Chapter 11 Cash Flows and Capital Budgeting
Before You Go On Questions and Answers
Section 11.1 1. Why do we care about incremental cash flows at the firm level when we evaluate ev aluate a project?
We care about incremental cash flows at the firm level because they reflect the impact of the project on the total cash flows that the firm produces. This is what the stockholders care about. The difference between the present value of the expected cash flows fl ows from the firm with the project and the present value of the expected cash flows from the firm without the project is precisely what the NPV of a project is. Our NPV estimate will be incorrect incorrect if we do not account for all of the incremental cash flows at the firm level.
2. Why is D&A first subtracted and then added back ba ck in FCF calculations?
By subtracting D&A, calculating the tax obligation, and then adding back D&A, we are accounting for the fact that D&A is a noncash n oncash charge that reduces the firm’s tax o bligation by the product of D&A and the tax rate (D&A x t ). ). If we did not do this, we would overstate the tax obligation and understate FCF.
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3. What types of investments should be included in FCF calculations?
All investments directly associated with the project should be included in FCF calculations. These can include both investments in tangible and intangible assets. They can also include investments in additions to working capital, such as for the credit a firm extends to its customers and inventories.
Section 11.2 1. What are the five general rules for calculating FCF? FC F?
(1) Include cash flows and only cash c ash flows in your calculations. (2) Include the impact of the project on cash flows from other product lines. (3) Include all opportunity costs. (4) Forget sunk costs. (5) Include only after-tax cash flows in the cash flow calculations.
2. What is the difference between nominal and real dollars? Why is it important not to mix them in an NPV analysis?
When most people talk about dollar d ollar amounts, they are referring to nominal dollars. Nominal dollars do not take into account changes in purchasing power. Real dollars are dollar amounts that are adjusted for changes in purchasing power. For example, 100 real dollars have the same purchasing power whether they are received today or at some future date. It is important not to
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mix nominal and real dollars in an NPV analysis because the discount rate is either a nominal rate, which is used to discount nominal dollars, or a real rate, which is used to discount real dollars. Since the discount rate must be either a nominal rate or a real rate, if real and nominal dollars are mixed in an NPV analysis, the NPV will be calculated incorrectly.
3. What is a progressive tax system? What is the difference between a firm’s marginal and average tax rates?
A progressive tax system is one in which the marginal tax rate at low levels of income inco me is lower than the marginal tax rate at high h igh levels of income. A firm’s marginal tax rate is the rate that it pays on the last dollar dollar earned while the average tax rate is the average rate paid on the th e firm’s total earnings (tax paid divided by taxable income).
4. How can FCF in the terminal te rminal year of a project’s life differ from FCF in the other years?
FCF in the terminal year can differ from FCF in other years in several ways. The Th e terminal year cash flows can include cash flows from the asset sales, including the actual proceeds from the sales themselves and taxes due or received if there is a gain or loss on the sale. Terminal year cash flows can also include cash flows associated with recovery of working capital. 5. Why is it important to understand that cash flow forecasts in an NPV analysis analysis are expected values?
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It is important to recognize that we are forecasting ex pected cash flows in an NPV analysis because uncertainties regarding project cash flows that are unique to the project should be reflected in the cash flow forecasts.
Section 11.3 1. What is the the difference between variable and fixed costs, costs, and what are examples of each? Variable costs vary directly with unit sales. Fixed costs do no t vary with unit sales. For an example of each, see the video game player scenario on page 379. Variable costs are those associated with purchasing the components for the player, p layer, the labor required, and sales and marketing. These costs will vary according to the number numbe r of units produced. Fixed costs are those associated with assembly space, and administrative expenses.
2. How are working working capital items forecast? Why are accounts receivable typically typically forecast as a percentage of revenue and accounts payable, and inventories as percentages of the cost of good sold? Working capital items are forecast using 1) cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4) accounts payable. Inventories are forecast as a percentage of the cost of goods sold because the COGS represent a measure of the amount of money invested in inventories. Accounts payable are forecast this way wa y because the COGS is a measure of the amount of money actually owed to suppliers.
Section 11.4 1. When can we not simply compare the NPVs of two mutually exclusive projects?
