202E13

P13-16Problem 13-16Basic Net Present Value AnalysisGiven:Renfree Mines, Inc., owns the mining rights to a large tract of land in a mountainous area. Thetract contains a mineral deposit that the company believes might be commercially attractive tomine and sell. An engineering and cost analysis has been made, and it is expected that thefollowing cash flows would be associated with opening and operating a mine in the area:Cost of equipment required$850,000$804,920.93Net annual cash receipts$230,000***Cost (NPV = 0)Working capital required$100,000$804,920.93Cost of road repairs in three years$60,000Salvage value of equipment in five years$200,000***Receipts from sales of ore, less out-of-pocket costs for salaries, utilities, insurance,and so forth.It is estimated that the mineral deposit would be exhausted after five years of mining. At thatpoint, the working capital would be released for reinvestment elsewhere. The Company'srequired rate of return is 14%.Required:Determine the net present value of the proposed mining project. Should the project be accepted?Explain.Ignore income taxes.0.12246555Timing ofCash14%PV ofTiming ofYearly Cash14%PV ofCashFlowPV TableCashCashFlowPV TableCashRelevant Items:FlowsAmountsFactorFlowsFlowsAmountsFactorFlowsCost of equipment requiredNow($850,000)1.000000($850,000.00)Now($950,000.00)1.000000($950,000.00)Working capital requiredNow($100,000)1.000000($100,000.00)End of Y1$230,000.000.877193$201,754.39Net annual cash receiptsEnd of Ys 1-5$230,0003.433081$789,608.62End of Y2$230,000.000.769468$176,977.53Cost of road repairs in three yearsEnd of Year 3($60,000)0.674972($40,498.29)End of Y3$170,000.000.674972$114,745.16Salvage value of equipment in 5 yearsEnd of Year 5$200,0000.519369$103,873.73End of Y4$230,000.000.592080$136,178.46Working capital releasedEnd of Year 5$100,0000.519369$51,936.87End of Y5$530,000.000.519369$275,265.39Net Present Value($45,079.07)3.433081($45,079.07)3.433081No, the project should not be accepted; it has a negative net present value. This means that the12.246555%IRRrate of return on the investment is less than the company's required rate of return of 14%($39,543.04)Note: Wrong NPVExcel formula is wrong($45,079.07)Corrected NPV

E13-10Exercise 13-10Internal Rate of Return and Net Present ValueGiven:Scalia's Cleaning Service is investigating the purchase of an ultrasound machine for cleaning windowblinds. The machine would cost $136,700, including invoice cost, freight, and training of employeesto operate it. Scalia's has estimated that the new machine would increase the company's cash flows,net of expenses, by $25,000 per year. The machine would have a 14-year useful life with no expectedsalvage value.Required:Ignore income taxes1.Compute the machine's internal rate of return to the nearest whole percent.IRR = the interest rate that yields a NPV = 0Annual cash inflows X Table Value ( Y%, 14 years) from PV of an Annuity Table - Cost = 0$25,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table - $136,700 = 0$25,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table = $136,700Table Value (Y%, 14 years) from PV of an Annuity Table = $136,700/$25,0005.468(pg. 678)From PV of an Annuity Table, scanning along the row for 14 periods yields 5.468 for an IRR equal to 16%2.Compute the machine's net present value. Use a discount rate of 16% and the format shown inExhibit 14-5. Why do you have a zero net present value?Amount of16%PresentItemYear(s)Cash flowTable FactorValueInitial InvestmentNow($136,700)1.00000($136,700)Net annual cash inflows1-14$25,0005.468$136,700Net present value$0The NPV is equal to zero because the discount rate used (16%) is also the IRR.3.Suppose that the new machine would increase the company's annual cash flows, net of expenses,by only $20,000 per year. Under these conditions, compute the internal rate of return to the nearestwhole percent.IRR = the interest rate that yields a NPV = 0Annual cash inflows X Table Value ( Y%, 14 years) from PV of an Annuity Table - Cost = 0$20,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table - $136,700 = 0$20,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table = $136,700Table Value (Y%, 14 years) from PV of an Annuity Table = $136,700/$20,0006.835From PV of an Annuity Table, scanning along the row for 14 periods yields:(136,700)(136,700)20,00025,000Interpolation20,00025,00012%6.6286.62816820,00025,000X?%6.8356.835000(0.206832)20,00025,0000.0111%6.9826.981865(0.353697)20,00025,00020,00025,000X=0.20683220,00025,0000.010.353697001120,00025,00020,00025,0000.353697 (X) = (0.01)(.206832)20,00025,0000.353697 (X) =0.0020683220,00025,000X =0.0058477120,00025,000X =0.584771%20,00025,00020,00025,000?% = 12% - 0.5848% =11.4152%Rounded to nearest whole % = 11%IRR11.405%15.998%NPV0.0000.000

