1. A project has an initial cost of $40,000, expected net cash inflows of $9,000 per *NPV*= -$40,000 + $9,000[(1/I) - (1/(I × (1 + I)N)] = -$40,000 +
... [Show More] $9,000[(1/0.11) - (1/(0.11 × (1 + year for 7 years, and a cost 0.11)7)] of capital of 11%. What is the project's NPV? (Hint: Begin by constructing a time line.) What is the project's IRR? What is the project's MIRR? What is the project's PI? What is the project's pay- back period? What is the project's dis- counted payback period? = $2,409.77. Financial calculator solution: Input CF0 = -40000, CF1-7 = 9000, I/YR = 11, and then solve for NPV = $2,409.77 Financial calculator solution: Input CF0 = -40000, CF1-8 = 9000, and then solve for *IRR* = 12.84%. *mirr* start at year zero. compound 9000 starting in year one all the way to year 7, so 7 times at 12 percent. add them up. (9000+9900+11089+12309+13663+15166+16834) Financial calculator: Obtain the FVA by inputting N = 7, I/YR = 11, PV = 0, PMT = 9000, and then solve for FV = $87,049. The MIRR can be obtained by inputting N = 7, PV = -40000, PMT = 0, FV = 88049, and then solving for I/YR = 11.93%. PV = $9,000[(1/I) - (1/(I × (1 + I)N)] = $9,000[(1/0.11) - (1/(0.11 × (1 + 0.11)7)] = $42,410. Financial calculator: Find present value of future cash flows by inputting N = 7, I/YR = 11, PMT = -9000, FV = 0, then solve for PV = $42,409. *PI*= PV of future cash flows/Initial cost = $42,409/$40,000 = 1.06. *payback period* Since the cash flows are a constant $9,000, cal- culate the payback period as: $40,000/$9,000 = 4.44, so the payback is about 4 years. The project's discounted payback period is cal- culated as follows: Year Ann Cf Discounted CF 11% Cum Discount- ed CF 0 -40,000 -40,000.00 1 9,000 8,108.11 (31,891.89) 2 9,000 7,304.60 (24,587.29) 3 9,000 6,580.72 (18,006.57) 4 9,000 5,928.58 (12,077.99) 5 9,000 5,341.06 (6,736.93) 6 9,000 4,811.77 (1,925.16) 7 9,000 4,334.93 2,409.77 2. Your division is consider- ing two investment pro- jects, each of which re- quires an up-front expen- diture of $15 million. You estimate that the invest- ments will produce the fol- lowing net cash flows: Year Project A Project B 1 $ 5,000,000 $20,000,000 2 10,000,000 10,000,000 3 20,000,000 6,000,000 What are the two projects' net present values, assum- The *discounted payback period* is 6 + years, or 6.44 years. a. Project A: Using a financial calculator, enter the following: CF0 = -15000000 CF1 = 5000000 CF2 = 10000000 CF3 = 20000000 I/YR = 10; NPV = $12,836,213. Change I/YR = 10 to I/YR = 5; NPV = $16,108,952. Change I/YR = 5 to I/YR = 15; NPV = $10,059,587. Project B: Using a financial calculator, enter the following: CF0 = -15000000 ing the cost of capital is 5%? 10%? 15%? b. What are the two projects' IRRs at these same costs of cap- ital? 3. Edelman Engineering is considering including two pieces of equipment, a truck and an overhead pul- ley system, in this year's capital budget. The pro- jects are independent. The cash outlay for the truck is $17,100 and that for the pulley system is $22,430. The firm's cost of capital is 14%. After-tax cash flows, including depreciation, are as follows: Year Truck Pulley CF1 = 20000000 CF2 = 10000000 CF3 = 6000000 I/YR = 10; NPV = $15,954,170. Change I/YR = 10 to I/YR = 5; NPV = $18,300,939. Change I/YR = 5 to I/YR = 15; NPV = $13,897,838. b. Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 43.97%. The IRR is independent of the WACC, so IRR doesn't change when the WACC changes. Using the data for Project B, enter the cash flows into a financial calculator and solve for IRRB = 82.03%. Again, the IRR is independent of the WACC, so IRR doesn't change when the WACC changes. Truck: NPV = -$17,100 + $5,100(PVIFA14%,5) = -$17,100 + $5,100(3.4331) = -$17,100 + $17,509 = $409. (Accept) Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 14, and then solve for NPV = $409. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 14.99% H 15%. MIRR: PV Costs = $17,100 Financial calculator: Obtain the FVA by inputting 1 $5,100 $7,500 N = 5, I/YR = 14, PV = 0, PMT = 5100, and 2 5,100 7,500 then solve for FV = $33,712. The MIRR can be 3 5,100 7,500 obtained by inputting N = 5, PV = -17100, PMT 4 5,100 7,500 = 0, FV = 33712, and then solving for I/YR = 5 5,100 7,500 14.54%. Calculate the IRR, the NPV, and the MIRR for each pro- ject, and indicate the cor- Pulley: rect accept-reject decision NPV = -$22,430 + $7,500(3.4331) = -$22,430 + for each. 4. Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is ex- pected to produce cash flows of $7,400 per year for 5 years. Calculate the $25,748 = $3,318. (Accept) Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 14, and then solve for NPV = $3,318. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 20%. MIRR: PV Costs = $22,430. Financial calculator: Obtain the FVA by inputting N = 5, I/YR = 14, PV = 0, PMT = 7500, and then solve for FV = $49,576. The MIRR can be obtained by inputting N = 5, PV = -22430, PMT = 0, FV = 49576, and then solving for I/YR = 17.19%. Project S Inputs 5 12 3000 0 Output= -10,814.33 NPVS = $10,814.33 - $10,000 = $814.33. Project L Inputs 5 12 7400 0 Output = -26,675.34 two projects' NPVs, IRRs, MIRRs, and PIs, assuming a cost of capital of 12%. Which project would be selected, assuming they are mutually exclusive, us- ing each ranking method? Which should actually be selected? 5. Your company is consider- ing two mutually exclusive NPVL = $26,675.34 - $25,000 = $1,675.34. Financial calculator solution, IRR: Input CF0 = -10000, CF1 = 3000, Nj = 5, IRRS = ? IRRS = 15.24%. Input CF0 = -25000, CF1 = 7400, Nj = 5, IRRL = ? IRRL = 14.67%. Financial calculator solution, MIRR: Project S Inputs 5 12 0 3000 Output= -19,058.54 PV costsS = $10,000. FV inflowsS = $19,058.54. Inputs 5 -10000 0 19058.54 Output= 13.77 MIRRS = 13.77%. Project L Inputs 5 12 0 7400 Output =-47,011.07 PV costsL = $25,000. FV inflowsL = $47,011.07. Inputs 5 -25000 0 47011.07 Output = 13.46 MIRRL = 13.46%. PIS = = 1.081. PIL = = 1.067. Thus, NPVL > NPVS, IRRS > IRRL, MIRRS > MIRRL, and PIS > PIL. The scale difference between Projects S and L results in the IRR, MIRR, and PI favoring S over L. However, NPV favors Project L; thus, L adds more value to the firm so L should be chosen. Because both projects are the same size you can just calculate each project's MIRR and projects, X and Y, whose costs and cash flows are shown below: Year X Y 0 $5,000 $5,000 1 1,000 4,500 2 1,500 1,500 3 2,000 1,000 4 4,000 500 The projects are equally risky, and their cost of capital is 12%. You must make a recommendation, and you must base it on the modified IRR (MIRR). Which project has the higher MIRR? 6. After discovering a new gold vein in the Colorado mountains, CTC Mining Corporation must decide whether to go ahead and develop the deposit. The most cost-effective method of mining gold is sulfuric acid extraction, a process that could result in environmental damage. Before proceeding with the extraction, CTC must spend $900,000 for new mining equipment and pay $165,000 for its installa- tion. The gold mined will net the firm an estimat- choose the project with the higher MIRR. (Re- member, MIRR gives conflicting results from NPV when there are scale differences between the projects.) 17.49% = MIRRX $5,000 = $9,529/(1 + MIRRX)4. 