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If we expect to replace at least one of the projects at the end of its life, we cannot simply compare the NPVs. Doing so would ignore the subsequent subsequ ent investment(s). You can only directly compare the NPVs of mutually exclusive projects under one condition — that that is, if you expect to terminate the project that is chosen (e.g., sell the lawn mower) on or before the end of the life of the shorterlived project.
2. How do we decide when to harvest an asset?
We choose the harvest date that maximizes the NPV of the asset. To identify this date, we compare the NPVs expected from harvesting the asset for each of the feasible harvest dates. The best date to harvest the asset is the date that produces the largest NPV, once the NPVs for all of the alternative harvest dates have been discounted d iscounted to the same point in time.
3. Under what circumstance would you replace an old machine that is still operating with a new one?
You should replace the old machine when the EAC of the new machine is lower than the EAC of the old machine (if revenues are the same for both machines) or when the annualized cash inflow from the replacement is greater.
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Self Study Problems
11.1
Explain why the announcement of a new investment is usually accompanied by a change in the firm’s stock price.
Solution:
firm’s investments cause changes in its future after-tax cash flows and stockholders are the A firm’s residual claimants (owners) of those cash flows. Therefore, the stock price should increase when stockholders expect an investment to have a positive NPV, and decrease when it is expected to have a negative NPV.
11.2
In calculating the NPV of a project, p roject, should we use all of the after-tax cash flows associated with the project, or incremental after-tax cash flows from the project? Why?
Solution:
We should use incremental cash flows of the project. Incremental cash flows reflect the amount by which the firm’s total cash flows will change if the project is adopted. In other words, incremental cash flows represent the net difference in cash revenues, costs, and investment outlays (in net working capital and capital c apital expenditures) at the firm level with and without the project, which is precisely what the stockholders stockh olders care about.
11.3
You are considering opening another restaurant in the TexasBurgers chain. The new restaurant will have annual revenue of $300,000 and operating expenses of $150,000. The
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annual depreciation and amortization for the assets used in the restaurant will equal $50,000. An annual capital expenditure of $10,000 will be required to offset wear-and-tear on the assets used in the restaurant, but no additions to working capital will be required. The marginal tax rate will be 40 percent. Calculate Cal culate the incremental annual free cash flow for the project
Solution:
The incremental annual free cash flow is calculated as:
FCF ($3 ($300,000 ,000 $150,000 ,000 $50,000 ,000) (1 0.4) .4) $50,000) ,000) $10 $10,000 ,000
$100,000
11.4
Sunglass Heaven, Inc., is launching a new store in a shopping mall in Houston. The annual revenue of the store depends on the weather conditions in the summer in Houston. The annual revenue will be $240,000 in a sizzling summer, with probability of 0.3; $80,000 in a cool summer, with probability of 0.2; and $150,000 $150,00 0 in a normal summer, with probability of 0.5. What is the expected annual revenue of the store?
Solution:
The expected annual revenue is: (0.3 × $240,000) + (0.2 × $80,000) + (0.5 × $150,000) = $163,000
11.5
Sprigg Lane Manufacturing, Inc., needs to purchase a new central air-conditioning system for a plant. There are two choices. ch oices. The first system costs $50,000 and is expected ex pected to last 10 years, and the second system costs $72,000 and is expected to last 15 years. Assume that the 7
opportunity cost of capital is 10 percent. Which air-conditioning system should Sprigg Lane purchase?
Solution:
The equivalent annual cost for each system is:
(1.1)10 EAC1 (0.1)($50, 00 000) $8,137.27 (1.1)10 1 (1.1)15 $9, 46 EAC2 (0.1)($72, 00 000) 466.11 (1.1)15 1 Therefore Sprigg Lane should purchase p urchase the first one.
Critical Thinking Questions
11.1
Do you agree or disagree with the following statement given the techniques discussed in this chapter? We can calculate future cash flows precisely and obtain an exact value for the NPV of an investment.
The statement is not true. Given the nature of the real business world, it is almost certain that the cash flows generated by a project will differ from the forecasts used to decide whether to proceed with the project. However, techniques discussed in this chapter provide an important and useful framework that helps minimize errors and ensures that forecasts are internally consistent. 8
11.2
What are the differences between cash flows used in capital budgeting calculations and past accounting earnings?
Cash flows used in capital budgeting calculations are forward looking; they are incremental after-tax cash flows based on forecast. Accounting earnings are backward looking; they represent a record of past performance and may not accurately reflect cash flows.
