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Problem 13-16 Basic Net Present Value Analysis Given: Renfree Mines, Inc., owns the mining rights to a large tract of land in a mountainous area. The tract contains a mineral deposit that the company believes might be commercially attractive to mine and sell. An engineering and cost analysis has been made, and it is expected that the following cash flows would be associated with opening and operating a mine in the area: Cost of equipment required $850,000 $804,920.93 Net annual cash receipts $230,000 *** Cost (NPV = 0) Working capital required $100,000 $804,920.93 Cost of road repairs in three years $60,000 Salvage 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 that point, the working capital would be released for reinvestment elsewhere. The Company's required rate of return is 14%. Required: Determine the net present value of the proposed mining project. Should the project be accepted? Ignore income taxes. Timing of Cash 14% PV of Cash Flow PV Table Cash Relevant Items: Flows Amounts Factor Flows Cost of equipment required Now ($850,000) 1.000000 ($850,000.00) Working capital required Now ($100,000) 1.000000 ($100,000.00) Net annual cash receipts End of Ys 1-5 $230,000 3.433081 $789,608.62 Cost of road repairs in three years End of Year 3 ($60,000) 0.674972 ($40,498.29) Salvage value of equipment in 5 years End of Year 5 $200,000 0.519369 $103,873.73 Working capital released End of Year 5 $100,000 0.519369 $51,936.87 Net Present Value ($45,079.07) No, the project should not be accepted; it has a negative net present value. This means that the rate of return on the investment is less than the company's required rate of return of 14% Explain. 0.12246555 Timing of Yearly Cash 14% PV of Cash Flow PV Table Cash Flows Amounts Factor Flows Now ($950,000.00) 1.000000 ($950,000.00) End of Y1 $230,000.00 0.877193 $201,754.39 End of Y2 $230,000.00 0.769468 $176,977.53 End of Y3 $170,000.00 0.674972 $114,745.16 End of Y4 $230,000.00 0.592080 $136,178.46 End of Y5 $530,000.00 0.519369 $275,265.39 3.433081 ($45,079.07) 3.433081 12.246555% IRR ($39,543.04) Note: Wrong NPV Excel formula is wrong ($45,079.07) Corrected NPV Exercise 13-10 Internal Rate of Return and Net Present Value Given: Scalia's Cleaning Service is investigating the purchase of an ultrasound machine for cleaning window blinds. The machine would cost $136,700, including invoice cost, freight, and training of employees to 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 expected salvage value. Required: Ignore income taxes 1. Compute the machine's internal rate of return to the nearest whole percent. IRR = the interest rate that yields a NPV = 0 Annual 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 = $136,700 Table Value (Y%, 14 years) from PV of an Annuity Table = $136,700/$25,000 5.468 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 in Exhibit 14-5. Why do you have a zero net present value? Amount of 16% Present Item Year(s) Cash flow Table Factor Value Initial Investment Now ($136,700) 1.00000 ($136,700) Net annual cash inflows 1-14 $25,000 5.468 $136,700 Net present value $0 The 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 nearest whole percent. IRR = the interest rate that yields a NPV = 0 Annual 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 = $136,700 Table Value (Y%, 14 years) from PV of an Annuity Table = $136,700/$20,000 6.835 From PV of an Annuity Table, scanning along the row for 14 periods yields: Interpolation 12% 6.628 6.628168 X ?% 6.835 6.835000 (0.206832) 0.01 11% 6.982 6.981865 (0.353697) X = 0.206832 0.01 0.353697001 0.353697 (X) = (0.01)(.206832) 0.353697 (X) = 0.00206832 X = 0.00584771 X = 0.584771% ?% = 12% - 0.5848% = 11.4152% Rounded to nearest whole % = 11% IRR NPV (pg. 678) RR equal to 16% (136,700) (136,700) 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 11.405% 15.998% 0.000 0.000 Exercise 13-3 Uncertain Future Cash Flows Given: 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 $750,000 and is expected to have a 10-year useful life with no salvage value. The company requires a minimum 15% rate of return on all equipment purchases. This equipment would provide intangible benefits such as greater flexibility and higher-quality output that are difficult to estimate and yet are quite significant. Required: 1. What dollar value per year would the intangible benefits