Relevant cash flows and NPV analysis test bank problems solutions

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FNAN 303 Solutions to test bank problems – relevant cash flows and NPV analysis Some answers may be slightly different than provided solutions due to rounding 1. Kwon Jewelers is evaluating a 1-year project that would involve an initial investment in equipment of $27,000 and an expected cash flow of $34,500 in 1 year. The project has a cost of capital of 8.74 percent and an internal rate of return of 27.78 percent. If Kwon Jewelers were to use $27,000 in cash from its bank account to purchase the equipment, the net present value of the project would be $4,727. However, Kwon Jewelers has no cash in its bank account, so using money from its account is not possible. Therefore, the firm would need to borrow money to raise the $27,000. If Kwon Jewelers were to borrow money to raise the $27,000, the interest rate on the loan would be 12.36 percent. Kwon Jewelers would receive $27,000 at the start of the project and would pay $30,337 one year later. What is the NPV of the project if Kwon Jewelers borrows $27,000 to pay for the project? (Spring 2014, test 4, question 1) (Spring 2015, final, question 15) (Fall 2015, final, question 11) (Fall 2017, test 3, question 4) If Kwon Jewelers borrows money to raise $27,000, then the NPV of the project would be $4,727. Projects should be evaluated solely on cash flows expected to be produced by assets. It does not matter if funds are borrowed to pay for the project or whether new stock is issued or whether the firm uses cash it already has. Ignore any and all cash flows associated with debt and equity including debt-issuance proceeds, debt payments, equity-issuance proceeds, dividends, and stock buybacks. Therefore, the NPV computed based on the assumption that Kwon Jewelers used $27,000 in cash that was in its bank account would be the same as the NPV computed based on the assumption that Kwon Jewelers borrowed the $27,000. Regardless of where the money for the project comes from, the NPV is $4,727. 2. Striped Potato is evaluating a project that would require the purchase of a piece of equipment for $365,000 today. During year 1, the project is expected to have relevant revenue of $216,000, relevant costs of $57,000, and relevant depreciation of $84,000. Striped Potato would need to borrow $365,000 today to pay for the equipment and would need to make an interest payment of $14,000 to the bank in 1 year. Relevant net income for the project in year 1 is expected to be $44,000. What is the tax rate expected to be in year 1? (Fall 2011, test 4, question 1) (Fall 2012, final, question 14) (Spring 2013, final, question 14) (Spring 2015, test 3, question 1) (Fall 2016, test 3, question 6) (Spring 2017, final, question 11) The $14,000 interest payment is not included in the analysis. Projects should be evaluated solely on cash flows expected to be produced by assets. It does not matter if funds are borrowed to pay for the project or whether new stock is issued or whether the firm uses cash it already has. Ignore any and all cash flows associated with debt and equity including debt-issuance proceeds, debt payments, equity-issuance proceeds, dividends, and stock buybacks. To solve: 1) Find expected taxable income 2) Find expected taxes paid 1

FNAN 303 Solutions to test bank problems – relevant cash flows and NPV analysis 3) Find the expected tax rate 1) Find expected taxable income Taxable income = EBIT = revenues – costs – depreciation 216,000 – 57,000 – 84,000 = 75,000 2) Find expected taxes paid Net income = taxable income – taxes paid 44,000 = 75,000 – taxes paid So taxes paid = 75,000 – 44,000 = 31,000 Tables are useful for steps 1 and 2 Given Step 1 Step 2 Year 1 Year 1 Year 1 Revenue 216,000 216,000 216,000 – Costs 57,000 57,000 57,000 – Annual depreciation 84,000 84,000 84,000 = EBIT = taxable income 75,000 75,000 – Taxes 31,000 = Net income 44,000 44,000 44,000 3) Find the expected tax rate The tax rate = taxes paid / taxable income = 31,000 / 75,000 = 0.4133 = 41.33% 3. Celebrity Food is evaluating the kale crisper project. During year 1, the kale crisper project is expected to have relevant revenue of $256,000, relevant variable costs of $87,000, and relevant depreciation of $11,000. In addition, Celebrity Food would have one source of fixed costs associated with the kale crisper project. Celebrity Food just signed a deal with Lights Camera Action to develop a advertising campaign for use in the project. The terms of the deal require Celebrity Food to pay Lights Camera Action either $18,000 in 1 year if the project is pursued or $34,000 in 1 year if the project is not pursued. Relevant net income for the kale crisper project in year 1 is expected to be $112,000. What is the tax rate expected to be in year 1? (Fall 2011, final, question 14) (Fall 2017, test 3, question 5) The cost is partially sunk in 1 year. Celebrity Food must pay $18,000 in 1 year if it does the project And Celebrity Food must pay $34,000 in 1 year if it does not do the project So the incremental cost would be $18,000 – $34,000 = -$16,000 Therefore, -$16,000 of the fixed cost should be included in the cost of the project in 1 year Note that the incremental effect of pursuing the project is to lower fixed costs. Since total costs = fixed costs + variable costs, total costs = (-$16,000) + $87,000 = $71,000 To solve: 2

