羅斯公司理財第六版習題答案第6章

1、chapter 6: some alternative investment rulesconcept questions - chapter 66.2list the problems of the payback period rule.1. it does not take into account the time value of money.2. it ignores payments after the payback period.3. the cutoff period is arbitrary.what are some advantages?1. it is simple

2、 to implement.2. it may help in controlling and evaluating managers.6.4what are the three steps in calculating aar?1. determine average net income.2. determine average investment3. divide average net income by average investment.what are some flaws with the aar approach?1. it uses accounting figures

3、.2. it takes no account of timing.3. the cutoff period is arbitrary.6.5how does one calculate the irr of a project?using either trial-and-error or a financial calculator, one finds the discount rate that produces an npv of zero.6.6what is the difference between independent projects and mutually excl

4、usiveprojects?an independent project is one whose acceptance does not affect the acceptance of another. a mutually exclusive project, on the other hand is one whose acceptance precludes the acceptance of another.what are two problems with the irr approach that apply to both independent and mutually

5、exclusive projects?1. the decision rule depends on whether one is investing of financing.2. multiple rates of return are possible.what are two additional problems applying only to mutually exclusive projects?1. the irr approach ignores issues of scale.2. the irr approach does not accommodate the tim

6、ing of the cash flows properly.6.7how does one calculate a projects profitability index?divide the present value of the cash flows subsequent to the initial investment by the initial investment.how is the profitability index applied to independent projects, mutually exclusive projects, and situation

7、s of capital rationing?1. with independent projects, accept the project if the pi is greater than 1.0 and reject if less than 1.0.2. with mutually exclusive projects, use incremental analysis, subtracting the cash flows of project 2 from project 1. find the pi. if the pi is greater than 1.0, accept

8、project 1. if less than 1.0, accept project 2.3. in capital rationing, the firm should simply rank the projects according to their respective pis and accept the projects with the highest pis, subject to the budget constrain.answers to end-of-chapter problemsquestions and problemsthe payback period r

9、ule6.1 fuji software, inc., has the following projects.year project a project b0 _$7,500 _$5,0001 4,000 2,5002 3,500 1,2003 1,500 3,000a. suppose fujis cutoff payback period is two years. which of these two projects should be chosen?b. suppose fuji uses the npv rule to rank these two projects. if th

10、e appropriate discount rate is 15 percent, which project should be chosen?6.1a.payback period of project a = 1 + ($7,500 - $4,000) / $3,500 = 2 yearspayback period of project b = 2 + ($5,000 - $2,500 -$1,200) / $3,000 = 2.43 yearsproject a should be chosen.b.npva = -$7,500 + $4,000 / 1.15 + $3,500 /

11、 1.152 + $1,500 / 1.153 = -$388.96npvb = -$5,000 + $2,500 / 1.15 + $1,200 / 1.152 + $3,000 / 1.153 = $53.83project b should be chosen.6.2 suppose peach paving company invests $1 million today on a new construction project. the project will generate annual cash flows of $150,000 in perpetuity. the ap

12、propriate annual discount rate for the project is 10 percent.a. what is the payback period for the project? if the peach paving company desires to have a 10-year payback period, should the project be adopted?b. what is the discounted payback period for the project?c. what is the npv of the project?6

13、.2a.payback period = 6 + $1,000,000 - ($150,000 6) / $150,000 = 6.67 yearsyes, the project should be adopted.b.$150,000 = $974,259the discounted payback period = 11 + ($1,000,000 - $974,259) / ($150,000 / 1.112)= 11.54 yearsc.npv = -$1,000,000 + $150,000 / 0.10 = $500,000the average accounting retur

14、n6.3 the annual, end-of-year, book-investment accounts for the machine whose purchase your firm is considering are shown below.purchase year year year yeardate 1 2 3 4gross investment $16,000 $16,000 $16,000 $16,000 $16,000less: accumulateddepreciation _0_ _4_,0_0_0_ _8_,0_0_0_ _1_2_,0_0_0_ _1_6_,_0

15、_0_0net investment $16,000 $12,000 $ 8,000 $ 4,000 $ 0if your firm purchases this machine, you can expect it to generate, on average, $4,500 peryear in additional net income.a. what is the average accounting return for this machine?b. what three flaws are inherent in this decision rule?6.3a.average