18.39% = MIRRY $1,000 = $1,636.37/(1 + MIRRY)4. Thus, since MIRRY > MIRRX, Project Y should be chosen. Alternative step: You could calculate NPVs, see that Project X has the higher NPV, and just calculate MIRRX. NPVX = $1,054.28 and NPVY = $1,243.19. a.Purchase price $ 900,000 Installation 165,000 Initial outlay $1,065,000 CF0 = -1065000; CF1-5 = 350000; I/YR = 14; NPV = ? NPV = $136,578; IRR = 19.22%. b. Ignoring environmental concerns, the project should be undertaken because its NPV is posi- tive and its IRR is greater than the firm's cost of capital. c. Environmental effects could be added by esti- mating penalties or any other cash outflows that might be imposed on the firm to help return the land to its previous state (if possible). These out- flows could be so large as to cause the project to ed $350,000 each year for the 5-year life of the vein. CTC's cost of capital is 14%. For the purposes of this problem, assume that the cash inflows occur at the end of the year. a. What are the project's NPV and IRR? b. Should this project be undertaken if environmen- tal impacts were not a con- sideration? c. How should environ- mental effects be consid- ered when evaluating this, or any other, project? How might these concepts af- fect the decision in part b? 7. Cummings Products is considering two mutual- ly exclusive investments whose expected net cash flows are as follows: EXPECTED NET CASH FLOWS Year Project A Pro- ject B 0 $400 $650 1 528 210 2 219 210 3 150 210 4 1,100 210 5 820 210 6 990 210 have a negative NPV—in which case the project should not be undertaken. a. graph npv on y axis, cost of capital on x axis. b. IRRA = 20.7%; IRRB = 25.8%. c. At r = 10%, Project A has the greater NPV, specifically $478.83 as compared to Project B's NPV of $372.37. Thus, Project A would be se- lected. At r = 17%, Project B has an NPV of $173.70 which is higher than Project A's NPV of $133.76. Thus, choose Project B if r = 17%. d. Here is the MIRR for Project A when r = 10%: PV costs = $400 + $528/(1.10)1 + $219/(1.10)2 + $150/(1.10)3 + $325/(1.10)7 = $1,340.47 7 325 210 a. Construct NPV profiles for Projects A and B. b. What is each project's IRR? c. If each project's cost of capital were 10%, which project, if either, should be selected? If the cost of capital were 17%, what would be the proper choice? d. What is each project's MIRR at the cost of capi- tal of 10%? At 17%? (Hint: Consider Period 7 as the end of Project B's life.) e. What is the crossover rate, and what is its signif- icance? TV inflows = $1,100(1.10)3 + $820(1.10)2 + $990(1.10)1 = $3,545.30. Now, MIRR is that discount rate which forces the PV of $3,545.30 in 7 years to equal $1,340.47: $1,340.47 = $3,545.30/(1 + MIRR)7 MIRRA = 14.91%. Here is the MIRR for Project B when r = 10%: PV costs = 600. TV of inflows: Financial calculator settings are N = 7, I/YR = 10, PV = 0, PMT = 210, and solve for FV = -1992.3059. Similarly, $650 = $1,992.31/(1 + MIRR)7 MIRRB = 17.35%. At r = 17%, MIRRA = 18.76%. MIRRB = 21.03%. e. To find the crossover rate, construct a Project which is the difference in the two projects' cash flows: Year Project = CFA - CFB 0 $250 1 738 2 429 3 360 4 890 5 610 6 780 7 535 = Crossover rate = 14.76%. 8. Your division is consider- ing two investment pro- jects, each of which re- quires an up-front expen- diture of $25 million. You estimate that the cost of capital is 10% and that the investments will produce the following after-tax cash flows (in millions of dol- lars): a. What is the regular pay- back period for each of the projects? Projects A and B are mutually exclusive, thus, only one of the projects can be chosen. As long as the cost of capital is greater than the crossover rate, both the NPV and IRR methods will lead to the same project selection. However, if the cost of capital is less than the crossover rate the two methods lead to different project se- lections—a conflict exists. When a conflict exists the NPV method must be used. Because of the sign changes and the size of the cash flows, Project has multiple