FNAN 303 Solutions to test bank problems – relevant cash flows and NPV analysis 1) Find expected taxable income 2) Find expected taxes paid 3) Find the expected tax rate 1) Find expected taxable income Taxable income = EBIT = revenues – costs – depreciation 256,000 – 71,000 – 11,000 = 174,000 2) Find expected taxes paid Net income = taxable income – taxes paid 112,000 = 174,000 – taxes paid So taxes paid = 174,000 – 112,000 = 62,000 Tables are useful for steps 1 and 2 Given & relevant costs Step 1 Step 2 Revenue 256,000 256,000 256,000 – Costs 71,000 71,000 71,000 – Annual depreciation 11,000 11,000 11,000 = EBIT = taxable income 174,000 174,000 – Taxes 62,000 = Net income 112,000 112,000 112,000 3) Find the expected tax rate The tax rate = taxes paid / taxable income = 62,000 / 174,000 = 0.3563 = 35.63% 4. Water’s Edge Resorts is evaluating a project that would require an initial investment in equipment of $500,000 and that is expected to last for 4 years. MACRS depreciation would be used where the depreciation rates in years 1, 2, 3, 4, and 5 are 25%, 45%, 15%, 10%. and 5%, respectively. For each year of the project, Water’s Edge Resorts expects relevant annual revenue associated with the project to be $648,000 and relevant annual costs associated with the project to be $472,000. The tax rate is 50 percent. What is (X plus Y) if X is the relevant operating cash flow (OCF) associated with the project expected in year 2 of the project and Y is the relevant OCF associated with the project expected in year 4 of the project? (Fall 2010, test 4, question 1) (Spring 2011, test 4, question 4) (Spring 2011, final, question 14) (Spring 2012, final, question 16) (Fall 2012, test 4, question 3) (Spring 2013, final, question 15) (Fall 2013, final, question 13) (Spring 2014, test 4, question 3) (Fall 2015, final, question 12) (Fall 2016, final, question 11) (Fall 2017, test 3, question 6) (Fall 2017, final, question 11) (Spring 2018, final, question 11) Year 2 Year 4 MACRS rate .45 .10 × Initial investment 500,000 500,000 = Annual depreciation 225,000 50,000 Revenue 648,000 648,000 3

FNAN 303 Solutions to test bank problems – relevant cash flows and NPV analysis – Costs 472,000 472,000 – Annual depreciation 225,000 50,000 = EBIT -49,000 126,000 × Tax rate 0.50 0.50 = Taxes paid -24,500 63,000 Net income = EBIT – taxes paid -24,500 63,000 OCF = net income + depreciation 200,500 113,000 OCF in year 2 + OCF in year 4 = 200,500 + 113,000 = 313,500 5. Based on the following information, what is the relevant operating cash flow (OCF) associated with the project expected to be in year 3? The project would require an initial investment in equipment of $120,000 that would be depreciated using MACRS where the depreciation rates in years 1, 2, 3, and 4 are 33%, 44%, 15%, and 8%, respectively. At the end of the project in 3 years, the equipment would be sold for an expected after-tax cash flow of $31,500. In year 3 of the project, relevant revenue associated with the project would be $39,000 and relevant costs associated with the project would be $27,000. The tax rate is 35 percent. (Fall 2009, test 4, question 3) (Spring 2010, test 4, question 9) (Spring 2010, final, question 8) (Spring 2016, test 3, question 8) The expected cash flow from capital spending is not relevant for OCF Year 3 MACRS rate 0.15 × Initial investment 120,000 = Annual depreciation 18,000 Revenues 39,000 – Costs 27,000 – Annual depreciation 18,000 = EBIT -6,000 × Tax rate 0.35 = Taxes paid -2,100 Net income = EBIT – taxes paid -3,900 OCF = net income + depreciation 14,100 6. Scarlet operates coffee shops in Ohio. The firm is evaluating the Cleveland project, which would involve opening a new coffee shop in Cleveland. During year 1, Scarlet would have total revenue of $335,000 and total costs of $171,000 if it pursues the Cleveland project, and the firm would have total revenue of $288,000 and total costs of $163,000 if it does not pursue the Cleveland project. Depreciation taken by the firm would be $203,000 if the firm pursues the project and $181,000 if the firm does not pursue the project. The tax rate is 25%. What is the relevant operating cash flow (OCF) for year 1 of the Cleveland project that Scarlet should use in its NPV analysis of the Cleveland project? (Spring 2013, test 4, question 3) (Spring 2015, final, question 16) (Spring 2017, test 3, question 7) (Spring 2018, test 3, question 6) 4