E13-3Exercise 13-3Uncertain Future Cash FlowsGiven:Union Bay Plastics is investigating the purchase of automated equipment that would save$100,000 each year in direct labor and inventory carrying costs. This equipment costs $750,000and is expected to have a 10-year useful life with no salvage value. The company requires aminimum 15% rate of return on all equipment purchases. This equipment would provideintangible benefits such as greater flexibility and higher-quality output that are difficult toestimate and yet are quite significant.Required:1.What dollar value per year would the intangible benefits have to be worth in order to makethe equipment an acceptable investment? (Ignore income taxes).If Union Bay Plastics uses a discount rate of 15% to calculate the NPV and the resulting NPVequals zero, then the investment would be earning a return of exactly 15%; the IRR = 15%.Therefore:Annual cash inflows X Table Value (15%, 10 years) from PV of an Annuity Table - Cost = 0(Annual cash inflows X 5.019) - $750,000 = 05.019 (Annual cash inflows) = $750,000Annual cash inflows = $750,000/5.019Annual cash inflows =$149,432.16$149,439.05Thus the dollar value per year of the intangible benefits must be worth at least:Annual cash inflows required$149,432.16$149,439.05Less known yearly savings100,000.00100,000.00Minimum yearly intangible benefits$49,432.16$49,439.05Proof($750,000.00)($750,000.00)$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05$149,432.16$149,439.05NPV =($34.57)$0.00IRR =14.998790%15.000000%

E13-7Exercise 13-7Payback Period and Simple Rate of ReturnGiven:The Heritage Amusement Park would like to construct a new ride called the Sonic Boom, whichthe park management feels would be very popular. The ride would cost $450,000 to construct,and it would have a 10% salvage value at the end of its 15-year useful life. The companyestimates that the following annual costs and revenues would be associated with the ride:Ticket revenues$250,000Less operating expenses:Maintenance$40,000Salaries90,000Depreciation27,000Insurance30,000Total Operating Expenses187,000Net Operating Income$63,000$945,000Required:Ignore income taxes1.Assume that the Heritage Amusement Park will not construct a new ride unless the rideprovides a payback period of six years or less. Does the Sonic Boom ride satisfy thisrequirement?Payback period =Investment Required / Net Uniform Annual Cash InflowNet Uniform Annual Cash InflowNet Operating Income$63,000Depreciation27,000Net Uniform Annual Cash Inflow$90,000Payback period =$450,000/$90,000Payback period =5.00yearsThe Sonic Boom has a payback less than the maximum 6-year limit.The Sonic Boom satisfies the payback criterion.2.Compute the simple accounting rate of return promised by the new ride. If Heritage AmusementPark requires a simple rate of return of at least 12%, does the Sonic Boom ride meet this($450,000)criterion?9000090000Simple accounting rate of return =AROR9000090000AROR =Annualized incremental NOI/Initial Investment Required9000090000AROR =$63,000/$450,0009000090000AROR =14.00%9000090000The Sonic Boom has an AROR greater than the minimum 12% requirement.90000The Sonic Boom satisfies the simple accounting rate or return criterion.90000900009000013500018.595%IRR

E13-5Exercise 13-5:Payback MethodGiven:The management of Weimar Inc., a civil engineering design company, is consideringan investment in a high-quality blueprint printer with the following cash flows:InvestmentCashCashYearOutflowInflow1$38,000$2,0002$6,000$4,0003$8,0004$9,0005$12,0006$10,0007$8,0008$6,0009$5,00010$5,000Required:1.Determine the payback period of the investment.InvestmentCashCashUnrecoveredYearOutflowInflowInvestment1($38,000)$2,000($36,000)2($6,000)$4,000($38,000)3$8,000($30,000)4$9,000($21,000)5*****$12,000($9,000)6*****$10,000$1,0007$8,000$9,0008$6,000$15,0009$5,000$20,00010$5,000$25,000Payback =50.905.9years2.Would the payback period be affected if the cash inflow in the last yearwas several times larger?Since the investment is recovered prior to the last year, the amountof the cash inflow in the last year has no effect on the payback period.

