Finance_Exam_2_Cheat_Sheet

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California State University, Fullerton *

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320

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Finance

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Jan 9, 2024

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Loan Payment (Principle to Loan and Interest) You have just taken out a $31,000 car loan with a 9% APR, compounded monthly. The loan is for five years. When you make your first payment in one month, how much of the payment will go toward the principal of the loan, and how much will go toward interest? C = P 1 r ( 1 − 1 ( 1 + r ) n ) = C = $ 31,000 1 0.00750 ( 1 − 1 ( 1 + 0.00750 ) 60 ) = $ 643.51 I YR = 9% 12 = 0.75% ∨ 0.0075 N = 5 Year x 12= 60 PV= $31K Interest payment = $31,000 x 0.75%= 232.5 Principle payment = $643.51-$232.5= $411.01 Real Rate and Nominal Rate If the rate of inflation is 5.6%, what nominal interest rate is necessary for you to earn a 3.6% real interest rate on your investment? Real Rate = Nominal Rate − Inflation Rate 1 + InflationRate Nominal Rate = Real Rate (1 + Inflation Rate) + Inflation Rate => 0.0410 x 1.0620 +0.0620 = . 1055 = 10.55% Historically, why were high inflation rates associated with high nominal interest rates? The real interest rate needs to be high enough so that individuals can expect their savings to have greater purchasing power in the future than in the present. Depreciation Expense Daily Enterprises is purchasing a $10.7 million machine. It will cost $56,000 to transport and install the machine. The machine has a depreciable life of five years and will have no salvage value. If Daily uses straight-line depreciation, what are the depreciation expenses associated with this machine? The yearly depreciation expenses associated with this machine are equal to the purchase cost plus installation cost of the machine divided by 5 years: Depreciation Expense = Purchase cost + Installation Number of Years Depreciation Expense = $ 10,700,000 + $ 56,000 5 = $ 2,151,200 per year Depreciation Tax Shield You have a depreciation expense of $558,000 and a tax rate of 42%. What is your depreciation tax shield? DepreciationTax Shield = Depreciation×Tax Rate DepreciationTax Shield = $ 558,000 × 0.42 = $ 234,360 Cash Flows Daily Enterprises is purchasing a $11.1 million machine. It will cost $42,000 to transport and install the machine. The machine has a depreciable life of five years using straight-line depreciation and will have no salvage value. The machine will generate incremental revenues of $4.8 million per year along with incremental costs of $1.6 million per year. Daily's marginal tax rate is 35%. You are forecasting incremental free cash flows for Daily Enterprises. What are the incremental free cash flows associated with the new machine? Free Cash Flows = After-tax Earnings + Depreciation – Capital Expenditures- Changes in NWC The free cash flow for year 0 will be: 0 + 0 – ($11,100,000 + $42,000) – 0 = -$11,142,000 The after-tax earnings for years 1-5 ¿ ( $ 4,800,000 − $ 1,600,000 − $ 11,100,000 + $ 42,000 5 ) × ( 1 − 0.35 ) = $ 631,540 Therefore, the free cash flow for years 1–5 will be: $ 631,540 + $ 11,100,000 + $ 42,000 5 − 0 − 0 = $ 2,859,940 Incremental Cash Flow You purchased a machine for $1.25 million three years ago and have been applying straight-line depreciation to zero for a seven-year life. Your tax rate is 40%. If you sell the machine today (after three years of depreciation) for $795,500, what is your incremental cash flow from selling the machine? Depreciation = initialcost Life of Equipment = $ 1,250,000 7 years = $ 178,571.43 per year Book Value = Initialcost − accumulated depreciation = $ 1,250,000 − 3 years×$ 178,571.42 = $ 714,285.71 Taxable Income = Sale Price − Book Value = $ 795,500 − $ 714,285.71 = $ 81,214.29 Taxes = Taxable Income× 0.4 = $ 81,214.29 × 0.4 = $ 32,485.72 incremental cashflow = Sale price − taxes = $ 795,00 − $ 32,485.72 = $ 763,014.28

 Interest and other financing−related expenses are excluded when determining a project's unlevered net income.  Only include as incremental expenses in your capital budgeting analysis the additional overhead expenses that arise because of the decision to take on the project. .  As a practical matter, to derive the forecasted cash flows of a project, financial managers often begin by forecasting earnings.  Many projects use a resource that the company already owns.  When making a capital budgeting decision, consider these: o the opportunity to lease out a warehouse instead of using it to house a new production line o the additional taxes a firm would have to pay in the next year o the change in direct labor expense due to the purchase of a new machine  Cannibalization : a decrease in the sales of a current project because of the launching of a new project  Sunk cost: Sunk cost in finance refers to past expenses that cannot be recovered or undone and should not influence future decisions

