CHAPTER Capital Budgeting Decision Criteria CHAPTER ORIENTATION Capital budgeting involves the decision making process with respect to the investment in fixed assets; specifically, it involves measuring the incremental cash flows associated with investment proposals and evaluating the attractiveness of these cash flows relative to the project's costs This chapter focuses on the various decision criteria CHAPTER OUTLINE I Methods for evaluating projects A The payback period method The payback period of an investment tells the number of years required to recover the initial investment The payback period is calculated by adding the cash inflows up until they are equal to the initial fixed investment Although this measure does, in fact, deal with cash flows and is easy to calculate and understand, it ignores any cash flows that occur after the payback period and does not consider the time value of money within the payback period To deal with the criticism that the payback period ignores the time value of money, some firms use the discounted payback period method The discounted payback period method is similar to the traditional payback period except that it uses discounted free cash flows rather than actual undiscounted free cash flows in calculating the payback period The discounted payback period is defined as the number of years needed to recover the initial cash outlay from the discounted free cash flows 226 B Present-value methods The net present value of an investment project is the present value of its free cash flows less the investment’s initial outlay n NPV = ∑ t =1 FCFt (1 + k) t - IO where: a FCFt = the annual free cash flow in time period t (this can take on either positive or negative values) k = the required rate of return or appropriate discount rate or cost of capital IO = the initial cash outlay n = the project's expected life The acceptance criteria are accept if NPV ≥ reject if NPV < b The advantage of this approach is that it takes the time value of money into consideration in addition to dealing with cash flows The profitability index is the ratio of the present value of the expected future free cash flows to the initial cash outlay, or n ∑ profitability index = a t =1 FCFt (1 + k) t IO The acceptance criteria are accept if PI ≥ 1.0 reject if PI < 1.0 b The advantages of this method are the same as those for the net present value c Either of these present-value methods will give the same accept-reject decisions to a project 227 C The internal rate of return is the discount rate that equates the present value of the project's future net cash flows with the project's initial outlay Thus the internal rate of return is represented by IRR in the equation below: n IO = ∑ t =1 FCFt (1 + IRR)t The acceptance-rejection criteria are: accept if IRR ≥ required rate of return reject if IRR < required rate of return The required rate of return is often taken to be the firm's cost of capital The advantages of this method are that it deals with cash flows and recognizes the time value of money; however, the procedure is rather complicated and time-consuming The net present value profile allows you to graphically understand the relationship between the internal rate of return and NPV A net present value profile is simply a graph showing how a project’s net present