump sum techniques to produce the present value of $18,021,147. Netting out the initial cost produces the NPV of $3,021,147. The IRR of Proposal #1 must be found using a trial and error process. By simply summing the cash flows we can determine that the NPV using a discount rate of 0% is $15,000,000. A discount rate of 9% was found above to produce an NPV of $3,021,147. Thus, a logical next guess might be 11%. The NPV using 11% is $1,214,448. A next logical guess of 12.5% produces an NPV of approximately zero and is therefore the IRR. Proposal #2 has an initial investment of $1,000,000 and produces a four year annuity and a final receipt of $2,000,000 in year 5 as the inflow2. Using the annuity formula or the anuity function of a financial calculator, the four year $100,000 stream can be discounted to a present value of (using 9% as r) $323,972. This value is then added to the present value of the $2,000,000 cash flow in year 5 of $1,299,863 for a total present value of cash inflows of $1,623,835. Netting out the initial cost produces the NPV of $623,835. A shortcut method is to view the proposal as a five year bond with a payment of $100,000 and a future value of $1,900,000. Note that the $1,900,000 is equal to the fifth year cash flow less the $100,000 of the cash flow that is already included as the fifth payment. This shortcut especially assists the computation of the IRR. The IRR of Proposal #2 can also be found using a trial and error process. By simply summing the cash flows we can determine that the NPV using a discount rate of 0% is $1,400,000. A discount rate of 9% was found above to produce an NPV of $623,835. Thus, a logical next guess might be 18%. The NPV using 18% is $143,225. The process continue until the final answer of that produces an NPV of approximately zero is found: 21.7%. Proposal 1 is better since it has the higher NPV. Even though Proposal 2 has a higher IRR, its smaller scale adds less value to the foundation. 17. NPV=$3,239.22, IRR=7.93%; Accept Note that this non-standard project starts with a positive cash flow and is followed by negative cash flows. The initial cash flow is a cash inflow of $20,000. The remaining cash flows are five annual outflows of $5,000 each. The NPV is found by discounting the annuity to —$16,760.78 and adding the initial proceeds of $20,000 to compute NPV=$3,239.22. 45 The IRR can be found using annuity shortcuts as 7.93%. However, it is essential to realize that this is a cost of borrowing, not a return on investing. Therefore, it signals a favorable opportunity since the required rate of return is 15% 18. NPV= —$70,931;IRR=0% and IRR= —63.65%; Reject The cashflows of the project are shown below: Year Cashflow 0 — $500,000 1 $200,000 2 $200,000 3 $200,000 4 — $ 100,000 The NPV is found as usual by discounting and summing all cash flows, being sure to carry negative signs since the last cashflow is negative. The NPV is —$70,931. A shortcut is to View the problem with n=4, A=$200,000, and FV= —$300,000 since the final cashflow of —$100,000 is the sum of the FV and A. The problem has up to two IRR’s since there are two sign changes. Trial and error will reveal 0% and —63.65%. as the IRR’s since they set the NPV=0. 19. WACC: 11.19% WACC = [% in Equity x Cost of Equity] + [% in Debt x Cost of Debt] WACC = [.58X 13.5%] + [42% x8%] = 7.83% + 3.36% = 11.19% 20a. The internal rates of return have been correctly computed since they all produce an NPV of $0 when inserted into the NPV formulae as the discount rate: Project Year Cash Flows Present Values (using IRR = —42.265%) Peanut 0 ($3,000) ($3,000) Butter: 1 $0 $0 2 $1,000 $3,000 3 $0 $0 NPV (sum): $0 Note that negative interest rates are handled exactly as positive interest rates: they are simply inserted into the formula (using a two year example): PV = FV/( (1+r) * (1+r)) PV = $1,000/ ( (1—.42265) * (1—.42265)) PV = $1,000/ (.57735 * .57735) PV = $3,000 46 Project Year Cash Flows Present Values (using IRR=0%) Chocolate: 0 $0 $0 1 $9,053 $9,053 2 $0 $0 3 ($9,053) ($9,053) NPV (sum): $0 Combining the cash flows into a single combined project: Project Year Cash Flows Present Values (using IRR=20%) Combined: 0 ($3,000) ($3,000) 1 $9,053 $7,544 2 $1,000 $694 3 ($9,053) ($5,239) NPV (sum): ($0) . The NPV’s using a discount rate of 15% can be found using the NPV formula as shown below: Project Year Cash Flows Present Values Peanut 0 ($3,000) ($3,000) Butter: 1 $0 $0 2 $1,000 $756 3 $0 $0 NPV (sum): ($2,244) Project Year Cash Flows Present Values Chocolate: 0 $0 $0 1 $9,053 $7,872 2 $0 $0 3 ($9,053) ($5,952) NPV (sum): $1,920 Combining the cash flows into a single combined project: Project Year Cash Flows Present Values Combined: 0 ($3,000) ($3,000) 1 $9,053 $7,872 2 $1,000 $756 3 ($9,053) ($5,952) NPV (sum): ($324) . The firm should accept Project Chocolate since it has a positive N PV and should reject Project Peanut Butter since it has a negative NPV. Notice that the NPV of the combination is negative, it indicates that the combination should be rejected, and it is equal to the combination of the individual NPV’s. The reason that IRR failed to generate correct decisions is that some of the projects are nonstandard. Project Chocolate is a borrowing project in which low IRR’s should be accepted and the Project Combined has multiple sign changes and thus may have more than one IRR. 47 CHAPTER 7 DISCUSSION QUESTIONS 1. The common link between almost all successful firms is that they possess some advantage that can not be quickly and easily duplicated. For some firms it is a patent or a special technology. For others, the advantage is a reputation or superior management. We can usually expect that the firms will remain in business for ten years, but will they still have the advantage that makes them special today? The important point is that success is linked to superior performance in the market for real assets where the market for real assets is broadly defined to include people, ideas, patents and so forth. Thus, the tools of this chapter, especially NPV, assist the financial manager in valuing real assets and making decisions regarding real assets. Conversely, few firms build successful records based upon their performance in trading financial assets. In other words, this chapter has demonstrated the tools involved in the primary method of maximizing shareholder wealth—making superior investment decisions. 