The questions were written in the questions.doc file. And there were some links in the questions like as we did during the lecture, so I provided the lecture slides as well.

HOMEWORK 5 1) The owner of a bicycle repair shop forecast revenues of $200,000 a year. Variable costs will be $60,000 and rental costs for the shop are $35,000 a year. Depreciation on the repair tools will be $15,000. The tax rate is 34%. Calculate the operating cash flow for the repair shop in the previous problem using all three methods we learned in the lecture. Confirm that all three approaches result in the same value for cash flow. 2) Your firm purchased machinery with a 7-year MACRS life for $15 million. The project, however, will end after 4 years. If the equipment can be sold for $5.5 million at the completion of the project, and your firm's tax rate is 34%, what is the after-tax cash flow from the sale of the machinery? Refer to the lecture slides for the 7-year MACRS schedule. 3) Revenues generated by a new product are forecast as follows: Year Revenues 1 $40,000 2 30,000 3 20,000 4 10,000 Thereafter 0 Expenses are expected to be 30% of revenues, and working capital required in each year is expected to be 20% of revenues in the following year. The product requires an investment of $35,000 in plant and equipment. a. What is the total initial investment in the product at year zero? Don't forget initial working capital. b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm's tax rate is 40%, what are the project cash flows each year? c. If the opportunity cost of capital is 14%, what is the project NPV? 4) Blooper Industries must replace its magnesium purification system. Quick & Dirty Systems sells a relatively cheap purification system for $10 million. The system will last 5 years. Do-ItRight sells a sturdier but more expensive system for $12 million; it will last for 8 years. Both systems entail $1 million in operating costs; both will be depreciated straight-line to a final value of zero over their useful lives; neither will have any salvage value at the end of its life. The firm's tax rate is 40%, and the discount rate is 13%. Which system should Blooper Industries install? Lecture 8 Using DCF Analysis To Make Investment Decisions Discount Cash Flows, Not Profits In the last lecture, we dealt with the mechanics of discounting and different methods of project evaluation. However, we were silent about what to discount. To calculate NPV, one needs to discount cash flows and not accounting profits. In lecture 2, we talked about reasons why accounting profits and cash flows may differ. Income statements show how well the firm has performed, but they do not track cash flows. Projects are attractive because of the cash they generate, either for distribution or reinvestment. Therefore, the focus of capital budgeting must be on cash flows, not profits. Incremental Cash Flows A project's present value depends on the extra cash flow that it produces. First, you need to forecast the firm's cash flows if you go ahead with the project. Then the cash flows if you don't accept the project should be forecasted. The difference is equal to the incremental cash flows. An incremental cash flow is a change in the firm's overall future cash flow that occurs as a direct consequence of the decision to take a project. Any cash flow that exists whether a project is taken or not is not a relevant cash flow. Incremental CF = CF with project - CF without project Indirect Effects (Side Effects) Incremental cash flows include all the resulting changes in the firm's overall future cash flows. When a new project impacts the cash flows of the other projects of the firm, then these changes must be accounted for. Positive effect - benefits to other projects An airline firm may establish a new route that brings new business to the existing routes Negative side effect - costs to other projects The most common negative side effect is erosion or cannibalism, where the introduction of a new product will reduce the sales of existing, similar products Sunk Costs A sunk cost is a cost we have already paid or have already incurred the liability to pay. They are past and irreversible outflows. Sunk costs remain the same whether or not you accept the project, they do not affect project NPV. This is not a relevant cost for a project because a decision to take the project or not does not change the fact that this cost has already been paid. A good example is consulting fees. Suppose a company hires a consultant to evaluate a possible investment project and a few weeks later the consultant turns in a report. After that point, the decision to take the project or not does not change the fact that the company has to pay consulting fees. Opportunity Costs The costs do not only include out-of-pocket costs. There are also opportunity costs associated with making certain decisions. Opportunity costs refer to the cost of lost options. The classic example of an opportunity cost is the use of land or plant that is already owned. Although the land or plant is already owned, they are not \"free.