value changes as the discount rate changes The IRR is the discount rate at which the NPV equals zero The primary drawback of the internal rate of return deals with the reinvestment rate assumption it makes The IRR implicitly assumes that the cash flows received over the life of the project can be reinvested at the IRR while the NPV assumes that the cash flows over the life of the project are reinvested at the required rate of return Since the NPV makes the preferred reinvestment rate assumption it is the preferred decision technique The modified internal rate of return (MIRR) allows the decision maker the intuitive appeal of the IRR coupled with the ability to directly specify the appropriate reinvestment rate a To calculate the MIRR we take all the annual free tax cash inflows, ACIFt's, and find their future value at the end of the project's life compounded at the required rate of return - this is called the terminal value or TV All cash outflows, ACOFt, are then discounted back to present at the required rate of return The MIRR is the discount rate that equates the present value of the free cash outflows with the present value of the project's terminal value b If the MIRR is greater than or equal to the required rate of return, the project should be accepted 228 ANSWERS TO END-OF-CHAPTER QUESTIONS 9-1 Capital budgeting decisions involve investments requiring rather large cash outlays at the beginning of the life of the project and commit the firm to a particular course of action over a relatively long time horizon As such, they are costly and difficult to reverse, both because of: (1) their large cost and (2) the fact that they involve fixed assets, which cannot be liquidated easily 9-2 The criticisms of using the payback period as a capital budgeting technique are: (1) (2) (3) It ignores the timing of the free cash flows that occur during the payback period It ignores all free cash flows occurring after the payback period The selection of the maximum acceptable payback period is arbitrary The advantages associated with the payback period are: (1) (2) (3) It deals with cash flows rather than accounting profits, and therefore focuses on the true timing of the project's benefits and costs It is easy to calculate and understand It can be used as a rough screening device, eliminating projects whose returns not materialize until later years These final two advantages are the major reasons why it is used frequently 9-3 Yes The payback period eliminates projects whose returns not materialize until later years and thus emphasizes the earliest returns, which in a country experiencing frequent expropriations would certainly have the most amount of uncertainty surrounding the later returns In this case, the payback period could be used as a rough screening device to filter out those riskier projects, which have long lives 9-4 The three, discounted cash flow capital budgeting criteria are the net present value, the profitability index, and the internal rate of return The net present value method gives an absolute dollar value for a project by taking the present value of the benefits and subtracting out the present value of the costs The profitability index compares these benefits and costs through division and comes up with a measure of the project's relative value—a