11.3
Suppose that FRA Corporation already has divisions in both Dallas and Houston. FRA is now considering setting up a third division in Austin. This expansion ex pansion will require one senior manager from Dallas and one from Houston to relocate to Austin. Ignore relocation expenses. ex penses. Is their annual compensation relevant to the decision to expand?
The annual compensations of existing senior managers are not incremental to the new investment and therefore are not relevant for capital budgeting analysis. This is consistent with our Rule 1 for incremental cash flow calculations: Include cash flows and only cash flows; do not include allocated costs unless they reflect re flect cash flows.
11.4
MusicHeaven,Inc., is a producer of MP3 players which currently have either 20 gigabytes or 30 gigabytes of storage. Now the company is considering launching a new production line making mini MP3 players with 5 gigabytes of storage. Analysts forecast that your company will be able to sell 1 million such mini MP3 players if the investment is taken. In making the
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investment decision, discuss what the company should consider other than the sales of the mini MP3 players.
The company’s launch of the new mini MP3 players may reduce its current sales of MP3 MP 3 players of bigger storage. This impact has to be considered. This is consistent with with our Rule 2 for incremental cash flow calculations: Include the impact of the project on cash flows from other product lines.
11.5
QualityLiving Trust is a real estate investment company that builds and remodels apartment buildings in northern California. It is currently considering considering remodeling a few idle buildings in its possession into luxury apartment buildings in San Jose. The company bought those tho se buildings eight months ago. How should the market value of the buildings be treated in evaluating this project?
Although the buildings are not currently in use, us e, the company can sell them at their market value rather than remodel them into in to apartments. Therefore, the market value of the buildings is the opportunity cost of the project and should be considered as cash outflow in the investment decision. This is consistent with our Rule 3 for incremental c ash flow calculations: Include all opportunity costs.
11.6
High-End Fashions, Inc., bought a production line of ankle-length skirts last year at a cost of $500,000. This year, however, miniskirts are in and ankle-length skirts are completely out of fashion. High-End has the option to rebuild the production line and use it to produce
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miniskirts, with an annual operating cost of $300,000 and expected revenue of $700,000. How should the company treat the cost of $500,000 of the old production line in evaluating the rebuilding plan?
The cost of the old production line occurred in the past. It cannot be changed whether or not the company rebuilds it into the miniskirt production line. Th erefore, High-End should not consider the cost of $500,000. This is consistent with our Rule 4 for incremental cash flow calculations: Forget sunk costs.
11.7
How is the MACRS depreciation method under und er IRS rules different from the straight-line depreciation allowed under GAAP rules? What is the implication of incremental after-tax cash flows from firms’ investments?
GAAP allows the straight-line straight-line depreciation method. In contrast, an ―accelerated‖ method of depreciation, Modified Accelerated Cost Recovery System (MACRS), has been used for U.S. federal tax calculations. The advantage of o f MACRS, relative to straight-line depreciation, is that it enables a firm to deduct depreciation changes sooner, thereby realizing the tax saving sooner and increasing the present value of the tax savings.
11.8
Explain the difference between marginal and average tax rates, and identify which of these rates is used in capital budgeting and why.
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The marginal tax rate is the rate paid on the next dollar earned. The average tax rate is the dollar value of total taxes paid divided by total income. The marginal tax rate is the appropriate rate to use in capital budgeting bud geting analysis because this is the tax rate that will be paid on the incremental income earned by the project.
11.9
Under what circumstances will will the sale of an asset result in taxable gain? gain? How do you estimate the taxes or benefits associated with the sale of an asset?
The sale of an asset results in a taxable taxab le gain when the selling price of the asset exceeds its book value.
Tax on the sale of an asset = (Selling price of asset – asset – Book Book value of asset) × t
11.10 When two mutually exclusive projects have different lives, how can an analyst determine
which is better? What is the underlying assumption in this method?
When we choose from mutually exclusive projects with different lives, instead of electing the project with higher NPV or lower net present value of costs, we should choose the project with higher Equivalent Annual Revenue or lower Equivalent Annual Cost. The underlying assumption is that we will continue to operate with the same equivalent annual revenue or equivalent annual cost in the future.
11.11 What is the opportunity cost of using an existing asset? Give an example of the opportunity
cost of using the excess capacity of a machine.