16、investment:($16,000 + $12,000 + $8,000 + $4,000 + 0) / 5 = $8,000average accounting return:$4,500 / $8,000 = 0.5625 = 56.25%b.1.aar does not consider the timing of the cash flows, hence it does not consider the time value of money.2.aar uses an arbitrary firm standard as the decision rule.3.aar uses

17、 accounting data rather than net cash flows.6.4 western printing co. has an opportunity to purchase a $2 million new printing machine. it has an economic life of five years and will be worthless after that time. this new investment is expected to generate an annual net income of $100,000 one year fr

18、om today and the income stream will grow at 7 percent per year subsequently. the company adopts a straight-line depreciation method (i.e., equal amounts of depreciation in each year). what is the average accounting return of the investment? supposing western printings aar cutoff is 20 percent, shoul

19、d the machine be purchased?6.4average investment = ($2,000,000 + 0) / 2 = $1,000,000average net income = $100,000 (1 + g)5 - 1 / g / 5 = $100,000a (1.075 - 1 / 0.07 / 5 = $115,014.78aar = $115,014.78 / $1,000,000 = 11.50%no, since the machines aar is less than the firms cutoff aar.6.5 nokia group ha

20、s invested $8,000 in a high-tech project. this cost is depreciated on an accelerated basis that yields $4,000, $2,500, $1,500 of depreciation, respectively, during its three-year economic life. the project is expected to produce income before tax of $2,000 each year during its economic life. if the

21、tax rate is 25%, what is the projects average accounting return (aar)?a. 44.44%b. 50.23%c. 66.67%d. 70.00%e. 82.21%the internal rate of return6.5a6.6 compute the internal rate of return on projects with the following cash flows.cash flows ($)year project a project b0 _3,000 _6,0001 2,500 5,0002 1,00

22、0 2,0006.6 pi = $40,000 / $160,000 = 1.04since the pi exceeds one accept the project.6.7 cpc, inc., has a project with the following cash flows.year cash flows ($)0 _8,0001 4,0002 3,0003 2,000a. compute the internal rate of return on the project.b. suppose the appropriate discount rate is 8 percent.

23、 should the project be adopted by cpc?6.7 the irr is the discount rate at which the npv = 0.-$3,000 + $2,500 / (1 + irra) + $1,000 / (1 + irra)2 = 0by trial and error, irra = 12.87%since project bs cash flows are two times of those of project a, the irrb = irra = 12.87%6.8 compute the internal rate

24、of return for the cash flows of the following two projects.cash flows ($)time a b0 _2,000 _1,5001 2,000 5002 8,000 1,0003 _8,000 1,5006.8a.solve x by trial and error:-$4,000 + $2,000 / (1 + x) + $1,500 / (1 + x)2 + $1,000 / (1 + x)3 = 0x = 6.93%b.no, since the irr (6.93%) is less than the discount r

25、ate of 8%.6.9 suppose you are offered $5,000 today and obligated to make scheduled payments as follows:year cash flows ($)0 5,0001 _2,5002 _2,0003 _1,0004 _1,000a. what is the irrs of this offer?b. if the appropriate discount rate is 10 percent, should you accept this offer?c. if the appropriate dis

26、count rate is 20 percent, should you accept this offer?chapter 6 some alternative investment rules 165d. what is the corresponding npv of the project if the appropriate discount rates are 10 percent and 20 percent, respectively? are the choices under the npv rule consistent with those of the irr rul

27、e?6.9find the irrs of project a analytically. since the irr is the discount rate that makes the npv equal to zero, the following equation must hold.-$200 + $200 / (1 + r) + $800 / (1 + r)2 - $800 / (1 + r)3 = 0$200 -1 + 1 / (1 + r) - $800 / (1 + r)2-1 + 1 / (1 + r) = 0-1 + 1 / (1 + r) $200 - $800 /

28、(1 + r)2 = 0for this equation to hold, either -1 + 1 / (1 + r) = 0 or $200 - $800 / (1 + r)2 = 0.solve each of these factors for the r that would cause the factor to equal zero. the resulting rates are the two irrs for project a. they are either r = 0% or r = 100%.note: by inspection you should have

29、 known that one of the irrs of project a is zero. notice that the sum of the un-discounted cash flows for project a is zero. thus, not discounting the cash flows would yield a zero npv. the discount rate which is tantamount to not discounting is zero. here are some of the interactions used to find t