2. Some people argue that the NPV requires a discount rate to be input whereas IRR analysis produces a discount rate (the IRR) and therefore is easier. However, it is important to realize that once the IRR is computed it must be compared to a benchmark in order to make a decision. Thus, using the IRR method requires a benchmark rate just as the NPV requires a discount rate. 3. Payback period is especially dangerous in circumstances including: a. comparing projects of different risk, b. comparing projects of uneven cash flows, c. analyzing projects with cash outflows after cash inflows, and d. making decisions requiring precision. Thus, a firm that has performed well in the past using payback period may not necessarily be able to continue to succeed using such a primitive method —— especially as its competitors improve their decision making. 4. It is extremely easy to fall into the trap of believing that nobody should make a decision that could cause death, injury or pollution. However, in a modern society everybody makes such decisions on a basis almost too numerous to mention. Note, virtually everytime a person gets behind the wheel of a vehicle, they are increasing the probabilities that someone will die or get injured and that increased pollution will result. People make these decisions in order to: a. travel further to work at a higher paying job, b. shop at a place with lower prices, c. avoid a toll road, d. work an extra day for overtime pay, and e. save time or money relative to using public transportation. 48 Note that when a consumer selects a product that is cheaper to the consumer, it is very often true that the cost savings to the consumer were created using procedures that placed somebody at a greater risk of death or injury. For example, pesticides allow cheaper food production but likely at great costs to the exposed farm workers. Heavily loeaded trucks produce transportation savings but are often more risky. The examples go on and on leading us to no conclusion other than that life is very often a tradeoff between money and safety which consumers accept. Similarly, when corporations make decisions they also must recognize that some projects will cause more injury, death and pollution than other projects. If potential injury or death were priceless disadvantages that should nix any project then no biulding, bridge, highway, machine, or vehicle would ever be built. No land would be cleared for farms, no houses built, etc. Obviously, the rational solution is to price potential death, injury and pollution as accurately as possible and to include these costs in a NPV analysis just as all other costs are included. When someone criticizes NPV analysis for not including such concepts, they should more accurately be viewed as criticizing the person using the NPV for omitting the costs, since NPV is designed to include all advantages (benefits) and disadvantages (costs). . One of the most popular criticisms of NPV is that it ignores the long run implications of a decision and will result in the long run destruction of the firm. As in question 4, when someone criticizes NPV for omitting the value of long run benefits and costs they should really be criticizing the person applying the NPV analysis since the NPV method requires that all benefits and costs be included —— including long run benefits and costs. Some people will argue that when long term advantages are discounted over long periods of time at high discount rates they are diminished in present values to the point of being undervalued. In this case, the person is really criticizing market interest rates since it is the market, not the NPV user, that determines interest rate levels. Note using discounting that an interest rate such as 18% will cause the present value of $1,000,000 due in 70 years to be less than $10. Thus a project with enormous benefits far into the future will be rejected since people trading in the marketplace have agreed that benefits far into the future are worth far less than benefits in the near term. Corporate financial managers have been hired by shareholders to serve them, not to squander their money by over—valuing long term benefits. . Without further information, the answer should be nothing. There are two potential tricks to high IRR’s. First, the IRR may be available for only a very brief period of time —— for example one second. Over a very brief period of time a high IRR is virtualy worthless. For example, $1,000,000 invested at 100% interest for just one minute will produce only about $1 in interest. Second, the opportunity may be limited in terms of how much money may be invested. For example, earning a 100% IRR for a period of two years is worth very little if only $1 can be 49 invested. Both tricks reflect the scale problem discussed in the chapter. That is, IRR ignores the scale of a project — — both the size of the project and the length of time involved. This is an important problem and it is trickier than this exaggeragted example implies. 50 ...
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This note was uploaded on 11/30/2011 for the course FINOPMGT 301 taught by Professor Lacey during the Spring '10 term at UMass (Amherst).

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Chapter 07 - R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. R. 7....

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