Week 4 Supplemental Problem Solutions

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BUSINESS 3

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Finance

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Jan 9, 2024

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8-7. 7. Excel Solution OpenSeas Inc. is evaluating the purchase of a new cruise ship. The ship would cost $500 million, and would operate for 20 years. OpenSeas expects annual cash flows from operating the ship to be $70 million (at the end of each year), and its cost of capital is 12%. Prepare an NPV profile of the purchase. Use Excel and Solver to determine the IRR. Is the purchase attractive based on these estimates? How far off could OpenSeas’ cost of capital be before your purchase decision would change? a. b. The IRR is the point at which the line crosses the x -axis. In this case, it falls very close to 13%. Using Excel, the IRR is 12.724192%. c. Yes, because the NPV is positive at the discount rate of 12%. d. The discount rate could be underestimated by 0.724192% before the investment decision would change. 8-17. *17. Excel Solution You are considering constructing a new plant to manufacture a new product. You anticipate that the plant will take a year to build and cost $100 million up front. Once built, it will generate cash flows of $15 million at the end of every year over the life of the plant. The plant will wear out 20 years after its completion. At that point, you expect to get $10 million in salvage value for the plant. Using a cost of capital of 12%, calculate the NPV. What is the IRR? Do the NPV and IRR rules agree in this case? Explain. Timeline: 0 1 2 3 21

Cash Flow –100 15 15 15 + 10 The NPV is NPV =- 100million + 15million .12 1 - 1 1 + .12 ( ) 20 æ è ç ö ø ÷ ´ 1 1 + .12 ( ) + 10million 1 + .12 ( ) 21 = $962,787.51 . The IRR is 12.132192%. So the two rules agree that the project should be accepted. 9-4. 4. Hyperion Inc. currently sells its latest high-speed colour printer, the Hyper 500, for $350. It plans to lower the price to $300 next year. Its cost of goods sold for the Hyper 500 is $200 per unit, and this year’s sales are expected to be 20,000 units. Suppose that if Hyperion drops the price to $300 immediately, it can increase this year’s sales by 25% to 25,000 units. What would be the incremental impact on this year’s EBIT of such a price drop? Suppose that for each printer sold, Hyperion expects additional sales of $75 per year in ink cartridges for the next three years, and Hyperion has a gross profit margin of 70% on ink cartridges. What is the incremental impact on EBIT for the next three years of a price drop this year? a. Change in EBIT = Gross profit with price drop – Gross profit without price drop = 25,000 × (300 – 200) – 20,000 ×(350 – 200) = –$500,000. a. Change in EBIT from Ink Cartridge sales = 25,000 × $75 × 0.70 – 20,000 × $75 × 0.70 = $262,500 Therefore, incremental change in EBIT for the next three years is Year 1: $262,500 – 500,000 = -$237,500 Year 2: $262,500 Year 3: $262,500. 9-7. 7. Excel Solution You are a manager at Northern Fibre, which is considering expanding its operations in synthetic fibre manufacturing. Your boss comes into your office, drops a consultant’s report on your desk, and complains, “We owe these consultants $1 million for this report, and I am not sure their analysis makes sense. Before we spend the $25 million on new equipment needed for this project, look it over and give me your opinion.” You open the report and find the following estimates (in thousands of dollars):

All of the estimates in the report seem correct. You note that the consultants used straight-line depreciation for the new equipment that will be purchased today (year 0), which is what the accounting department recommended for financial reporting purposes. Canada Revenue Agency allows a CCA rate of 30% on the equipment for tax purposes. The report concludes that because the project will increase earnings by $4.875 million per year for 10 years, the project is worth $48.75 million. You think back to your halcyon days in finance class and realize there is more work to be done! First, you note that the consultants have not factored in that the project will require $10 million in working capital upfront (year 0), which will be fully recovered in year 10. Next, you see they have attributed $2 million of selling, general, and administrative expenses to the project, but you know that $1 million of this amount is overhead that will be incurred even if the project is not accepted. Finally, you know that accounting earnings are not the right thing to focus on!

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A. Given the available information, what are the free cash flows in years 0 through 10 that should be used to evaluate the proposed project? B. If the cost of capital for this project is 14%, what is your estimate of the value of the new project? a. Before the free cash flows can be calculated, the CCA deductions must be determined and used instead of depreciation. The CapEx amount is $25 million. Using Eq. 7.1 and 7.2, the UCC and CCA amounts are (in $thousands): Year 1 2 3 4 5 6 7 8 9 10 UCC 12,50 0 21,25 0 14,87 5 10,41 3 7,28 9 5,10 2 3,57 1 2,50 0 1,75 0 1,22 5 CCA 3,750 6,375 4,463 3,124 2,18 7 1,53 1 1,07 1 750 525 368 The free cash flows are (in thousands): Year 0 1 2 3 4 5 6 7 8 9 10 Cost of machine cash flow –25,000 Cash flow from change in net working capital –10,000 10,000 Sales revenue 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 Minus cost of goods sold 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 Equals gross profit 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 Minus general, sales, and administrative expense 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 Plus overhead that would have occurred anyway 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Minus CCA 3,750 6,375 4,463 3,124 2,187 1,531 1,071 750 525 368 Equals net operating income 7,250 4,625 6,538 7,876 8,813 9,469 9,929 10,250 10,475 10,632 Minus income tax @ 35% 2,538 1,619 2,288 2,757 3,085 3,314 3,475 3,587 3,666 3,721 Equals Net income 0 4,713 3,006 4,249 5,120 5,729 6,155 6,454 6,662 6,809 6,911 Plus CCA 3,750 6,375 4,463 3,124 2,187 1,531 1,071 750 525 368 Plus machine and change in net working capital cash flows –35,000 0 0 0 0 0 0 0 0 0 10,000 Equals free cash flow –35,000 8,463 9,381 8,712 8,243 7,915 7,686 7,525 7,413 7,334 17,279 B.The free cash flows in the previous table should not be used to calculate the NPV as there are CCA tax shields in years 11 and onward. If only the free cash flows shown in (a) are used for the NPV, the result will underestimate the project’s actual NPV. We can calculate the free cash flows excluding CCA effects and calculate the PV of CCA tax shields separately. This is shown below. Year 0 1 2 3 4 5 6 7 8 9 10 Cost of machine cash flow –25,000

Cash flow from change in net working capital –10,000 10,000 Sales revenue 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 Minus cost of goods sold 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 Equals gross profit 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 Minus general, sales, and administrative expense 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 Plus overhead that would have occurred anyway 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Minus CCA not included as analyzed separately Equals net operating income 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000 Minus income tax @ 35% 3,850 3,850 3,850 3,850 3,850 3,850 3,850 3,850 3,850 3,850 Equals Net income 7,150 7,150 7,150 7,150 7,150 7,150 7,150 7,150 7,150 7,150 Plus CCA not included as analyzed separately Plus cost of machine and change in net working capital cash flows – 35,000 0 0 0 0 0 0 0 0 0 10,000 Equals free cash flow excluding CCA tax shields – 35,000 7,150 7,150 7,150 7,150 7,150 7,150 7,150 7,150 7,150 17,150 (Note: Consistent with the tables above, all dollar values are expressed in $thousands.) NPV of FCF excluding CCA tax shields = 9 10 7,150 1 17,150 35,000 1 $4,992.66 .14 1.14 1.14   - + - + =     PV of CCA tax shields = .14 1 25,000 0.30 .35 2 $5,599.58 .14 .30 1 .14 æ ö + ç ÷ è ø ´ ´ ´ = + + NPV = 4,992.66 + 5,599.58 = $10,592.25