30、he irr by trial and error. sophisticated calculators can compute this rate without all of the tedium involved in the trial-and-error method.npv = -$150 + $50 / 1.3 + $100 / 1.32 + $150 / 1.33 = $15.91npv = -$150 + $50 / 1.4 + $100 / 1.42 + $150 / 1.43 = -$8.60npv = -$150 + $50 / 1.37 + $100 / 1.372

31、+ $150 / 1.373 = -$1.89npv = -$150 + $50 / 1.36 + $100 / 1.36 2 + $150 / 1.363 = $0.46npv = -$150 + $50 / 1.36194 + $100 / 1.361942 + $150 / 1.361943 = $0.0010npv = -$150 + $50 / 1.36195 + $100 / 1.361952 + $150 / 1.361953 = -$0.0013npv = -$150 + $50 / 1.361944 + $100 / 1.3619442 + $150 / 1.3619443

32、= $0.0000906thus, the irr is approximately 36.1944%.6.10 as the chief financial officer of the orient express, you are offered the following twomutually exclusive projects.year project a project b0 _$5,000 _$100,0001 3,500 65,0002 3,500 65,000a. what are the irrs of these two projects?b. if you are

33、told only the irrs of the projects, which would you choose?c. what did you ignore when you made your choice in part (b)?d. how can the problem be remedied?e. compute the incremental irr for the projects.f. based on your answer to part (e), which project should you choose?g. suppose you have determin

34、ed that the appropriate discount rate for these projectsis 15 percent. according to the npv rule, which of these two projects should beadopted?6.10a.solve r in the equation:$5,000 - $2,500 / (1 + r) - $2,000 / (1 + r)2 - $1,000 / (1 + r)3 - $1,000 / (1 + r)4 = 0by trial and error,irr = r = 13.99%b.s

35、ince this problem is the case of financing, accept the project if the irr is less than the required rate of return.irr = 13.99% 10%reject the offer.c.irr = 13.99% 20%accept the offer.d.when r = 10%:npv = $5,000 - $2,500 / 1.1 - $2,000 / 1.12 - $1,000 / 1.13 - $1,000 / 1.14 = -$359.95when r = 20%:npv

36、 = $5,000 - $2,500 / 1.2 - $2,000 / 1.22 - $1,000 / 1.23 - $1,000 / 1.24 = $466.82yes, they are consistent with the choices of the irr rule since the signs of the cash flows change only once.6.11 consider two streams of cash flows, a and b. cash flow a consists of $5,000 starting three years from to

37、day and growing at 4 percent in perpetuity. cash flow b consists of _$6,000 starting two years from today and continuing in perpetuity. assume the appropriate discount rate is 12 percent.a. what is the present value of each stream?b. what is the irr of a project c, which is a combination of projects

38、 a and b; that is, c _ a _ b?c. if it is assumed that the discount rate is always positive, what is the rule related to irr for assessing project c that would correspond to the npv rule?6.11a.project a:npv = -$5,000 + $3,500 / (1 + r) + $3,500 / (1 + r)2 = 0irr = r = 25.69%project b:npv = -$100,000

39、+ $65,000 / (1 + r) + $65,000 / (1 + r)2 = 0irr = r = 19.43%b.choose project a because it has a higher irr.c.the difference in scale is ignored.d.apply the incremental irr method.e.c0c1c2b - a-$95,000$61,500$61,500npv = -$95,000 + $61,500 / (1 + r) + $61,500 / (1 + r)2 = 0incremental irr = r = 19.09

40、%f.if the discount rate is less than 19.09%, choose project b. otherwise, choose project a.g.npva = -$5,000 + $3,500 / 1.15 + $3,500 / 1.152 = $689.98npvb = -$100,000 + $65,000 / 1.15 + $65,000 / 1.152 = $5,671.08choose project b.6.12 project a involves an investment of $1 million, and project b inv

41、olves an investment of $2 million. both projects have a unique internal rate of return of 20 percent. is the following statement true or false? explain your answer.for any discount rate between 0 percent and 20 percent, inclusive, project b has an npv twice as great as that of project a.6.12a.pva =