IRRs. Thus, the IRR function for some calculators will not work (it will work, however, on a BAII Plus). The HP can be "tricked" into giving the roots by selecting an initial guess near one of the roots. After you have keyed Project Delta's cash flows into the CFj register of an HP-10B, you will see an "Er- ror-Soln" message. Now enter 10 STO IRR/YR and the 14.76% IRR is found. Then enter 100 STO IRR/YR to obtain IRR = 246.02%. Similarly, Excel can also be used. Payback A (cash flows in thousands): Annual Period Cash Flows Cumulative 0 ($25,000) ($25,000) 1 5,000 (20,000) 2 10,000 (10,000) 3 15,000 5,000 4 20,000 25,000 PaybackA = 2 + $10,000/$15,000 = 2.67 years. Payback B (cash flows in thousands): Annual Period Cash Flows Cumulative 0 ($25,000) ($25,000) 1 20,000 (5,000) 2 10,000 5,000 3 8,000 13,000 b. What is the discounted payback period for each of the projects? c. If the two projects are in- dependent and the cost of capital is 10%, which pro- ject or projects should the firm undertake? d. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm un- dertake? e. If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake? f. What is the crossover rate? g. If the cost of capital is 10%, what is the mod- ified IRR (MIRR) of each project? Year Project A Project B 1 5 20 2 10 10 3 15 8 4 20 6 4 6,000 19,000 PaybackB = 1 + $5,000/$10,000 = 1.50 years. b. Discounted Payback A (cash flows in thou- sands): Annual per. Discounted @10% Cash Flows Cash Flows Cumulative 0 ($25,000) ($25,000.00) ($25,000.00) 1 5,000 4,545.45 (20,454.55) 2 10,000 8,264.46 (12,190.09) 3 15,000 11,269.72 (920.37) 4 20,000 13,660.27 12,739.90 Discounted PaybackA = 3 + $920.37/$13,660.27 = 3.07 years. Discounted Payback B (cash flows in thou- sands): Annual per. Discounted @10% Cash Flows Cash Flows Cumulative 0 ($25,000) ($25,000.00) ($25,000.00) 1 20,000 18,181.82 (6,818.18) 2 10,000 8,264.46 1,446.28 3 8,000 6,010.52 7,456.80 4 6,000 4,098.08 11,554.88 Discounted PaybackB = 1 + $6,818.18/$8,264.46 = 1.825 years. c.NPVA = $12,739,908; IRRA = 27.27%. NPVB = $11,554,880; IRRB = 36.15%. Both projects have positive NPVs, so both pro- jects should be undertaken. d. At a discount rate of 5%, NPVA = $18,243,813. At a discount rate of 5%, NPVB = $14,964,829. At a discount rate of 5%, Project A has the high- er NPV; consequently, it should be accepted. e. At a discount rate of 15%, NPVA = $8,207,071. At a discount rate of 15%, NPVB = $8,643,390. At a discount rate of 15%, Project B has the higher NPV; consequently, it should be accept- ed. f. Project = Year CFA - CFB 0 $ 0 1 (15) 2 0 3 7 4 14 IRR = Crossover rate = 13.5254% H 13.53%. g. Use 3 steps to calculate MIRRA @ r = 10%: Step 1: Calculate the NPV of the uneven cash inflow stream, so its FV can then be calculated. With a financial calculator, enter the cash inflow stream into the cash flow registers being sure to enter 0 for CF0, then enter I/YR = 10, and solve for NPV = $37,739,908. Step 2: Calculate the FV of the cash inflow stream as follows: Enter N = 4, I/YR = 10, PV = -37739908, and PMT = 0 to solve for FV = $55,255,000. Step 3: Calculate MIRRA as follows: Enter N = 4, PV = -25000000, PMT = 0, and FV 9. Talbot Industries is con- sidering launching a new product. The new manufac- turing equipment will cost $17 million, and produc- tion and sales will require an initial $5 million in- vestment in net operating working capital. The com- pany's tax rate is 40%. a. What is the initial invest- ment outlay? b. The company spent and = 55255000 to solve for I/YR = 21.93%. Use 3 steps to calculate MIRRB @ r = 10%: Step 1: Calculate the NPV of the uneven cash inflow stream, so its FV can then be calculated. With a financial calculator, enter the cash inflow stream into the cash flow registers being sure to