benefit/cost ratio On the other hand, the internal rate of return tells us the rate of return that the project earns In the capital budgeting area, these methods generally give us the same accept-reject decision on projects but many times rank them differently As such, they have the same general advantages and disadvantages, although the calculations associated with the internal rate of return method can become quite tedious and it assumes cash flows over the life of the life of the project are reinvested at the IRR The advantages associated with these discounted cash flow methods are: (1) They deal with cash flows rather than accounting profits (2) They recognize the time value of money (3) They are consistent with the firm's goal of shareholder wealth maximization 229 9-5 The advantage of using the MIRR, as opposed to the IRR technique is that the MIRR technique allows the decision maker to directly input the reinvestment rate assumption With the IRR method it is implicitly assumed that the cash flows over the life of the project are reinvested at the IRR SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 9-1A (a) (b) (c) (d) 9-2A (a) (b) IO = FCFt [PVIF IRR%,t yrs ] $10,000 = $17,182 [PVIF IRR%,8 yrs] 0.582 = PVIFIRR%,8 yrs Thus, IRR = 7% $10,000 = $48,077 [PVIF IRR%,10 yrs ] 0.208 = PVIFIRR%,10 yrs Thus, IRR = 17% $10,000 = $114,943 [PVIF IRR%,20 yrs ] 0.087 = PVIFIRR%,20 yrs Thus, IRR = 13% $10,000 = $13,680 [PVIF IRR%,3 yrs] 731 = PVIFIRR%,3 yrs Thus, IRR = 11% I0 = FCFt [PVIFA IRR%,t yrs ] $10,000 = $1,993 [PVIFA IRR%,10 yrs ] 5.018 = PVIFA IRR%,10 yrs Thus, IRR = 15% $10,000 = $2,054 [PVIFA IRR%,20 yrs ] 4.869 = PVIFA IRR%,20 yrs Thus, IRR = 20% 230 (c) (d) 9-3A (a) $10,000 = $1,193 [PVIFA IRR%,12 yrs ] 8.382 = PVIFA IRR%,12 yrs Thus, IRR = 6% $10,000 = $2,843 [PVIFA IRR%,5 yrs ] 3.517 = PVIFA IRR%,5 yrs Thus, IRR = 13% $10,000 = $2,000 (1 + IRR)1 + $5,000 (1 + IRR) + $8,000 (1 + IRR)3 Try 18%: $10,000 = $2,000(0.847) + $5,000 (0.718) + $8,000 (0.609) = $1,694 + $3,590 + $4,872 = $10,156 = $2,000 (0.840) + $5,000 (0.706) + $8,000 (0.593) = $1,680 + $3,530 + $4,744 = $9,954 Thus, IRR = approximately 19% $10,000 = $5,000 $2,000 + + (1 + IRR)1 (1 + IRR)2 (1 + IRR)3 = $8,000 (0.769) + $5,000 (0.592) + $2,000 (0.455) = $6,152 + $2,960 + $910 = $10,022 = $8,000 (0.763) + $5,000 (0.583) + $2,000 (0.445) = $6,104 + $2,915 + $890 = $9,909 = approximately 30% Try 19% $10,000 (b) $8,000 Try 30% $10,000 Try 31%: $10,000 Thus, IRR 231 (c) $10,000 = $2,000 t =1 (1 + IRR)t ∑ + $5,000 (1 + IRR )6 Try 11% $10,000 = $2,000 (3.696) + $5,000 (0.535) = $7,392 + $2,675 = $10,067 = $2,000 (3.605) + $5,000 (0.507) = $7,210 + $2,535 = $9,745 Thus, IRR = approximately 11% NPV = Try 12% $10,000 9-4A (a) (b) (c) (d) $450,000 t =1 (1 + 09) t ∑ - $1,950,000 = $450,000 (4.486) - $1,950,000 = $2,018,700 - $1,950,000 = $68,700 = $2,018,700 $1,950,000 = 1.0352 $1,950,000 = $450,000 [PVIFA IRR%,6 yrs ] 4.333 = PVIFA IRR%,6 yrs IRR = about 10% (10.1725%) PI Yes, the project should be accepted 232 9-5A (a) Payback Period = $80,000/$20,000 = years Discounted Payback Period Calculations: Year Undiscounted Cash Flows PVIF10%,n -$80,000 20,000 20,000 20,000 20,000 20,000 20,000 1.000 909 826 751 683 621 564 Discounted Cash Flows Cumulative Discounted Cash Flows -$80,000 18,180 16,520 15,020 