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The opportunity cost of using an existing asset in a project is the present value of the change in the firm’s cash flows that is attributed to the fact that this a sset is being used in the project. For example, by using the excess capacity of a machine, you may accelerate the wear-andtear of the machine and hence will need to replace it sooner. The present value of the added annualized costs is the opportunity cost of using the excess capacity.
o f 11.12 You are providing financial advice to a shrimp farmer who will be harvesting his last crop of farm-raised shrimp. His current shrimp crop is very young and will therefore grow and become more valuable as their weight increases. Describe how you would determine the appropriate time to harvest the entire crop of shrimp.
Assuming that the price of shrimp is directly (and linearly) related to the weight of the shrimp, then the optimal point in time to harvest the shrimp would be where the rate of weight increase is no longer greater than the opportunity cost of capital for the shrimp farmer. Alternatively, the appropriate time is when the value valu e increase of the shrimp is no longer greater than the opportunity cost of capital.
Questions and Problems
BASIC
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11.1 Calculating project cash flows: Why do we use forecasted incremental after-tax cash flows
instead of forecasted accounting earnings in estimating the NPV of a project? LO 1
Solution:
Accounting earnings can differ from cash flows for a number of reasons, making accounting earnings an unreliable measure of the costs and benefits of a project. For example, ease of manipulating earnings components such as accounts receivable and depreciation may result in distorted estimation of capital budgeting; using forecasted cash flows eliminates such possibilities. In addition, because there is time value of money, cash flows better reflect reflect the actual available funds to be distributed to shareholders at each point in time.
11.2 The FCF calculation: How do we calculate incremental after-tax free cash flow from the
forecasted earnings of a project? What are the common adjustment items? LO 2
Solution:
We need to adjust for the depreciation and amortization tax shield, capital expenditures, ex penditures, and changes in working capital (including receivables and payables).
11.3 The FCF calculation: How do we adjust for depreciation when we calculate incremental after-
tax cash flow from EBITDA? What is the intuition for the adjustment? LO 2
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Solution:
There are two ways to adjust ad just for depreciation: (1) subtract depreciation from EBITDA, multiply it by (1 – (1 – tax tax rate), and then add depreciation back; (2) add the tax shield from depreciation (depreciation multiplied by tax rate) to revenue. These two methods yield the same results. The intuition is that although depreciation itself is not a cash flow inflow or outflow, increase in depreciation will result in a decrease in taxable income. This saving on tax is treated as cash inflow in calculating incremental after-tax cash flows.
11.4
Nominal versus real cash flows: What is the difference between nominal and real dollars?
Which rate of return should we use to discount each type of these cash flows in the future? LO 2
Solution:
Nominal dollars are dollars stated as we usually think of them, without any adjustment for for changes in purchasing power over ove r time. Real dollars are dollars stated so that their purchasing power remains constant. We should use nominal rate of return to discount future nominal dollars and real rate of return to discount future real dollars. By doing this, we will get meaningful present values in today’s dollars and purchasing p urchasing power.
11.5
Taxes and depreciation: What is the difference between the average tax rate and the
marginal tax rate? Which one should we use in calculating the incremental after-tax cash flows?
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LO 2
Solution:
In a progressive tax system, the marginal tax rate is different from the average tax rate. The average tax rate is the total amount of tax divided by total amount of money earned, while the marginal tax rate is the rate paid on the last dollar earned. Since a firm already pays taxes, the appropriate tax rate used for the firm’s new project is the tax rate that the firm will pay on any additional profits that are earned because the project is adopted. Therefore, we use the marginal tax rate in calculating incremental after-tax cash flows.
11.6
Computing terminal-year FCF: Healthy Potions, Inc., a pharmaceutical company, bought a
machine that produces pain-reliever medicine at a cost of $2 million five years ago.. The Th e machine has been depreciated over the past five years, and the current book value is $800,000. The company decides to sell the machine now at its market price of $1 million. The marginal tax rate is 30 percent. What are the relevant cash flows? How do they change if the market price of the machine is $600,000 instead? LO 2
Solution:
The relevant cash flows include the sale price of the machine, as well as the tax on the capital gain: $1,000,000 – $1,000,000 – 0.3 0.3 × ($1,000,000 – ($1,000,000 – 800,000) 800,000) = $940,000
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When the market price of the machine is changed to $600,000, the relevant cash flows include the sale price and tax saving on capital loss: $1,000,000 + 0.3 × (800,000 – (800,000 – 600,000) 600,000) = $1,060,000
11.7
Cash flows from operations: What are variable costs and fixed costs? What are some
examples of each? How are these thes e costs estimated in forecasting operating expenses? LO 3
Solution:
Variable costs vary directly with unit sales, while fixed costs do not. Variable costs are those associated with purchasing the components for the player, p layer, the labor required, and sales and marketing. These costs will vary according to the number numbe r of units produced. Fixed costs are those associated with assembly space, and administrative expenses.