enter 0 for CF0, then enter I/YR = 10, and solve for NPV = $36,554,880. Step 2: Calculate the FV of the cash flow stream as follows: Enter N = 4, I/YR = 10, PV = -36554880, and PMT = 0 to solve for FV = $53,520,000. Step 3: Calculate MIRRB as follows: Enter N = 4, PV = -25000000, PMT = 0, and FV = 53520000 to solve for I/YR = 20.96%. According to the MIRR approach, if the 2 pro- jects were mutually exclusive, Project A would be chosen because it has the higher MIRR. This is consistent with the NPV approach. a. Equipment $ 17,000,000 NWC Investment 5,000,000 Initial investment outlay $22,000,000 b. No, last year's $150,000 expenditure is con- sidered a sunk cost and does not represent an incremental cash flow. Hence, it should not be included in the analysis. c. The potential sale of the building represents an opportunity cost of conducting the project in that building. Therefore, the possible after-tax sale price must be charged against the project as a cost. expensed $150,000 on re- search related to the new product last year. Would this change your answer? Explain. c. Rather than build a new manufacturing facility, the company plans to install the equipment in a building it owns but is not now us- ing. The building could be sold for $1.5 million after taxes and real estate commissions. How would this affect your answer? 10. The financial staff of Cairn Communications has iden- tified the following infor- mation for the first year of the roll-out of its new proposed ser- vice: Projected sales $18 million Operating costs (not in- cluding depreciation) $ 9 million Depreciation $ 4 million Interest expense $ 3 mil- lion The company faces a 40% tax rate. What is the pro- ject's operating cash flow for the first year (t = 1)? Operating Cash Flows: t = 1 Sales revenues $18,000,000 Operating costs 9,000,000 Depreciation 4,000,000 Operating inc. before taxes $5,000,000 Taxes (40%) 2,000,000 Operating income after taxes $3,000,000 Add back depreciation 4,000,000 Operating cash flow $ 7,000,000 11. Allen Air Lines must liq- uidate some equipment that is being replaced. The equipment originally cost $12 million, of which 75% has been depreciated. The used equipment can be sold today for $4 million, and its tax rate is 40%. What is the equipment's af- ter-tax net salvage value? 12. Although the Chen Com- pany's milling machine is old, it is still in rela- tively good working order and would last for anoth- er 10 years. It is inefficient compared to modern stan- dards, though, and so the com- pany is considering re- placing it. The new milling machine, at a cost of $110,000 delivered and in- stalled, would also last for 10 years and would pro- duce after-tax cash flows (labor savings and de- preciation tax savings) of $19,000 per year. It would have zero salvage value at the end of its life. The firm's WACC is 10%, and its marginal tax rate is 35%. Should Chen buy the new machine? Equipment's original cost $12,000,000 Depreciation (80%) 9,000,000 Book value $ 3,000,000 Gain on sale = $4,000,000 - $3,000,000 = $1,000,000. Tax on gain = $1,000,000(0.4) = $400,000. AT net salvage value = $4,000,000 - $400,000 = $3,600,000. Cash outflow = $40,000. Increase in annual after-tax cash flows: CF = $9,000. Place the cash flows on a time line: 0 1 2 10 | 10 | | • • • | -110,000 19,000 19,000 19,000 With a financial calculator, input the appropriate cash flows into the cash flow register, input I/YR = 10, and then solve for NPV = $6,746.78. Thus, Chen should purchase the new machine. 