have to be worth in order to make the equipment an acceptable investment? (Ignore income taxes). If Union Bay Plastics uses a discount rate of 15% to calculate the NPV and the resulting NPV equals 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 = 0 5.019 (Annual cash inflows) = $750,000 Annual cash inflows = $750,000/5.019 Annual cash inflows = $149,432.16 $149,439.05 Thus the dollar value per year of the intangible benefits must be worth at least: Annual cash inflows required $149,432.16 $149,439.05 Less known yearly savings 100,000.00 100,000.00 Minimum yearly intangible benefits $49,432.16 $49,439.05 Proof ($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 $149,439.05 NPV = ($34.57) $0.00 IRR = 14.998790% 15.000000% Exercise 13-7 Payback Period and Simple Rate of Return Given: The Heritage Amusement Park would like to construct a new ride called the Sonic Boom, which the 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 company estimates that the following annual costs and revenues would be associated with the ride: Ticket revenues $250,000 Less operating expenses: Maintenance $40,000 Salaries 90,000 Depreciation 27,000 Insurance 30,000 Total Operating Expenses 187,000 Net Operating Income $63,000 $945,000 Required: Ignore income taxes 1. Assume that the Heritage Amusement Park will not construct a new ride unless the ride provides a payback period of six years or less. Does the Sonic Boom ride satisfy this requirement? Payback period = Investment Required / Net Uniform Annual Cash Inflow Net Uniform Annual Cash Inflow Net Operating Income $63,000 Depreciation 27,000 Net Uniform Annual Cash Inflow $90,000 Payback period = $450,000 / $90,000 Payback period = 5.00 years The 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 Amusement Park requires a simple rate of return of at least 12%, does the Sonic Boom ride meet this criterion? Simple accounting rate of return = AROR AROR = Annualized incremental NOI / Initial Investment Required AROR = $63,000 / $450,000 AROR = 14.00% The Sonic Boom has an AROR greater than the minimum 12% requirement. The Sonic Boom satisfies the simple accounting rate or return criterion. e Amusement ($450,000) 90000 90000 90000 90000 90000 90000 90000 90000 90000 90000 90000 90000 90000 90000 135000 18.595% IRR Exercise 13-5: Payback Method Given: The management of Weimar Inc., a civil engineering design company, is considering an investment in a high-quality blueprint printer with the following cash flows: Investment Cash Cash Year Outflow Inflow 1 $38,000 $2,000 2 $6,000 $4,000 3 $8,000 4 $9,000 5 $12,000 6 $10,000 7 $8,000 8 $6,000 9 $5,000 10 $5,000 Required: 1. Determine the payback period of the investment. Investment Cash Cash Unrecovered Year Outflow Inflow Investment 1 ($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 $1,000 7 $8,000 $9,000 8 $6,000 $15,000 9 $5,000 $20,000 10 $5,000 $25,000 Payback = 5 0.90 5.9 years 2. Would the payback period be affected if the cash inflow in the last year was several times larger? Since the investment is recovered prior to the last year, the amount of the cash inflow in the last year has no effect on the payback period. Problem 13-17 Preference Ranking of Investment Projects Given: Austin Company is investigating four different investment opportunities. Information on the four projects under study is given below: Project Number 1 2 3 4 Investment required ($480,000) ($360,000) ($270,000) ($450,000) Present value of cash inflows (10%) 567,270 433,400 336,140 522,970 Net present value $87,270 $73,400 $66,140 $72,970 Life of Project (in years) 6 12 6 3 Internal Rate of Return 16% 14% 18% 19% Since the company's required rate of return is 10%, a 10% discount rate has been used tn the NPV calculations above. Limited funds are available for investment, so the company can not accept all of the available projects. Required: Break-even point: 400 Fixed Expenses Total Expenses Total Sales 1. Compute the project profitability index for each investment project. Project profitability index = NPV / Investment Required Project Number 1 2 3 4 Net present value $87,270 $73,400 $66,140 $72,970 Investment required $480,000 $360,000 $270,000 $450,000 Project profitability index 0.1818125 0.2038889 0.244963 0.1621556 Present value of cash inflows (10%)/Investment Req. 1.1818125 1.2038889 1.244963 1.1621556 2. Rank the four projects according to preference, in terms of: Project Number 1 2 3 4 a. NPV 1 2 4 3 b. PPI 3 2 1 4 c. IRR 3 4 2 1 3. Which ranking do you prefer? Why? Which ranking is best depends on the company's opportunities for reinvesting funds as they are released from a project. IRR: The internal rate of return method assumes that any released funds are reinvested at the internal rate of return. This means that funds released from project #4 would have to be reinvested at a rate or return of 19%, but another project yielding such a high rate of return might be difficult to find. PPI: The project profitability index approach assumes that funds released from a project are reinvested at a rate of return equal to the discount rate, which in this case is only 10%. On balance, the PPI is generally regarded as the most dependable method of ranking competing projects. NPV: The net present value is inferior to the project profitability index as a ranking device because it does not properly consider the amount of investment. For example, it ranks project #3 fourth because of its low NPV; yet this project is the best in terms of the amount of cash inflow generated per dollar invested. ($1,560,000) (Not in text) case is only Problem 13C-6 Net Present Value Analysis Including Income Taxes Given: The Crescent Drilling Company owns the drilling rights to several tracts of land on which natural gas has been found. Th on some of the tracts is somewhat marginal, and the company is unsure whether it would be profitable to extract and sell these tracts contain. One such tract is tract 410, on which the following information has been gathered: Investment in equipment needed for extraction work Working capital investment needed Annual cash receipts from sale of gas, net of related cash operating expenses (before taxes) Cost of restoring the land at completion of extraction work The natural gas in tract 410 would be exhausted after 10 years of extraction work. The equipment would have a useful life it could be sold for only 15% of its original cost when extraction was completed. For tax purposes, the company would de equipment over 10 years using straight-line depreciation and assuming zero salvage value. The tax rate is 30%, and the c tax discount rate is 10%. The working capital would be released for use elsewhere at the completion of the project. Break-even point: 400 Required: 1. Compute the NPV of tract 410. Timing of Cash After Cash Flow Tax Normal Acctg. Approach Flows Amounts Effect Investment in equipment Now ($600,000) None Working capital required Now ($85,000) None Net annual cash receipts End of Ys 1-10 $110,000 70% Tax Savings (Depreciation tax shield) End of Ys 1-10 $60,000 30% Restoration Expense End of Year 10 ($70,000) 70% Salvage value of equipment in 10 years End of Year 10 $90,000 None Tax Outflow from Salvage Gain End of Year 10 $90,000 30% Working capital released End of Year 10 $85,000 None Net Present Value Normal Finance Approach Year 0 (Now) Year 1 Year 2 Net annual cash receipts $110,000 $110,000 Less Depreciation Expense (60,000) (60,000) Less Restoration Expense Taxable Salvage Gain Income Before Taxes $50,000 $50,000 Less Income Taxes (30%) (15,000) (15,000) Net Income $35,000 $35,000 Add back depreciation 60,000 60,000 Operating Cash Flow $95,000 $95,000 Working capital released Cash Inflow $95,000 $95,000 Table Factor 10% (PV of $1 Table) 0.909091 0.826446 PV of cash inflows $621,902.66 $621,902.66 $86,363.64 $78,512.40 Initial 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 Y1 Finance Acctg. Net of Tax Net annual cash receipts $110,000 $110,000 $77,000 Less Depreciation Expense (60,000) 18,000 Less Restoration Expense Taxable Salvage Gain Income Before Taxes $50,000 Less Income Taxes (30%) (15,000) (15,000) Net Income $35,000 Add back depreciation 60,000 Operating Cash Flow $95,000 $95,000 $95,000 Calculation of Cash Inflow Y10 Finance Acctg. Net of Tax Net annual cash receipts $110,000 $110,000 $77,000 Less Depreciation Expense (60,000) 18,000 Less Restoration Expense (70,000) (70,000) (49,000) Taxable Salvage Gain 90,000 90,000 63,000 Income Before Taxes $70,000 Less Income Taxes (30%) (21,000) (21,000) Net Income $49,000 Add back depreciation 60,000 Operating Cash Flow $109,000 $109,000 $109,000 ural gas has been found. The amount of gas profitable to extract and sell the gas that n gathered: $600,000 $85,000 $110,000 $70,000 ment would have a useful life of 15 years, but