Capital Budgeting Problem – Devon Dynamics Revised – Round figures to the nearest million.  As financial manager at Devon Dynamics, you are considering a new 4 year project that will require the purchase of a new machine for a new factory with a cost $400 million plus an additional $40 million to ship and install. o Initial Investment: $400 mil + $40 mil= $440 mil  Devon has been offered $25 million to sell the factory space instead of pursuing doing the project. The $25 million offered will the opportunity lost.  The new machine will have a useful life of 4 years and be fully depreciated to zero book value using the straight line method. Depreciation Expense : Initial Inv – Salvage Val ( assume 0 if not specified ) ¿ of years = $ 440 − $ 0 4 = $ 110 million  A study costing $500,000 was done by the company which determined this machine is expected to increase sales by $300 million a year and increase costs by $120 million in the first year. Sales will grow by 5% per year and costs are 40% of sales over the life of the project. The study is a sunk cost ($500,000), and we will not factor in future analysis.  Additional inventory and parts of are to be purchased - which will increase net working capital. The net working capital requirement is 10% of next year’s sales. This level of net working capital requirement for the project will continue until fully recovered at the end of the project. Additional Inventory and Parts is Net Working Capitol.  At the end of 4 years, Devon expects to sell the machine for $35 million.  The tax rate is 40%, and the cost of capital is 12%. Tax on Sale= ( SP-BV) x T = (35-0) x 0.40 = 14 (CF 0 = -495, CF 1 =151.5, CF 2 =155.9, CF 3 =161.42, CF 4 =224.75) NPV @ 12 I/Y = 22.2758 and IRR= 13.98% (red key CST) -------------------------------- Time Period -------------------------- 0 1 2 3 4 Incremental Sales (g=5%) 0 $ 300 $300x (0.05) 1 = $ 315 $300x (0.05) 2 = $ 330.75 $300x (0.05) 3 = $ 347.2876 - Incremental Costs (40% of sales) 0 $300x(-0.40)= -$120 $315x(-0.40)= -$126 $330.75x(-0.40)= -$132.3 $120x(-0.40)= -$138.9150 - Depreciation Expense 0 -$110 -$110 -$110 -$110 Earnings Before Interest & Taxes (EBIT) 0 $ 300 -$120 -$110= $70 $ 315 -$126 -$110= $79 $330.75 -$132.3 -$110= $88.45 $ 347.2876 -$138.915 -$110= $98.3726 - Taxes (40% of sales) 0 (-70 x 0.4) = - $28 (-79 x 0.4) = -$31.6 (-88.45 x 0.4) = -$35.38 (-98.3726 x 0.4) = -$39.3490 Incremental Earnings 0 ($70 - $28) = $42 ($79 - $31.6) = $47.4 ($88.45 - $35.38) = $53.07 ($98.3726 - $39.3490) = $59.0236 + Depreciation Expense 0 +$110 +$110 +$110 +$110 Operating Cash Flow 0 $152 $157.4 $163.07 ($110 + $59.0236) = $169.0236 - Initial Investment -$440 - Change in Net Working Capital = -$300 (.10)- $0= - $30 315(.10)-$30= -$1.5 $330.75(.10) - $31.5= -$1.5 $347.2876(.10) - $33.075= -$1.654 = 0 (.10) + 34.728 = $34.728 - Opportunity Costs -$25 + Selling Price at end of useful life $35 - Tax on Selling Price = ($35 - $0) x 0.4 = -$14 Free Cash Flow -$495 151.5 $155.9 $161.4160 ($169.02+$34.7+$35-$14)= $224.75 NPV @ 12= If the equipment were sold at the end of year 3 for $110 million instead of year 4 for $35 million, what would be the NPV of the project and would you accept or reject the project? The new NPV @12% is 18.9 and the IRR is 10% What is the tax shield for year 2 using straight line depreciation? $110 x 0.4= $44 m What is the tax shield for year 2 using MACRS depreciation (32%)? Depreciation = $440 x 0.32 = 141  $141 x 0.41 = $56 m What would be the change in cash flow for year 2 using MACRS depreciation? $56 - $44 = $12 mm What is the change in cash flow be for year 4 under MACRS vs. Straight Line Depreciation? What is the tax shield for year 4 using straight line depreciation? $110 x 0.4 = What is the tax shield for year 4 using MACRS depreciation? What is the tax on sale of equipment in year 4 under straight line depreciation? What is the tax on sale of equipment in year 4 under MACRS depreciation? Steps: 1. What is the initial investment? 2. What are the sunk costs (exclude)? What are the opportunity costs (include)? 3. What is the annual depreciation expense? What is the depreciation tax shield? 4. What is the change in net working capital? How is it calculated year by year? 5. What are the time period 0 cash flows? 6. What are the incremental revenues, costs and taxes? 7. What are the incremental earnings? What are the operating cash flows? 8. What are the terminal cash flows? How do you calculate the tax on selling price? 9. What is the free cash flows from periods 0 – 4? 10. Solve for the Net Present Value and IRR of the project. Would you accept the project? At what cost of capital would you not accept the project? 11. If the machine was depreciated using MACRS 5 year and the MACRS two year rate is 32%, what is the depreciation expense associated with year 2? What is the depreciation tax shield in year 2 under MACRS? What is the depreciation tax shield for year 2 under straight line depreciation? Would you expect MACRS to lead to higher cash flow and if so by how much? Why do companies choose to use the highest depreciation method allowable?

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