13. The president of the com- pany you work for has asked you to evaluate the proposed acquisition of a new chromatograph for a. The net cost is $89,000: Price ($70,000) Modification (15,000) Change in NWC (4,000) the firm's R&D department. ($89,000) The equipment's basic price is $70,000, and it would cost anoth- er $15,000 to modify it for special use by your firm. The chromatograph, which falls into the MACRS 3-year class, would be sold after 3 years for $30,000. The MACRS rates for the b. The operating cash flows follow: Year 1 Year 2 Year 3 After-tax savings $15,000 $15,000 $15,000 Depreciation shield 11,332 15,113 5,035 Net cash flow $26,332 $30,113 $20,035 Notes: 1. The after-tax cost savings is $25,000(1 - T) = first three years are 0.3333, $25,000(0.6) = $15,000. 0.4445, and 0.1481. Use of the equipment would re- quire an increase in net working capital (spare parts inventory) of $4,000. The machine would have no effect on revenues, but it is expected to save the firm $25,000 per year in before-tax operating costs, mainly labor. The firm's marginal feder- al-plus-state tax rate is 40%. a. What is the Year-0 net cash flow? b. What are the net operat- ing cash flows in Years 1, 2, and 3? 2. The depreciation expense in each year is the depreciable basis, $85,000, times the MACRS allowance percentage of 0.3333, 0.4445, and 0.1481 for Years 1, 2 and 3, respectively. Depre- ciation expense in Years 1, 2, and 3 is $28,331, $37,783, and $12.589. The depreciation shield is calculated as the tax rate (40%) times the depreciation expense in each year. c.The additional end-of-project cash flow is $24,519: Salvage value $30,000 Tax on SV* (9,481) Return of NWC 4,000 $24,519 *Tax on SV = ($30,000 - $6,299)(0.4) = $9,481. Note that the remaining BV in Year 4 = $85,000(0.0741) = $6299. c. What is the additional (nonoperating) cash flow in Year 3? d. If the project's cost of capital is 10%, should the chromatograph be pur- chased? 14. Shao Industries is con- sidering a proposed pro- ject for its capital budget. The company estimates the project's NPV is $12 million. This estimate as- sumes that the economy and market conditions will be average over the next few d. The project has an NPV of -$6,700. Thus, it should not be accepted. Year Net Cash Flow 0 ($89,000) 1 26,332 2 30,113 3 44,555 With a financial calculator, input the following: CF0 = -89000, CF1 = 26332, CF2 = 30113, CF3 = 44555, and I/YR = 10 to solve for NPV = -$6,700.18. E(NPV) = 0.05(-$70) + 0.20(-$25) + 0.50($12) + 0.20($20) + 0.05($30) = -$3.5 + -$5.0 + $6.0 + $4.0 + $1.5 = $3.0 million. ÃNPV = [0.05(-$70 - $3)^2 + 0.20(-$25 - $3)^2 + 0.50($12 - $3^)2 + 0.20($20 - $3)^2 + 0.05($30 - $3)^2]0.5 = $23.622 million. years. The company's CFO, CVNPV = = 7.874. however, forecasts there is only a 50% chance that the economy will be aver- age. Recognizing this un- certainty, she has also per- formed the following sce- nario analysis: Scenario, Probability, NPV Recession, 0.05, $70 mil- lion Below average, 0.20, 25 million Average, 0.50, 12 million Above average, 0.20, 20 million Boom, 0.05, 30 million What is the project's ex- pected NPV, its standard deviation, and its coeffi- cient of variation? 15. The Bartram-Pulley Com- pany (BPC) must decide between two mutually ex- clusive investment pro- jects. Each project costs $6,750 and has an expect- ed life of 3 years. Annual net cash flows from each project begin 1 year af- ter the initial investment is made and have the fol- lowing probability distribu- tions: Project A Probability, Net Cash Flows 0.2, $6,000 0.6, 6,750 0.2, 7,500 Project B 0.2 $ 0 0.6 6,750 0.2 18,000 BPC has decided to evalu- ate the riskier project at a a. Expected annual cash flows: Project A: Probability * Cash Flow = Est Cash Flow 0.2 $6,000 $1,200 0.6 6,750 4,050 0.2 7,500 1,500 Expected annual cash flow = $6,750 Project B: Probability * Cash Flow = Est Cash Flow 0.2 $ 0 $ 0 0.6 6,750 4,050 0.2 18,000 3,600 Expected annual cash flow = $7,650 Coefficient of variation:CV= SD/Expected Value= SD NPV/Expected NPV Project A: Square root of (-750)^2 (.2) + (0)^2(.6)+(750)^2(.2)= 474.34 Project B: Square rot of (-7650)^2(.2)+ (-900)^2(.6) + (10350)^2(.2)=5797.84 CVA = $474.34/$6,750 = 0.0703. CVB = $5,797.84/$7,650 = 0.7579. 