P13-17Problem 13-17Preference Ranking of Investment ProjectsGiven:Austin Company is investigating four different investment opportunities. Information on thefour projects under study is given below:Project Number1234Investment required($480,000)($360,000)($270,000)($450,000)($1,560,000)Present value of cash inflows (10%)567,270433,400336,140522,970Net present value$87,270$73,400$66,140$72,970Life of Project (in years)61263Internal Rate of Return16%14%18%19%Since the company's required rate of return is 10%, a 10% discount rate has been used tn theNPV calculations above. Limited funds are available for investment, so the company can notaccept all of the available projects.Required:1.Compute the project profitability index for each investment project.Project profitability index =NPV/Investment RequiredProject Number1234Net present value$87,270$73,400$66,140$72,970Investment required$480,000$360,000$270,000$450,000Project profitability index0.18181250.20388888890.2449629630.1621555556Present value of cash inflows (10%)/Investment Req.1.18181251.20388888891.2449629631.1621555556(Not in text)2.Rank the four projects according to preference, in terms of:Project Number1234a.NPV1243b.PPI3214c.IRR34213.Which ranking do you prefer? Why?Which ranking is best depends on the company's opportunities for reinvesting fundsas they are released from a project.IRR:The internal rate of return method assumes that any released funds are reinvestedat the internal rate of return.This means that funds released from project #4 would have to be reinvested at arate or return of 19%, but another project yielding such a high rate of return mightbe difficult to find.PPI:The project profitability index approach assumes that funds released from a projectare reinvested at a rate of return equal to the discount rate, which in this case is only10%. On balance, the PPI is generally regarded as the most dependable method ofranking competing projects.NPV:The net present value is inferior to the project profitability index as a ranking devicebecause it does not properly consider the amount of investment.For example, it ranks project #3 fourth because of its low NPV; yet this project isthe best in terms of the amount of cash inflow generated per dollar invested.

Fixed ExpensesTotal ExpensesTotal SalesBreak-even point: 400 persons, or $12,000 in salesBreak-even point: 400 persons, or $12,000 in salesBreak-even point: 400 persons, or $12,000 in sales

P13C-6Problem 13C-6Net Present Value Analysis Including Income TaxesGiven:The Crescent Drilling Company owns the drilling rights to several tracts of land on which natural gas has been found. The amount of gason some of the tracts is somewhat marginal, and the company is unsure whether it would be profitable to extract and sell the gas thatthese tracts contain. One such tract is tract 410, on which the following information has been gathered:Investment in equipment needed for extraction work$600,000Working capital investment needed$85,000Annual cash receipts from sale of gas, net of related cash operating expenses (before taxes)$110,000Cost of restoring the land at completion of extraction work$70,000The natural gas in tract 410 would be exhausted after 10 years of extraction work. The equipment would have a useful life of 15 years, butit could be sold for only 15% of its original cost when extraction was completed. For tax purposes, the company would depreciate theequipment over 10 years using straight-line depreciation and assuming zero salvage value. The tax rate is 30%, and the company's after-tax discount rate is 10%. The working capital would be released for use elsewhere at the completion of the project.Required:1.Compute the NPV of tract 410.Timing ofCashAfterCash10%PV ofCashFlowTaxFlowPV TableCashNormal Acctg. ApproachFlowsAmountsEffectAmountsFactorFlowsInvestment in equipmentNow($600,000)None($600,000)1.000000($600,000.00)Working capital requiredNow($85,000)None($85,000)1.000000($85,000.00)Net annual cash receiptsEnd of Ys 1-10$110,00070%$77,0006.144567$473,131.67Tax Savings (Depreciation tax shield)End of Ys 1-10$60,00030%$18,0006.144567$110,602.21Restoration ExpenseEnd of Year 10($70,000)70%($49,000)0.385543($18,891.62)Salvage value of equipment in 10 yearsEnd of Year 10$90,000None$90,0000.385543$34,698.90Tax Outflow from Salvage GainEnd of Year 10$90,00030%($27,000)0.385543($10,409.67)Working capital releasedEnd of Year 10$85,000None$85,0000.385543$32,771.18Net Present Value($63,097.34)Normal Finance ApproachYear 0 (Now)Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10Net annual cash receipts$110,000$110,000$110,000$110,000$110,000$110,000$110,000$110,000$110,000$110,000Less Depreciation Expense(60,000)(60,000)(60,000)(60,000)(60,000)(60,000)(60,000)(60,000)(60,000)(60,000)Less Restoration Expense(70,000)Taxable Salvage Gain90,000Income Before Taxes$50,000$50,000$50,000$50,000$50,000$50,000$50,000$50,000$50,000$70,000Less Income Taxes (30%)(15,000)(15,000)(15,000)(15,000)(15,000)(15,000)(15,000)(15,000)(15,000)(21,000)Net Income$35,000$35,000$35,000$35,000$35,000$35,000$35,000$35,000$35,000$49,000Add back depreciation60,00060,00060,00060,00060,00060,00060,00060,00060,00060,000Operating Cash Flow$95,000$95,000$95,000$95,000$95,000$95,000$95,000$95,000$95,000$109,000Working capital released85,000Cash Inflow$95,000$95,000$95,000$95,000$95,000$95,000$95,000$95,000$95,000$194,000Table Factor 10% (PV of $1 Table)0.9090910.8264460.7513150.6830130.6209210.5644740.5131580.4665070.4240980.385543PV of cash inflows$621,902.66$621,902.66$86,363.64$78,512.40$71,374.91$64,886.28$58,987.53$53,625.02$48,750.02$44,318.20$40,289.27$74,795.40Initial Investment in equipment(600,000.00)Initial Investment in Working Capital(85,000.00)Net Present Value($63,097.34)Net Present Value (Adj. Excel Formula)($63,097.34)2.Would you recommend that the investment project be undertaken?No, the investment project should not be undertaken. The NPV is negative.Calculation of Cash Inflow Y1FinanceAcctg.Net of TaxNet annual cash receipts$110,000$110,000$77,000Less Depreciation Expense(60,000)18,000Less Restoration ExpenseTaxable Salvage GainIncome Before Taxes$50,000Less Income Taxes (30%)(15,000)(15,000)Net Income$35,000Add back depreciation60,000Operating Cash Flow$95,000$95,000$95,000Calculation of Cash Inflow Y10FinanceAcctg.Net of TaxNet annual cash receipts$110,000$110,000$77,000Less Depreciation Expense(60,000)18,000Less Restoration Expense(70,000)(70,000)(49,000)Taxable Salvage Gain90,00090,00063,000Income Before Taxes$70,000Less Income Taxes (30%)(21,000)(21,000)Net Income$49,000Add back depreciation60,000Operating Cash Flow$109,000$109,000$109,000