FNAN 303 Solutions to test bank problems – relevant cash flows and NPV analysis In evaluating the Cleveland project, Scarlet should use incremental revenue, incremental costs, and incremental depreciation, which is what those values would be with the project minus what they would be without the project. The incremental effects reflect the effect of the project, which is what is of interest. Incremental revenue = revenue with project – revenue without project = $335,000 – $288,000 = $47,000 Incremental costs = costs with project – costs without project = $171,000 – $163,000 = $8,000 Incremental depreciation = depreciation with project – depreciation without project = $203,000 – $181,000 = $22,000 Year 1 Revenue 47,000 – Costs 8,000 – Annual depreciation 22,000 = EBIT 17,000 × Tax rate 0.25 = Taxes paid 4,250 Net income = EBIT – taxes 12,750 + Annual depreciation 22,000 = OCF 34,750 Alternatively (can look at net income with project minus net income without project or can compute net income from incremental revenue, costs, and depreciation) With in year 1 Without in year 1 Incremental in year 1 Revenue 335,000 288,000 47,000 – Costs 171,000 163,000 8,000 – Annual depreciation 203,000 181,000 22,000 = EBIT -39,000 -56,000 17,000 × Tax rate 0.25 0.25 0.25 = Taxes paid -9,750 -14,000 4,250 Net income = EBIT – taxes -29,250 -42,000 12,750 + Annual depreciation 203,000 181,000 22,000 OCF = net income + dep 173,750 139,000 34,750 7. Spotted Potato is evaluating project A, which would require the purchase of a piece of equipment for $550,000. During year 1, project A is expected to have relevant revenue of $311,000, relevant costs of $104,000, and some depreciation. Spotted Potato would need to borrow $550,000 for the equipment and would need to make an interest payment of $40,000 to the bank in year 1. Relevant net income for project A in year 1 is expected to be $94,000 and operating cash flows for project A in year 1 are expected to be $166,000. Straight-line depreciation would be used. What is the tax rate expected to be in year 1? (Fall 2013, test 4, question 2) The $40,000 interest payment is not included in the analysis. Projects should be evaluated solely on cash flows expected to be produced by assets. It does not matter if funds are borrowed to pay for the project or whether new stock is issued or whether the firm uses cash it already has. Ignore any and all cash flows 5

FNAN 303 Solutions to test bank problems – relevant cash flows and NPV analysis associated with debt and equity including debt-issuance proceeds, debt payments, equity-issuance proceeds, dividends, and stock buybacks. The fact that straight-line depreciation is used is not relevant. The depreciation expense can be found from OCF = net income + depreciation. To solve: 1) Find expected depreciation in year 1 2) Find expected taxable income 3) Find expected taxes paid 4) Find the expected tax rate 1) Find expected depreciation in year 1 OCF = net income + depreciation 166,000 = 94,000 + depreciation Depreciation = 166,000 – 94,000 = 72,000 2) Find expected taxable income Taxable income = EBIT = revenues – costs – depreciation 311,000 – 104,000 – 72,000 = 135,000 3) Find expected taxes paid Net income = taxable income – taxes paid 94,000 = 135,000 – taxes paid So taxes paid = 135,000 – 94,000 = 41,000 Tables are useful for steps 1, 2, and 3 Given Step 1 Step 2 Step 3 Year 1 Year 1 Year 1 Year 1 Revenue 311,000 311,000 311,000 311,000 – Costs 104,000 104,000 104,000 104,000 – Annual depreciation 72,000 72,000 = EBIT = taxable income 135,000 135,000 – Taxes 41,000 = Net income 94,000 94,000 94,000 94,000 + Annual depreciation 72,000 72,000 72,000 = OCF 166,000 166,000 166,000 166,000 4) Find the expected tax rate The tax rate = taxes paid / taxable income = 41,000 / 135,000 = 0.3037 = 30.37% 8. Spotted Potato is evaluating a project that would require the purchase of a piece of equipment for $496,000 today. During year 1, the project is expected to have relevant revenue of $404,000, relevant costs of $157,000, and relevant depreciation of $111,000. Spotted Potato would need to borrow $496,000 today for the equipment and would need to make an interest payment of $28,000 to the bank in 1 year. Relevant operating cash flow for the project in year 1 is expected to be $193,000. What is the tax rate expected to be in year 1? (Fall 2014, test 4, question 1) 6

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