12% rate and the less risky b. Project B is the riskier project because it has project at a 10% rate. a. What is the expected val- ue of the annual net cash flows from each project? What is the coefficient of variation (CV)? (Hint: BÃ = $5,798 and CVB = 0.76.) b. What is the risk-adjusted NPV of each project? c. If it were known that Pro- ject B is negatively corre- lated with other cash flows of the firm whereas Pro- ject A is positively corre- lated, how would this affect the decision? If Project B's cash flows were negative- ly correlated with gross domestic product (GDP), would that influence your assessment of its risk? 16. The Yoran Yacht Compa- ny (YYC), a prominent sailboat builder in New- port, may design a new 30-foot sailboat based on the "winged" keels first in- troduced on the 12-meter yachts that raced for the America's Cup. First, YYC would have to the greater variability in its probable cash flows, whether measured by the standard deviation or the coefficient of variation. Hence, Project B is evaluated at the 12 percent cost of capital, while Project A requires only a 10 percent cost of capital. Project A: With a financial calculator, input the appropriate cash flows into the cash flow regis- ter, input I/YR = 10, and then solve for NPV = $10,036.25. Project B: With a financial calculator, input the appropriate cash flows into the cash flow reg- ister, input I = 12, and then solve for NPV = $11,624.01. Project B has the higher NPV; therefore, the firm should accept Project B. c. The portfolio effects from Project B would tend to make it less risky than otherwise. This would tend to reinforce the decision to accept Project B. Again, if Project B were negatively correlated with the GDP (Project B is profitable when the economy is down), then it is less risky and Project B's acceptance is reinforced. a. Using a financial calculator, input the fol- lowing: CF0 = -10000, CF1 = -500000, CF2 = -1000000, = 3000000, and I/YR = 12 to solve for NPV = $881,718.29 =$881,718. or, (3 mill/1.12^3) - (1 mill/1.12^2) - (500000/1.12) -10,000 The other NPVs were determined in the same manner. If the project is of average risk, it should be accepted because the expected NPV of the invest $10,000 at t = 0 for the design and mod- el tank testing of the new boat. YYC's managers be- lieve there is a 60% proba- bility that this phase will be successful and the project will continue. If Stage 1 is not successful, the project will be abandoned with zero sal- vage value. The next stage, if undertak- en, would consist of mak- ing the molds and produc- ing two prototype boats. This would cost $500,000 at t = 1. If the boats test well, YYC would go into production. If they do not, the molds and prototypes could be sold for $100,000. The managers estimate the probability is 80% that the boats will pass testing and that Stage 3 will be under- taken. Stage 3 consists of con- verting an unused produc- tion line to produce the new design. This would cost $1 million at t = 2. If the economy is strong at this point, the net value of sales would be $3 million; if the economy is weak, the net total project is positive. b.