\" At the very least we could sell the land; consequently if we choose to use it, we cost ourselves the selling price of the asset. Shutdown Cash Flows The end of a project almost always brings additional cash flows. Nuclear power plants need to be decommissioned at very large costs. Coal mines need to be closed down and their surrounding environments need rehabilitation. However, shutdown cash flows need not be always negative. For example, the company may be able to sell some of the plant, equipment or real estate that was dedicated to the project once it is over. This is called the salvage value. Overhead Costs Overhead costs such as rent, heat or electricity may not be related to a particular project but they may need to be paid nonetheless. Therefore, when the accountant assigns costs to the firm's projects, a charge for overhead is usually made. The principle of incremental cash flows states that we should only include the extra expenses that would result from the project. Taxes Taxes will change as the firm's taxable income changes. Consequently, we have to consider cash flows on an after-tax basis. When we say incremental cash flows, we always mean after-tax incremental cash flows. Separate Investment and Financing Decisions Suppose you finance a project partially with debt. How should you treat the proceeds from the debt issue and the interest and principal payments on the debt? Answer: You should neither subtract the debt proceeds from the required investment nor recognize the interest and principal payments as cash outflows. Capital budgeting focuses exclusively on the project cash flows, not the cash flows associated with alternative financing schemes. This allows us to separate the analysis of the investment decision from the financing decision. First, you ask whether the project has a positive net present value, assuming all equity-financing. Calculating Cash Flow It is helpful to think of a project's cash flow as composed of three elements: Total Cash Flow = + Operating Cash Flows (OCF) - Net Capital Spending (NCS) - Increases in Net Working Capital ( NWC) 1. Operating Cash Flow Operating cash flows consist of revenues from the sales of products and services less the costs of production and any taxes. Suppose a new heating system costs $100,000 but reduces heating costs by $30,000 a year. The firm's tax rate is 35%. The new system does not change revenues, but thanks to the cost savings, income increases by $30,000. Therefore, incremental OCF is 1. Operating Cash Flow You need to look out for depreciation when calculating OCF. Depreciation is not a cash expense, but it affects the tax that the company pays. Here are three possible ways to deal with this: Dollars In Minus Dollars Out: Take only the items from the income statement that represent actual cash flows OCF = Revenues - Cash Expenses - Taxes Adjusted Accounting Profits: Add back depreciation OCF = After-tax Profit + Depreciation Add back depreciation tax shield: OCF = (Revenues - Cash Exp.) (1 - tax) + (Depreciation) (tax) 1. Operating Cash Flow A project generates revenues of $1,000, cash expenses of $600 and depreciation charges of $200 in a particular year. The firm's tax bracket is 35%. Net income is calculated as follows: Method 1: OCF = 1,000 - 600 - 70 = $330 Method 2: OCF = 130 + 200 = $330 Method 3: OCF = (1,000 - 600) 0.65 + 200 0.35 = $330 2. Net Capital Spending To get a project off the ground, a company typically needs to make considerable upfront investments in plant, equipment, research, marketing and so on. These upfront investments are negative cash flows because cash goes out the door. At the end of the project, a company can sell the assets or redeploy them elsewhere in the business. This salvage value (net of any taxes) if the equipment is sold represents a cash inflow to the firm. Final cash flows may also be negative if there are significant shutdown costs. 3. Investment in NWC Net working capital = Current assets - Current liabilities Mosts projects require that the firm invest in net working capital in addition to long-term assets and this results in cash outflows. Most projects will require an increase in NWC initially as inventories and receivables are built. Net working capital may change during the life of the project and the firm may need to make additional investments in NWC. NWC is generally recovered at the end of the project (cash inflow). 