13,660 12,420 11,280 Discounted Payback Period = 5.0 + 4,200/11,280 = 5.37 years (b) (c) (d) 9-6A (a) NPV = $20,000 t =1 (1 + 10) t ∑ - $80,000 = $20,000 (4.355) - $80,000 = $87,100 - $80,000 = $7,100 = $87,100 $80,000 = 1.0888 $80,000 = $20,000 [PVIFA IRR%,6 yrs ] 4.000 = PVIFA IRR%,6 yrs IRR = about 13% (12.978%) NPVA = PI NPVB $12,000 t =1 (1 + 12) t ∑ - $50,000 = $12,000 (4.111) - $50,000 = $49,332 - $50,000 = -$668 = $13,000 t =1 (1 + 12) t ∑ - $70,000 = $13,000 (4.111) - $70,000 = $53,443 - $70,000 = -$16,557 233 -$80,000 -61,820 -45,300 -30,280 -16,620 -4,200 7,080 (b) = $49,332 $50,000 = 0.9866 = $53,443 $70,000 = 0.7635 $50,000 = $12,000 [PVIFA IRR%,6 yrs ] 4.1667 = PVIFA IRR%,6 yrs IRRA = 11.53% $70,000 = $13,000 [PVIFA IRR%,6 yrs ] 5.3846 = PVIFA IRR%,6 yrs IRRB = 3.18% PIA PIB (c) Neither project should be accepted 9-7A (a) Project A: Payback Period = years + $100/$200 = 2.5 years Project A: Discounted Payback Period Calculations: Year Undiscounted Discounted Cash Flows PVIF10%,n Cash Flows -$1,000 600 300 200 100 500 1.000 909 826 751 683 621 234 -$1,000 545 248 150 68 311 Cumulative Discounted Cash Flows -$1,000 -455 -207 -57 11 322 Discounted Payback Period = 3.0 + 57/68 = 3.84 years Project B: Payback Period = years + $2,000/$3,000 = 2.67 years Project B: Discounted Payback Period Calculations: Year Undiscounted Cash Flows PVIF10%,n Discounted Cash Flows Cumulative Discounted Cash Flows -$10,000 5,000 1.000 909 -$10,000 4,545 -$10,000 -5,455 3,000 3,000 3,000 3,000 826 751 683 621 2,478 2,253 2,049 1,863 -2,977 -724 1,325 3,188 Discounted Payback Period = 3.0 + 724/2,049 = 3.35 years Project C: Payback Period = years + $1,000/$2,000 = 3.5 years Project C: Discounted Payback Period Calculations: Year Undiscounted Cash Flows -$5,000 1,000 1,000 2,000 2,000 2,000 PVIF10%,n Discounted Cash Flows Cumulative Discounted Cash Flows 1.000 909 826 751 683 621 -$5,000 909 826 1,502 1,366 1,242 -$5,000 -4,091 -3,265 -1,763 -397 845 235 Discounted Payback Period = 4.0 + 397/1,242 = 4.32 years 9-8A NPV9% NPV11% NPV13% NPV15% Project Traditional Payback Discounted Payback A Accept Reject B Accept Reject C Reject Reject = $1,000,000 t =1 (1 + 09) t ∑ - $5,000,000 = $1,000,000 (5.535) - $5,000,000 = $5,535,000 - $5,000,000 = $535,000 = $1,000,000 t =1 (1 + 11) t ∑ - $5,000,000 = $1,000,000 (5.146) - $5,000,000 = $5,146,000 - $5,000,000 = $146,000 = $1,000,000 - $5,000,000 t = (1 + 13)t = $1,000,000 (4.799) - $5,000,000 = $4,799,000 - $5,000,000 = -$201,000 = ∑ $1,000,000 t =1 (1 + 15) t ∑ - $5,000,000 = $1,000,000 (4.487) - $5,000,000 = $4,487,000 - $5,000,000 = -$513,000 9-9A Project A: $50,000 = $10,000 (1 + IRR A )1 + + $15,000 (1 + IRR A ) $25,000 (1 + IRR A ) 236 + + $20,000 (1 + IRR A )3 $30,000 (1 + IRR A )5 Try 23% $50,000 = $10,000(.813) + $15,000(.661) + $20,000(.537) + $25,000(.437) + $30,000(.355) = $8,130 + $9,915 + $10,740 + $10,925 + $10,650 = $50,360 = $10,000(.806) + $15,000(.650) +$20,000(.524) Try 24% $50,000 + $25,000(.423) + $30,000(.341) = $8,060 + $9,750 + $10,480 + $10,575 + $10,230 = $49,095 = just over 23% $100,000 = $25,000 [PVIFA IRR%,5 yrs] 4.00 = PVIFA IRR%,5 yrs Thus, IRR = 8% $450,000 = $200,000 [PVIFA IRR%,3 yrs ] 2.25 = PVIFA IRR%,3 yrs Thus, IRR = 16% Thus, IRR Project B: Project C: 9-10A (a) (b) NPV NPV = $18,000 t =1 (1 + 10) t ∑ - $100,000 = $18,000(6.145) - $100,000 = $110,610 - $100,000 = $10,610 = = = = (c) 10 10 $18,000 t =1 (1 + 15) t ∑ - $100,000 $18,000(5.019) - $100,000 $90,342 - $100,000 -$9,658 If the required rate of return is 10% the project is acceptable as in part (a) 237 (d) 9-11A (a) (b) (c) $100,000 = 5.5556 = $18,000 [PVIFA IRR%,10 yrs ] PVIFA IRR%,10 yrs IRR = Between 12% and 13% (12.41%) n ACOFt t =0 (1 + k) t ∑ n ∑ = t =0 ACIFt (1 + k) n − t (1 + MIRR)n $3,000,000(FVIFA10%10years ) $10,000,000 = $10,000,000 = $10,000,000 = (1 + MIRR )10 MIRR = 16.9375% $10,000,000 = $10,000,000 = $10,000,000 = (1 + MIRR )10 MIRR = 18.0694% $10,000,000 = $10,000,000 = $10,000,000 = (1 + MIRR )10 MIRR = 19.2207% (1 + MIRR)10 $3,000,000(15.937) (1 + MIRR )10 $47,811,000 $3,000,000(FVIFA12%10years ) (1 + MIRR)10 $3,000,000(17.549) (1 + MIRR )10 $52,647,000 $3,000,000(FVIFA14%10 years ) (1 + MIRR )10 $3,000,000(19.337) (1 + MIRR )10 $58,011,000 238 SOLUTION TO INTEGRATIVE PROBLEM Capital budgeting decisions involve investments requiring rather large cash outlays at the beginning of the life of the project and commit the firm to a particular course of action over a relatively long time horizon As such, they are both costly and difficult to reverse, both because of: (1) their large cost; (2) the fact that they involve fixed assets which cannot be liquidated easily Axiom 5: The Curse of Competitive Markets—Why It's Hard to Find Exceptionally Profitable Projects deals with the problems associated with finding profitable projects When we introduced that axiom we stated that exceptionally successful investments involve the reduction of competition by creating barriers to entry either through product differentiation or cost advantages In effect, without barriers to entry, whenever extremely profitable projects are found competition rushes in, driving prices and profits down unless there is some barrier to entry Payback periodA = years + Payback PeriodB = 20,000 years 50,000 110,000 years 40,000 = = 3.4 years 2.75 years Project B should be accepted while project A should be rejected The disadvantages of the payback period are: 1) ignores the time value of money, 2)ignores cash flows occurring after the payback period, 3)selection of the maximum acceptable payback period is arbitrary Discounted Payback Period Calculations, Project A: Cumulative Year Undiscounted Cash Flows -$110,000 20,000 30,000 40,000 50,000 70,000 PVIF12%,n 1.000 893 797 712 636 567 Discounted Cash Flows -$110,000 17,860 23,910 28,480 31,800 39,690 Discounted Payback Period = 4.0 + 7,950/39,690 = 4.20 years 239 Cash Flows -$110,000 -92,140 -68,230 -39,750 -7,950 31,740 Discounted Payback Period Calculations, Project B: Year Undiscounted Cash Flows PVIF12%,n -$110,000 40,000 40,000 40,000 40,000 40,000 1.000 893 797 712 636 567 Discounted Cash Flows Cumulative Discounted Cash Flows -$110,000 35,720 31,880 28,480 25,440 22,680 -$110,000 -74,280 -42,400 -13,920 11,520 34,200 Discounted Payback Period = 3.0 + 13,920/25,440 = 3.55 years Using the discounted payback period method and a 3-year maximum acceptable project hurtle, neither project should be accepted The major problem with the discounted payback period comes in setting the firm's maximum desired discounted payback period This is an arbitrary decision that affects which