11.8
Cash flows from operations: When forecasting operating expenses, explain the difference
between a fixed cost and a variable cost. LO 3
Solution:
Fixed costs are operating expenses that do not vary with the number of units sold, sol d, while variable costs vary directly with the number of units sold.
11.9
Investment cash flows: Zippy Corporation just purchased computing equipment for $20,000.
The equipment will be depreciated using a five-year MACRS depreciation schedule. If the
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equipment is sold at the end of its fourth year for $12,000, what are the after-tax proceeds from the sale, assuming the marginal tax rate is 35%. 35 %. LO 2
Solution:
The 5-year depreciation schedule allows us to depreciate 20 percent of the value of the equipment in year 1, 32 percent in year two, 19.20 percent in year 3, and 11.52 percent in year four after the purchase. The associated depreciation charges in years 1 through 4 in order are $4,000, $6,400, $ 3,840, and $2,304 respectively. Total depreciation at the end of year 4 $16,544, so the book value of the equipment equipment when sold is $3,456. Since the equipment is sold for $12,000 the tax on the sale of the asset is equal to ($12,000-$3,456) × 0.35 = $2,990.40.
The total after tax proceeds are $12,000 - $2,990.40 = $9,009.60
11.10 Investment cash flows: Six Twelve is considering opening up a new convenience store in
downtown New York City. The expected annual revenue is $800,000. To estimate the increase in working capital, analysts estimate the ratio of cash and cash-equivalents to revenue to be 0.03, and the ratio of receivables, inventories, and payables to revenue to be 0.05, 0.10, and 0.04, respectively in the same industry. What is the incremental cash flow related to working capital when the store is opened? LO 2
Solution:
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Cash flow related to working capital in year 0 = $(800,000) × (0.03 + 0.05 +.10 - .04) = $(($112,000)
11.11 Investment cash flows: Keswick Supply Company wants to set up a division that provides
copy and fax services to businesses. Customers will be given 20 days to pay for such services. The annual revenue of the division is estimated to be $25,000. Assuming that the customers take the full 20 days to pay, p ay, what is the incremental cash flow related to working capital when the store is opened? LO 2
Solution:
The average accounts receivable balance will be (20days/365days/year) ×100% ×25,000 = 5.48% × 25,000 = $1,370.
Alternatively, the average daily credit sale = $25,000 / 365 = $68.49, and it takes 20 days, on average, to collect the sale.
Therefore, the incremental cash flow related to working capital c apital when the store is opened: 20 × $68.49 = $1,369.86, or about $1,370.
11.12 Expected cash flows: Define expected cash flows and explain why this concept is important
in evaluating projects. LO 2
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Solution:
Expected cash flows are probability-weighted averages of the future cash flows generated by a project under alternative scenarios. In the real business world there are a lot of uncertainties. Future cash flows may vary across different states of the world. It is not possible to estimate a unique number of cash flow for all states. We can estimate the expected cash flows across different states and use that as an estimation of future cash flows. The cash flows that are discounted in an NPV analysis an alysis are the expected incremental cash flows the project will produce.
11.13 Projects with different lives: Explain the concept of equivalent annual cost and how it is
used to compare projects with different lives. LO 4
Solution:
The equivalent annual cost co st (EAC) is the annualized cost of an investment stated in nominal dollars. In other words, it is the annual pa yment from an annuity with a life equal to that of a project that has the same NPV as the project. Since it is a measure of the annual cost or cash inflow from a project, the EAC for one project can be compared directly with the EAC from another project, regardless of the lives of those two projects.
11.14. Replace an existing asset: Explain how we decide the optimal time to replace an existing
asset with a new one.
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LO 4
Solution:
The optimal time to replace an existing asset with a new one is if the benefits b enefits of replacing the machine exceed the costs.