poses, the company would depreciate the The tax rate is 30%, and the company's after- mpletion of the project. Fixed Expenses Total Expenses Total Sales Cash 10% PV of Flow PV Table Cash Amounts Factor Flows ($600,000) 1.000000 ($600,000.00) ($85,000) 1.000000 ($85,000.00) $77,000 6.144567 $473,131.67 $18,000 6.144567 $110,602.21 ($49,000) 0.385543 ($18,891.62) $90,000 0.385543 $34,698.90 ($27,000) 0.385543 ($10,409.67) $85,000 0.385543 $32,771.18 ($63,097.34) Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 $110,000 $110,000 $110,000 $110,000 $110,000 $110,000 $110,000 (60,000) (60,000) (60,000) (60,000) (60,000) (60,000) (60,000) $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 (15,000) (15,000) (15,000) (15,000) (15,000) (15,000) (15,000) $35,000 $35,000 $35,000 $35,000 $35,000 $35,000 $35,000 60,000 60,000 60,000 60,000 60,000 60,000 60,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 0.751315 0.683013 0.620921 0.564474 0.513158 0.466507 0.424098 $71,374.91 $64,886.28 $58,987.53 $53,625.02 $48,750.02 $44,318.20 $40,289.27 Year 10 $110,000 (60,000) (70,000) 90,000 $70,000 (21,000) $49,000 60,000 $109,000 85,000 $194,000 0.385543 $74,795.40 Problem 13-22 Net Present Value Analysis of a Lease or Buy Decision Given: Blinko Products wants an airplane for use by its corporate staff. The airplane that the company wishes to acquire, a Z Purchase alternative. If the Zephyr II is purchased, then the costs incurred by the company would be as follows: Purchase cost of the plane $850,000 Annual cost of servicing, licenses, and taxes $9,000 Repairs: First 3 years (per year) $3,000 Fourth year $5,000 Fifth year $10,000 The plane would be sold after 5 years. Based on current resale values, the company would be able to sell it for abo the 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 dam years, a the end of which time the deposit would be refunded. The lease would require an annual rental payment o of Year 1). As part of this lease cost, the manufacturer would provide all servicing and repairs, license the plane, a plane would revert to the manufacturer, as owner. Blinko Products' required rate of return is 18% Break-even point: 400 Required: Ignore income taxes. Total Expenses Fixed Expenses Total Sales 1. Use the total-cost approach to determine the present value of the cash flows associated with each alternative. Timing of Amount of PV Table Purchase alternative. Cash Flows Cash Flows Factor (18%) Purchase cost of the plane Now ($850,000) 1.000000 Annual cost of servicing, etc. End of Ys 1-5 ($9,000) 3.127171 Repairs: First Three Years End of Ys 1-3 ($3,000) 2.174273 Fourth Year End of Year 4 ($5,000) 0.515789 Fifth Year End of Year 5 ($10,000) 0.437109 Resale value of the plane End of Year 5 $425,000 0.437109 Timing of Amount of PV Table Lease alternative. Cash Flows Cash Flows Factor (18%) Damage Deposit Now ($50,000) 1.000000 Annual Lease Payments End of Ys 1-5 ($200,000) 3.127171 Refund of Deposit End of Year 5 $50,000 0.437109 Net present value in favor of the leasing option 2. 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 at the company wishes to acquire, a Zephyr II, can be either purchased or leased e as follows: mpany would be able to sell it for about one-half of its original cost at the end of deposit of $50,000 to cover any damage during use. The lease would run for five d require an annual rental payment of $200,000 (the first payment is due at the end cing and repairs, license the plane, and pay all taxes. At the end of five-years, the 2.174273 PV of Timing of Amount of PV Table PV of Cash Flow Cash Flows Cash Flows Factor (18%) Cash Flow ($850,000.00) Now ($850,000) 1.000000 ($850,000.00) (28,144.54) End of Year 1 (12,000) 0.847458 (10,169.49) End of Year 2 (12,000) 0.718184 (8,618.21) (6,522.82) End of Year 3 (12,000) 0.608631 (7,303.57) (2,578.94) End of Year 4 (14,000) 0.515789 (7,221.04) (4,371.09) End of Year 5 406,000 0.437109 177,466.34 185,771.42 ($705,845.98) ($705,845.98) 3.127171 ($705,845.98) PV of Timing of Amount of PV Table PV of Cash Flow Cash Flows Cash Flows Factor (18%) Cash Flow ($50,000.00) Now ($50,000) 1.000000 ($50,000.00) (625,434.20) End of Year 1 (200,000) 0.847458 (169,491.53) 21,855.46 End 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) $52,267.23 $52,267.23 $52,267.23 cash outflows is less negative under the leasing option.

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