3. Investment in NWC A company makes an initial (year 0) investment of $10 million in inventories of plastic and steel for its blade plant. Then in year 1 it accumulates an additional $20 million of raw materials. The total level of inventories is now $30 million, but the cash expenditure in year 1 is simply the $20 million addition to inventory. This investment in additional inventory results in a cash flow of -$20 million. Notice that the increase in NWC is an investment in the project. Later on, say, in year 5, the company begins planning for the next-generation blade. At this point, it decides to reduce its inventory of raw material from $20 million to $15 million. This reduction in inventory investment frees up $5 million of cash, which is a positive cash flow. 3. Investment in NWC These calculations can be summarized as follows: In years 0 and 1, there is a net investment in NWC corresponding to a negative cash flow. In years 2 to 4, there is no investment in NWC, so its level remains unchanged. In year 5, the firm begins to disinvest in NWC, the total declines which provides a positive cash flow. Example Suppose a company thinks it can sell 50,000 cans of soup per year at a price of $4 per can. It costs $2.50 per can to make the product and a new product like this typically has a three year life. Fixed costs for the project are $12,000 per year. Also, the company has to invest $90,000 in manufacturing equipment at the beginning. This cost is going to be totally depreciated over the life of the project. Moreover, the project requires a $20,000 investment in net working capital and this investment will be recovered at the end of the project. The tax rate is 34% and the opportunity cost of capital for this project is %20. Should the company start producing or not? Pro Forma Income Statement Projected Cash Flows OCF = (Revenues - Cash Exp.) (1 - tax) + (Depreciation) (tax) = (200,000 - 137,000) 0.66 + (30,000) 0.34 = $51,780 Making The Decision Now that we have the cash flows, we can apply the techniques that we learned earlier Use the NPV formula to calculate the net present value of the project: NPV = -110,000 + 51,780/1.2 + 51,780/1.2 2 + 71,780/1.23 = 10,648 You can also calculate the internal rate of return (IRR) 0 = -110,000 + 51,780/(1+r) + 51,780/(1+r) 2 + 71,780/ (1+r)3 r = 25.8% The project should be accepted since NPV is positive and IRR exceeds the opportunity cost of capital. Further Note on Depreciation The depreciation expense used for capital budgeting should be the depreciation schedule required by the laws for tax purposes. Straight-line Depreciation D = (Initial cost - salvage value) / expected economic life Salvage value = the worth of the asset when the firm disposes it Very few assets are depreciated straight-line for tax purposes Modified Accelerated Cost Recovery System An asset's class establishes its life for tax purposes. Once the asset's life is determined, the depreciation in each year is computed by multiplying the cost of the asset by a fixed percentage. The expected salvage value and the expected economic life are not explicitly considered. After-tax Salvage Value If the salvage value is different from the book value of the asset, then there is a tax effect. Book value = Initial Cost - Accumulated depreciation After-tax Salvage Value = Salvage - Tax rate (Salvage - Book value) Depreciation and After-Tax Salvage You purchase equipment for $100,000 and it costs $10,000 to have it delivered and installed. Based on past information, you believe that you can sell the equipment for $17,000 when you are done with it in 6 years. The company's marginal tax rate is 40%. What is the depreciation expense each year and the aftertax salvage in year 6 for each of the following situations? Straight-Line Depreciation Suppose the appropriate depreciation schedule is straight-line D = (110,000 - 17,000) / 6 = 15,500 every year for 6 years BV in year 6 = 110,000 - 6(15,500) = 17,000 After-tax salvage = 17,000 - .4(17,000 - 17,000) = 17,000 Three-Year MACRS BV in year 6 = 110,000 - 36,663 - 48,884 - 16,302 - 8,151 = 0 After-tax salvage = 17,000 - .4(17,000 - 0) = $10,200 Seven-Year MACRS BV in year 6 = 110,000 - 15,719 - 26,939 - 19,239 - 13,739 - 9,823 - 9,823 = $14,718 After-tax salvage = 17,000 - .4(17,000 - 14,718) = $16,087 Example: Cost Cutting Your company is considering a new computer system that will initially cost $1 million. It will save $300,000 a year in inventory and receivables management costs. The system is expected to last for five years and will be depreciated using 3-year MACRS. The system is expected to have a salvage value of $50,000 at the end