42、$5,000 / (0.12 - 0.04) / 1.122 = $49,824.61pvb = (-$6,000 / 0.12) / 1.12 = -$44,642.86b.the irr for project c must solve$5,000 / (x - 0.04) / (1 + x)2 + (-$6,000 / x) / (1 + x) = 0$5,000 / (x - 0.04) - $6,000 (1 + x) / x = 025 x2 + 3.17 x - 1 =0x = -3.17 - (110.0489)0.5 / 50 or -3.17 + (110.0489)0.5

43、 / 50the relevant positive root is irr = x = 0.1464 = 14.64%c.to arrive at the appropriate decision rule, we must graph the npv as a function of the discount rate. at a discount rate of 14.64% the npv is zero. to determine if the graph is upward or downward sloping, check the npv at another discount

44、 rate. at a discount rate of 10% the npv is $14,325.07 = $68,870.52 - $54,545.54. thus, the graph of the npv is downward sloping. from the discussion in the text, if an npv graph is downward sloping, the project is an investing project. the correct decision rule for an investing project is to accept

45、 the project if the discount rate is below 14.64%.npv$14,325.070r14.64%10% the profitability index6.13 suppose the following two mutually exclusive investment opportunities are available to the deangelo firm. the appropriate discount rate is 10 percent.year project alpha project beta0 _$500 _$2,0001

46、 _300 _3002 700 1,8003 600 1,700a. what is the npv of project alpha and project beta?b. which project would you recommend for the deangelo firm?6.13generally, the statement is false. if the cash flows of project b occur early and the cash flows of project a occur late, then for a low discount rate t

47、he npv of a can exceed the npv of b. examples are easy to construct.c0c1c2irrnpv 0%a:-$1,000,000$0$1,440,0000.20$440,000b:-2,000,0002,400,00000.20400,000in one particular case, the statement is true for equally risky projects. if the lives of the two projects are equal and in every time period the c

48、ash flows of the project b are twice the cash flows of project a, then the npv of project b will be twice as great as the npv of project a for any discount rate between 0% and 20%.6.14 the firm for which you work must choose between the following two mutually exclusive projects. the appropriate disc

49、ount rate for the projects is 10 percent.profitabilityc0 c1 c2 index npva _$1,000 $1,000 $500 1.32 $322b _500 500 400 1.57 285the firm chose to undertake a. at a luncheon for shareholders, the manager of a pension fund that owns a substantial amount of the firms stock asks you why the firm chose pro

50、ject a instead of project b when b is more profitable.how would you justify your firms action? are there any circumstances under which the pension fund managers argument could be correct?6.14a.npva = $756.57 - $500 = $256.57npvb = $2,492.11 - $2,000 = $492.11b.choose project beta.6.15 the treasurer

51、of davids, inc., has projected the cash flows of projects a, b, and c as follows. suppose the relevant discount rate is 12 percent a year.year project a project b project c0 _$100,000 _$200,000 _$100,0001 70,000 130,000 75,0002 70,000 130,000 60,000a. compute the profitability indices for each of th

52、e three projects.b. compute the npvs for each of the three projects.c. suppose these three projects are independent. which projects should davids accept based on the profitability index rule?d. suppose these three projects are mutually exclusive. which project should davids accept based on the profi

53、tability index rule?e. suppose davids budget for these projects is $300,000. the projects are not divisible. which projects should davids accept?6.15although the profitability index is higher for project b than for project a, the npv is the increase in the value of the company that will occur if a p

54、articular project is undertaken. thus, the project with the higher npv should be chosen because it increases the value of the firm the most. only in the case of capital rationing could the pension fund manager be correct.6.16 bill plans to open a self-serve grooming center in a storefront. the groom

55、ing equipment will cost $160,000. bill expects the after-tax cash inflows to be $40,000 annually for seven years, after which he plans to scrap the equipment and retire to the beaches of jamaica.assume the required return is 15%. what is the projects pi? should it be accepted?comparison of investmen

56、t rules6.16a.pia = ($70,000 / 1.12 + $70,000 / 1.122) / $100,000 = 1.183pib = ($130,000 / 1.12 + $130,000 / 1.122) / $200,000 = 1.099pic = ($75,000 / 1.12 + $60,000 / 1.122) / $100,000 = 1.148b.npva = -$100,000 + $118,303.57 = $18,303.57npvb = -$200,000 + $219,706.63 = $19,706.63npvc = -$100,000 + $114,795.92 = $14,795.92c.accept all three projects because pis of all the three projects are greater than one.d.based on the pi rule, project c ca