INTERMEDIATE
11.15 Nominal versus real cash flows: You are buying a sofa. You will pay $200 today and make
three consecutive annual payments of $300 in the future. The real rate of return is 10 percent, and the expected inflation rate is 4 percent. What is the actual price of the sofa? LO 2
Solution:
We can calculate it in two different d ifferent ways: (1)
Use nominal dollars and nominal rate of return: Nominal rate of return = (1 + 10%) × (1 + 4%)-1 = 14.4% Price = 200 + 300 / (1 + 14.4%) + 300/(1 + 14.4%)2 + 300 / (1 + 14.4%)3 = $891.84
(2)
Use real dollars and a real rate of return: Real annual payments are: 300 / (1 + 4%) = 288.46, 300 / (1 + 4%)2 = 277.37, and 300 / (1 + 4%)3 = 266.70 Price = 200 + 288.46/(1 + 10%) + 277.37/(1 + 10.4%)2+266.7 / (1+10.4%)3 =891.84
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Note that we get identical results as long as we are consistent in using nominal or real cash flows and corresponding discount rates.
11.16 Nominal versus real cash flows: You are graduating in two years. You want to invest your
current savings of $5,000 in bonds and use the proceeds to purchase a new car when you graduate and start to work. You can invest the money in either Bond A, a two-year bond with a 3 percent annual interest rate, or Bond B, an inflation-indexed two-year bond paying 1 percent real interest above the inflation rate (assume this bond makes annual interest payments). The inflation rate over the next two years is expected to be 1.5 percent. Assume that both bonds are default free and have the same market price. Which bond should you invest in? LO 2
Solution:
The nominal interest rate is 3 percent for bond A, and (1 + 1%) × (1 +1.5%) – +1.5%) – 1 = 2.52% for the inflation-indexed bond B. You should invest in bond A.
11.17 Marginal and average tax rates: Given the U.S. Corporate Tax Rate Schedule in Exhibit
11.6, what is the marginal tax rate and average tax rate of a corporation that generates a taxable income of $12 million in 2010? Solution:
The marginal tax rate is 35 percent.
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The total tax payable is 3,400,000 + (12,000,000-10,000,000) ×35% = $4,100,000 Therefore the average tax rate = 4,100,000 / 12,000,000 = 34.2% LO 1
11.18 Investment cash flows: Healthy Potions, Inc., is considering investing in a new production
line for eye drops. Other than investing in the equipment, the company compan y needs to increase its cash and cash equivalents by $10,000, increase the level of inventory by $30,000, increase accounts receivable by $25,000, and increase accounts payable by $5,000 at the beginning of the investment. Healthy Potions will recover these changes chan ges in working capital at the end of the project 10 years later. Assume the appropriate discount rate to be 12 percent. What are the relevant cash flows given the above information? LO 1
Solution:
The relevant cash flow related to working capital at the beginning of the project p roject is: ($10,000)+$30,000+$25,000 - $5,000 = ($60,000) The present value of relevant cash c ash flow related to working capital at the end of the project is: 60,000 / (1 + 0.12)10 = $19,318.39
11.19 Cash flows from operations: Given the soaring price of gasoline, Ford is considering
introducing a new production line of gas-electric hybrid sedans. The expected annual unit sales of the hybrid cars is 30,000; the price is $22,000 per car. Variable costs of production are $10,000 per car. The fixed overhead including salary of top executives is $80 million per year.
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However, the introduction of the hybrid h ybrid sedan will decrease Ford’s sales of regular sedans by 10,000 cars per year; the regular sedans have a unit price of $20,000 and unit variable cost of $12,000, and fixed costs of $250,000 per year. Depreciation costs of the production plant are $50,000 per year. The marginal tax rate is 40 percent. What is the incremental annual cash flow from operations? LO 1
Solution:
Step One: Revenue: $22,000 × 30,000 machines =$660,000,000 Step Two: Op Exp: $10,000 × 30,000 machines = $300,000,000, plus lost net revenue from regular sedans = ($20,000 – ($20,000 – $12,000) $12,000) × 10,000 = $80,000,000; total Op Exp = $380,000,000 Step Three: D&A: $50,000 Step Four: Plug information into the text book template as below.