P13-22Problem 13-22Net Present Value Analysis of a Lease or Buy DecisionGiven:Blinko Products wants an airplane for use by its corporate staff. The airplane that the company wishes to acquire, a Zephyr II, can be either purchased or leasedPurchase alternative.If the Zephyr II is purchased, then the costs incurred by the company would be as follows:Purchase cost of the plane$850,000Annual cost of servicing, licenses, and taxes$9,000Repairs:First 3 years (per year)$3,000Fourth year$5,000Fifth year$10,000The plane would be sold after 5 years. Based on current resale values, the company would be able to sell it for about one-half of its original cost at the end ofthe five-year period.Lease alternative.If the Zephyr II is leased, then the company would have to make an immediate deposit of $50,000 to cover any damage during use. The lease would run for fiveyears, a the end of which time the deposit would be refunded. The lease would require an annual rental payment of $200,000 (the first payment is due at the endof Year 1). As part of this lease cost, the manufacturer would provide all servicing and repairs, license the plane, and pay all taxes. At the end of five-years, theplane would revert to the manufacturer, as owner.Blinko Products' required rate of return is 18%Required: Ignore income taxes.1.Use the total-cost approach to determine the present value of the cash flows associated2.174273with each alternative.Timing ofAmount ofPV TablePV ofTiming ofAmount ofPV TablePV ofPurchase alternative.Cash FlowsCash FlowsFactor (18%)Cash FlowCash FlowsCash FlowsFactor (18%)Cash FlowPurchase cost of the planeNow($850,000)1.000000($850,000.00)Now($850,000)1.000000($850,000.00)Annual cost of servicing, etc.End of Ys 1-5($9,000)3.127171(28,144.54)End of Year 1(12,000)0.847458(10,169.49)Repairs:End of Year 2(12,000)0.718184(8,618.21)First Three YearsEnd of Ys 1-3($3,000)2.174273(6,522.82)End of Year 3(12,000)0.608631(7,303.57)Fourth YearEnd of Year 4($5,000)0.515789(2,578.94)End of Year 4(14,000)0.515789(7,221.04)Fifth YearEnd of Year 5($10,000)0.437109(4,371.09)End of Year 5406,0000.437109177,466.34Resale value of the planeEnd of Year 5$425,0000.437109185,771.42($705,845.98)($705,845.98)3.127171($705,845.98)Timing ofAmount ofPV TablePV ofTiming ofAmount ofPV TablePV ofLease alternative.Cash FlowsCash FlowsFactor (18%)Cash FlowCash FlowsCash FlowsFactor (18%)Cash FlowDamage DepositNow($50,000)1.000000($50,000.00)Now($50,000)1.000000($50,000.00)Annual Lease PaymentsEnd of Ys 1-5($200,000)3.127171(625,434.20)End of Year 1(200,000)0.847458(169,491.53)Refund of DepositEnd of Year 5$50,0000.43710921,855.46End of Year 2(200,000)0.718184(143,636.89)($653,578.74)End of Year 3(200,000)0.608631(121,726.17)End of Year 4(200,000)0.515789(103,157.78)End of Year 5(150,000)0.437109(65,566.38)($653,578.74)($653,578.74)Net present value in favor of the leasing option$52,267.23$52,267.23$52,267.232.Which alternative would you recommend that the company accept? Why?The company should accept the leasing alternative. The present value of the cash outflows is less negative under the leasing option.


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202E13