ÃN2PV = 0.24($881,718 - $117,779)2 + 0.24(-$185,952 - $117,779)2+ 0.12(-$376,709 - $117,779)2 + 0.4(-$10,000 - $117,779)2= 198,078,470,853. ÃNPV = $445,060. CVNPV = = 3.78. Since the CV is 3.78 for this project, while the firm's average project has a CV of 1.0 to 2.0, this project is of high risk. value would be $1.5 mil- lion. Both net values occur at t = 3, and each state of the economy has a probabili- ty of 0.5.YYC's corporate cost of capital is 12%. a. Assume this project has average risk. Construct a decision tree and deter- mine the project's expect- ed NPV. b. Find the project's stan- dard deviation of NPV and coefficient of variation of NPV. If YYC's average pro- ject had a CV of between 1.0 and 2.0, would this pro- ject be of high, low, or av- erage stand-alone risk? 17. Kim Hotels is interested in developing a new ho- tel in Seoul. The compa- ny estimates that the ho- tel would require an ini- tial investment of $20 mil- lion. Kim expects the hotel will produce positive cash flows of $3 million a year at the end of each of the next a. year 0 1 2 20 -20 3 3 3 NPV= 1.074 million b. wait one year tax imposed 50% probability 0 1 2 3 21 0 -20 2.2 2.2 2.2 20 years. The project's cost PV at year 1 15.45 of capital is 13%. a. What is the project's net present value? tax not imposed 50% probability 0 1 2 3 21 0 -20 3.8 3.8 3.8 Pv at year 1 26.69 b. Kim expects the cash flows to be $3 million a year, but it recognizes that the cash flows could actu- ally be much higher or low- er, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a 50% chance that the tax will be imposed, in which case the yearly cash flows will be only $2.2 million. At the same time, there is a 50% chance that the tax will not be imposed, in which case the yearly cash flows will be $3.8 million. Kim is de- ciding whether to proceed with the hotel today or to wait a year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $20 million. Assume that all cash flows are dis- counted at 13%. Use deci- sion-tree analysis to deter- mine whether Kim should proceed with the project today or wait a year before deciding. 18. The Karns Oil Company is deciding whether to drill Tax imposed: NPV @ Yr. 1 = (-20+15.45)/(1.13) = -4.027 Tax not imposed: NPV @ Yr = (-20 +26.69)/ (1.13) = 5.920 Expected NPV = .5(-4.027) + .5(5.920) = 0.947 Note though, that if the tax is imposed, the NPV of the project is negative and therefore would not be undertaken. The NPV if you use the op- tion to wait one year is evaluated as... 0.5($0) + (0.5)($ 5.920) = $2.96 million. Since the NPV of waiting one year is greater than going ahead and proceeding with the pro- ject today, it makes sense to wait. a. year 0 1 2 3 4 -8 4 4 4 4 for oil on a tract of land the company owns. The com- pany estimates the project would cost $8 million to- day. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly con- fident about its cashflow forecast, in 2 years it will have more information about the local geology and about the price of oil. Karns estimates that if it waits 2 years then the pro- ject would cost $9 mil- lion. Moreover, if it waits 2 years, then there is a 90% chance that the net cash flows would be $4.2 million a year for 4 years and a 10% chance that they would be $2.2 mil- lion a year for 4 years. As- sume all cash flows are discounted at 10%. a. If the company chooses to drill today, what is the project's net present val- ue? b. Using decision-tree analysis, does it make sense to wait 2 years be- NPV= 4.6795 Million b. Wait 2 years 10% Prob 0 1 2 3 4 5 6 0 0 -9 2.2 2.2 2.2 2.2 PV at year 2 6.974 90% Prob 0 1 2 3 4 5 6 0 0 -9 4.2 4.2 4.2 4.2 PV at year 2 13.313 Low CF scenario: NPV = (-9 + 6.974)/(1.1)2 = -$1.674 High CF scenario: NPV = (-9 + 13.313)/(1.1)2 = $3.564 Expected NPV = .1(-1.674) + .9(3.564) = 3.040 If the cash flows are only $2.2 million, the NPV of the project is negative and, thus, would not be undertaken. The NPV value using the option to wait two years is evaluated as 0.10($0) + 0.90($3.564) = $3.208 million. Since the NPV of waiting two years is less than going ahead and proceeding with the project today, it makes sense to drill today. fore deciding whether to drill? [Show Less]