projects are accepted and which ones are rejected Thus, while the discounted payback period is superior to the traditional payback period, in that it accounts for the time value of money in its calculations, its use should be limited due to the problem encountered in setting the maximum desired payback period In effect, neither method should be used NPVA n = ∑ t =1 = = FCFt (1 + k) t - IO $20,000(PVIF 12%, year) + $30,000 (PVIF 12%, years ) + $40,000(PVIF 12%, years ) + $50,000 (PVIF 12%, years ) + $70,000(PVIF12%, years ) - $110,000 $20,000(.893) + $30,000 (.797) + $40,000 (.712) + $50,000 (.636) + $70,000 (.567) - $110,000 NPVB = $17,860 + $23,910 + $28,480 + $31,800 + $39,690 - $110,000 = $141,740-$110,000 = $31,740 = $40,000(PVIFA 12%, years ) - $110,000 = $40,000(3.605) - $110,000 = $144,200-$110,000 = $34,200 Both projects should be accepted 240 The net present value technique discounts all the benefits and costs in terms of cash flows back to the present and determines the difference If the present value of the benefits outweighs the present value of the costs, the project is accepted, if not, it is rejected PIA PIB =  n   ∑ FCFt   t =1   t   (1 + k)      IO = $141,740 $110,000 = 1.2885 = $144,200 $110,000 = 1.3109 Both projects should be accepted 10 The net present value and the profitability index always give the same accept reject decision When the present value of the benefits outweighs the present value of the costs the profitability index is greater than one, and the net present value is positive In that case, the project should be accepted If the present value of the benefits is less than the present value of the costs, then the profitability index will be less than one, and the net present value will be negative, and the project will be rejected 11 For both projects A and B all of the costs are already in present dollars and, as such, will not be affected by any change in the required rate of return or discount rate All the benefits for these projects are in the future and thus when there is a change in the required rate of return or discount rate their present value will change If the required rate of return increased, the present value of the benefits would decline which would in turn result in a decrease in both the net present value and the profitability index for each project 12 IRRA = 20.9698% IRRB = 23.9193% 13 The required rate of return does not change the internal rate of return for a project, but it does affect whether a project is accepted or rejected The required rate of return is the hurdle rate that the project's IRR must exceed in order to accept the project 14 The net present value assumes that all cash flows over the life of the project are reinvested at the required rate of return, while the internal rate of return implicitly assumes that all cash flows over the life of the project are reinvested over the remainder of the project's life at the IRR The net present value method makes the most acceptable, and conservative assumption and thus is preferred 241 15 Project A: n n ACOFt t =0 (1 + k) t ∑ = ∑ t =0 ACIFt (1 + k) n − t (1 + MIRR) n = $20,000(FVIF12% , years) + $30,000(FVIF12% , years) + $40,000(FVIF12% , years) + $50,000(FVIF12% , year) + $70,000 (1 + MIRR A ) $110,000 = $20,000(1.574) + $30,000(1.405) + $40,000(1.254) + $50,000(1.120) + $70,000 (1 + MIRR A ) $110,000 = $31,480 + $42,150 + $50,160 + $56,000 + $70,000 (1 + MIRR A ) $110,000 = (1 + MIRR A )5 MIRRA = 17.8247% $110,000 $249,790 Project B: $40,000(FVIFA12%,5years ) $110,000 = $110,000 = $110,000 = (1 + MIRR B )5 MIRRB = 18.2304% (1 + MIRR B )5 $40,000(6.353) (1 + MIRR B )5 $254,120 Both projects should be accepted because their MIRR exceeds the required rate of return The modified internal rate of return is superior to the internal rate of return method because MIRR assumes the reinvestment rate of cash flows is the required rate of return 242 Solutions to Problem Set B 9-1B (a) (b) (c) (d) 9-2B (a) (b) (c) (d) IO = FCFt [PVIFIRR%,t yrs] $10,000 = $19,926 [PVIFIRR%,8 yrs] 0.502 = PVIFIRR%,8 yrs Thus, IRR = 9% $10,000 = $20,122 [PVIFIRR%,12 yrs] 0.497 = PVIFIRR%,12 yrs Thus, IRR = 6% $10,000 = $121,000 [PVIFIRR%,22 yrs] 0.083 = PVIFIRR%,22 yrs Thus, IRR = 12% $10,000 = $19,254 [PVIF IRR%,5 yrs] 0.519 = PVIFIRR%,5 yrs Thus, IRR = 14% IO = FCFt [PVIFA IRR%,t yrs ] $10,000 = $2,146 [PVIFA IRR%,10 yrs ] 4.66 = PVIFA IRR%,10 yrs Thus, IRR = 17% $10,000 = $1,960 [PVIFA IRR%,20 yrs ] 5.102 = PVIFA IRR%,20 yrs Thus, IRR = 19% $10,000 = $1,396 [PVIFA IRR%,12 yrs ] 7.163 = PVIFA IRR%,12 yrs] Thus, IRR = 9% $10,000 = $3,197 [PVIFA IRR%,5 yrs] 3.128 = PVIFA IRR%,5 yrs Thus, IRR = 18% 243 9-3B (a) $10,000 = $3,000 (1 + IRR)1 + $5,000 (1 + IRR) $7,500 + (1 + IRR)3 Try 21%: $10,000 = $3,000(0.826) + $5,000 (0.683) + $7,500 (0.564) = $2,478+ $3,415 + $4,230 = $10,123 = $3,000 (0.820) + $5,000 (0.672) + $7,500 (0.551) = $2,460 + $3,360 + $4,132.50 = $9,952.50 Thus, IRR = approximately 22% $12,000 = (1 + IRR)1 = $9,000 (0.800) + $6,000 (0.640) + $2,000 (0.512) = $7,200 + $3,840 + $1,024 = $12,064 = $9,000 (0.794) + $6,000 (0.630) + $2,000 (0.500) = $7,146 + $3,780 + $1,000 = $11,926 Thus, IRR = nearest percent is 25% $8,000 = Try 22% $10,000 (b) $9,000 + $6,000 (1 + IRR)2 + $2,000 (1 + IRR)3 Try 25% $12,000 Try 26%: $12,000 (c) ∑ t =1 $2,000 (1 + IRR) t + $5,000 (1 + IRR)6 Try 18% $8,000 = $2,000 (3.127) + $5,000 (0.370) = $6,254 + $1,850 = $8,104 = $2,000 (3.058) + $5,000 (0.352) = $6,116 + $1,760 = $7,876 = nearest percent is 18% Try 19% $8,000 Thus, IRR 244 9-4B (a) (b) (c) (d) 9-5B (a) (b) (c) (d) 9-6B (a) NPV PI = $750,000 t =1 (1 + 11) t ∑ - $2,500,000 = $750,000 (4.231) - $2,500,000 = $3,173,250 - $2,500,000 = $673,250 = $3,173,250 $2,500,000 = 1.2693 $2,500,000 = $750,000 [PVIFA IRR%,6 yrs] 3.333 = PVIFA IRR%,6 yrs IRR = about 20% (19.90%) Yes, the project should be accepted Payback Period = $160,000/$40,000 = years NPV = $40,000 t =1 (1 + 10) t ∑ - $160,000 = $40,000 (4.355) - $160,000 = $174,200 - $160,000 = $14,200 = $174,200 $160,000 = 1.0888 $160,000 = $40,000 [PVIFA IRR%,6 yrs ] 4.000 = PVIFA IRR%,6 yrs IRR = about 13% (12.978%) NPVA = PI NPVB $12,000 t =1 (1 + 12) t ∑ - $45,000 = $12,000 (4.111) - $45,000 = $49,332 - $45,000 = $4,332 = $14,000 t =1 (1 + 12) t ∑ - $70,000 = $14,000 (4.111) - $70,000 = $57,554 - $70,000 = -$12,446 245 (b) = $49,332 $45,000 = 1.0963 = $57,554 $70,000 = 0.822 $45,000 = $12,000 [PVIFA IRR%,6 yrs ] 3.75 = PVIFA IRR%,6 yrs IRRA = 15.34% $70,000 = $14,000 [PVIFA IRR%,6 yrs ] 5.0000 = PVIFA IRR%,6 yrs IRRB = 5.47% PIA PIB (c) Project A should be accepted 9-7B (a) Project A: Payback Period = years = years + $1,000/$3,000 = 2.33 years = years + $1,000/$2,000 = 3.5 years Project B: Payback Period Project C: Payback Period 9-8B NPV9% = Project Payback Period Method A Accept B Accept C Reject $2,500,000 t =1 (1 + 09) t ∑ - $10,000,000 = $2,500,000 (5.535) - $10,000,000 = $13,837,500 - $10,000,000 = $3,837,500 NPV11% = $2,500,000 t =1 (1 + 11) t ∑ - $10,000,000 = $2,500,000 (5.146) - $10,000,000 = $12,865,000 - $10,000,000 = $2,865,000 246 NPV13% = $2,500,000 t =1 (1 + 13) t - $10,000,000 = $2,500,000 (4.799) - $10,000,000 = $11,997,500 - $10,000,000 = $1,997,500 NPV15% = 9-9B ∑ $2,500,000 t =1 (1 + 15) t ∑ - $10,000,000 = $2,500,000 (4.487) - $10,000,000 = $11,217,500 - $10,000,000 = $1,217,500 Project A: $75,000 = $10,000 (1 + IRR A ) + + $10,000 (1 + IRR A ) $25,000 (1 + IRR A ) + + $30,000 (1 + IRR A )3 $30,000 (1 + IRR A )5 Try 10% $75,000 = $10,000(.909) + $10,000(.826) + $30,000(.751) + $25,000(.683) + $30,000(.621) = $9,090 + $8,260 + $22,530 + $17,075 + $18,630 = $75,585 = $10,000(.901) + $10,000(.812) +$30,000(.731) Try 11% $75,000 + $25,000(.659) + $30,000(.593) Thus, IRR = $9,010 + $8,120 + $21,930+ $16,475 + $17,790 = $73,325 = just over 10% $95,000 = $25,000 [PVIFA IRR%,5 yrs ] 3.80 = PVIFA IRR%,5 yrs Thus, IRR = just below 10% = $150,000 [PVIFA IRR%,3 yrs ] 2.633 = PVIFA IRR%,3 yrs Thus, IRR = just below 7% Project B: Project C: $395,000 247 10 9-10B (a) NPV = ∑ t =1 (b) NPV $25,000 - $150,000 (1 + 09) t = $25,000(6.418) - $150,000 = $160,450 - $150,000 = $10,450 = 10 $25,000 t =1 (1 + 15) t ∑ - $150,000 = $25,000(5.019) - $150,000 = $125,475 - $150,000 = -$24,525 (c) If the required rate of return is 9% the project is acceptable in part (a) It should be rejected in part (b) with a negative NPV (d) $150,000 = $25,000 [PVIFA IRR%,10 yrs ] 6.000 = PVIFA IRR%,10 yrs IRR = Between 10% and 11% (10.558%) n ACOFt t= (1 + k) t 9-11B (a) b) ∑ n = n-t ∑ ACIFt (1 + k) t =0 (1 + MIRR)n $2,000,000(FVIFA10%,8years ) $8,000,000 = $8,000,000 = $8,000,000 = (1 + MIRR)8 MIRR = 14.0320% $8,000,000 = $8,000,000 = $8,000,000 = (1 + MIRR)8 MIRR = 15.0749% (1 + MIRR)8 $2,000,000(11.436) (1 + MIRR)8 $22,872000 $2,000,000(FVIFA12%,8years ) (1 + MIRR)8 $2,000,000(12.300) (1 + MIRR)8 $24,600,000 248 c) $2,000,000(FVIFA14%,8years ) $8,000,000 = $8,000,000 = $8,000,000 = (1 + MIRR)8 MIRR = 16.1312% (1 + MIRR)8 $2,000,000(13.233) (1 + MIRR)8 $26,466,000 FORD'S PINTO (Ethics in Capital Budgeting) OBJECTIVE: To force the students to recognize the role ethical behavior plays in all areas of Finance DEGREE OF DIFFICULTY: Easy Case Solution: With ethics cases there are no right or wrong answers - just opinions Try to bring out as many opinions as possible without being judgmental 249 ... assumed that the cash flows over the life of the project are reinvested at the IRR SOLUTIONS TO END-OF -CHAPTER PROBLEMS Solutions to Problem Set A 9-1A (a) (b) (c) (d) 9-2A (a) (b) IO = FCFt [PVIF... PVIF10%,n Discounted Cash Flows Cumulative Discounted Cash Flows 1.000 909 826 751 683 621 -$5,000 909 826 1,502 1,366 1,242 -$5,000 -4 ,091 -3,265 -1,763 -397 845 235 Discounted Payback Period = 4.0 +... IRR A )3 $30,000 (1 + IRR A )5 Try 10% $75,000 = $10,000(. 909) + $10,000(.826) + $30,000(.751) + $25,000(.683) + $30,000(.621) = $9 ,090 + $8,260 + $22,530 + $17,075 + $18,630 = $75,585 = $10,000(.901)