of year 5. There is no impact on net working capital. The marginal tax rate is 40%. The required return is 8%. Depreciation and Capital Investment Depreciation expenses are calculated as follows: MACRS Depreciation Schedule Year 1 Percentage 33.33% Depreciation Expense 333,300 2 3 44.44% 14.82% 444,400 148,200 4 7.41% 74,100 5 0% 0 Capital investment at the beginning would be $1,000,000 if the project is taken. (50,000 - 0) = 30,000 would be recovered at year 5. An after-tax salvage value of 50,000-0.4 Operating Cash Flows The easiest way to calculate OCF's is as follows: OCF = (Sales - Costs)(1 - Tax rate) + Depreciation*(Tax rate) This is a cost cutting project, so sales are zero. Annual cost saving is $300,000 and this enters the above equation as negative. For year 1, OCF = 300,000 (1 - 0.4) + 333,300 (0.4) = $313,200 For year 2, OCF = 300,000 (1 - 0.4) + 444,400 (0.4) = $357,760 For year 3, OCF = 300,000 (1 - 0.4) + 148,200 (0.4) = $239,280 and so on... Year Operating Cash Flow 0 1 2 3 4 5 313,320 357,760 239,280 209,640 180,000 Project Evaluation Year Operating Cash Flow Capital Investment Investment in NWC Total Cash Flow 0 1 2 3 4 5 313,320 357,760 239,280 209,640 180,000 -1,000,000 30,000 0 0 -1,000,000 313,320 357,760 239,280 209,640 210,000 Is this project worth taking? NPV with 8% = $83,794.96 IRR = 11.45% The firm should take this cost cutting project. Example: Equivalent Annual Cost Analysis A company is trying to decide between two different conveyor belt systems. System A costs $430,000, has a four-year life and requires $110,000 in pretax annual operating costs. System B costs $570,000, has a six-year life and requires $98,000 in pretax annual operating costs. Both systems are depreciated straight-line to zero over their lives and will have zero salvage value. Whichever project is chosen, it will be replaced when it wears out. If the tax rate is 34 percent and the discount rate is 11 percent, which project should the firm choose? System A There are no NWC considerations. The system has no salvage value at the end of its life. The system costs $430,000 at year 0. Depreciation expense is 430,000 / 4 = $107,500. OCF is calculated using the tax-shield approach. OCF = (Sales - Costs) * (1-tax) + Depreciation * tax = (0 - 110,000)*0.66 + 107,500 * 0.34 = -36,050 Year 0 1 2 3 Operating Cash Flow -36,050 -36,050 -36,050 Capital Investment -430,000 Total Cash Flow -430,000 -36,050 -36,050 -36,050 NPV with 11% discount rate = -541,843.17 4 -36,050 -36,050 System B There are no NWC considerations. The system has no salvage value at the end of its life. The system costs $570,000 at year 0. Depreciation expense is 570,000 / 6 = $95,000. OCF is calculated using the tax-shield approach. OCF = (Sales - Costs) * (1-tax) + Depreciation * tax = (0 - 98,000)*0.66 + 95,000 * 0.34 = -32,380 Year 0 1 2 3 4 Operating CF -32,380 -32,380 -32,380 -32,380 Capital Investment -570,000 Total Cash Flow -570,000 -32,380 -32,380 -32,380 -32,380 NPV with 11% discount rate = -706,984.82 5 -32,380 -32,380 6 -32,380 -32,380 Comparison What equal annual costs over the life of the project will give us the same NPV? A: 541,843.17 = EAC * (PVIFA11%,4) = {[1 - (1/1.114)] / 0.11} * EAC = 3.10245 * EAC EAC = $174,650.33 B: 706,984.82 = EAC * (PVIFA 11%,6) = {[1 - (1/1.116)] / 0.11} * EAC = 4.2305 * EAC EAC = $167,114.64 System B should be chosen since it has a lower EAC. Question 1 Your firm is contemplating the purchase of a new $720,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $75,000 at the end of that time. You will save $260,000 before taxes per year on order processing costs, and you will be able to reduce working capital by $110,000 (this is a onetime reduction). If the tax rate is 35 percent, what is IRR for this project? Question 2 Consider a project to supply 100 million postage stamps per year to U.S. postal service for the next 5 years. You have an idle parcel of land available that cost $2,400,000 five years ago; if the land were sold today, it would net you $2,700,000 after-tax. The land can be sold for $3,200,000 after taxes in five years. You will need to install $4,100,000 in new manufacturing plant and equipment to actually produce stamps; this plant and equipment will be depreciated straight-line to zero over the project's fiveyear life. The equipment can be sold for $540,000 at the end of the project. You will also need $600,000 in initial net working capital for the project and an additional $50,000 every year thereafter. Your production costs are $0.5 cents per stamp, and you have fixed costs of $950,000 per year. If the tax rate is 34 percent and your required return on the project is 12 percent, what bid price should you submit on the contract