= = x = + = =
ΔNR ΔOpEx ΔEBITDA ΔD&A ΔEBIT (1-t) ΔNOPAT ΔD&A ΔCFO ΔCapEx ΔAWC ΔFCF
660,000,000 -380,000,000 280,000,000 -50,000 279,950,000 0.60 167,970,000 50,000 168,020,000 0 0 168,020,000
Alternatively , the incremental annual cash flow from operations is:
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((22,000-10,000) ×30,000-(20,000-12,000) ×10,000) ×(1-0.4) + 50,000 ×0.4 = 168,020,000 Note that the fixed costs are not included in the incremental cash flows calculations, since they exist regardless of the hybrid sedan investment.
11.20 FCF and NPV for a project: Archers Daniels Midland Company is considering buying a
new farm that it plans to operate for 10 years. The farm will require an initial investment of $12 million. This investment will consist of $2 million for land and $10 million for trucks and other equipment. The land, all trucks, and all other equipment is expected to be sold at the end of 10 years for a price of $5 million, $2 million above book value. The farm is expected to produce revenue of $2 million each year, and annual cash flow from operations equals $1.8 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this investment. LO 1
Solution:
Cash flow of investment in year 0 is: $(12,000,000) Annual cash flows from operations = $1,800,000 Present value of free cash flows:
PV(FC PV(FCF F110 ) Annu Annual al CF PV Annu Annuit ity y fact factor or
1- 1 10 (1.10) =$1,800,000 0.10 $11,060220.79 Book value of asset = $3,000,000 25
Sale price of asset = $5,000,000 Tax on sale of an asset = (Selling price of asset - Book value v alue of asset) × t = $2,000,000 × 0.35 = $700,000 PV of after-tax salvage value in year 10 is:
($5,00 ,000,00 ,000 $700,00 ,000)
1 $1,65 ,657,83 ,836.15 (1.10)10
NPV $12, $12, 000, 000, 000 $11, $11, 060, 060, 220.79 220.79 1, 657,836.15 657,836.15
$718,056.94 Since NPV > 0, project should be accepted.
11.21 Projects with different lives: You are trying to choose between purchasing one of two
machines for a factory. Machine A costs $15,000 to purchase and has a three-year life. Machine B costs $17,700 to purchase but has a four year life. Regardless of which machine you purchase, it will have to be replaced at the end of its its operating life. Which machine should you choose? Assume a marginal tax rate rate of 35% and a discount rate rate of 15%. LO 4
Solution
Since the machines have difference d ifference purchase costs and different operating lives, you should choose the machine that has the lowest equivalent annual cost (EAC).
(1 k )t EACA k NPVt t (1 k ) 1 (1.15)3 (0.15)( $15, 00 $6, 569.55 000) (1.15)3 1
(1.15) 4 $6,199.69 EAC B (0 (0.15)( $17, 70 700) (1.15) 4 1
You should choose machine B because it has the lowest equivalent annual cost.
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11.22 Projects with different lives: You are starting a family pizza parlor and need to buy a
motorcycle for delivery orders. You have two models in mind. Model A costs $9,000 and is expected to run for six years; model B is more expensive, with a price of $14,000 and an expected life of 10 years. The annual maintenance costs are $800 for model A and $700 for model B. Assume that the opportunity cost of capital is 10 percent. Which one should you buy? LO 4 Solution:
You need first calculate the NPV of costs for each of the motorcycles: 1 1 (1.10) 6 NPVA $9,000 ( $800) $12,484.21 0.10 1 1 10 (1.10) NPVB $14,000 ( $700) $18,301.20 0.10 Then you need to calculate the EAC of each model:
(1 k )t EACA k NPVt t (1 k ) 1 (1.10) 6 (0.10)( $12, 48 $2, 866.47 484.21) (1.10)6 1
(1.10)10 $2, 97 EACB (0.10)( $18, 30 301.20) 978.44 (1.10)10 1 Since EAC is lower for model A, you should buy model A.
27
11.23 When to harvest an asset: Predator LLC, a leveraged buyout specialist, recently bought a
company and wants to determine the optimal time to sell it. The partner in charge of this investment has estimated the after-tax cash flows at different times as follows: $700,000 if sold one year later; $1,000,000 if sold two years later; $1,200,000 if sold three years later; and $1,300,000 if sold four years later. The opportunity cost of capital is 12 percent. When should Predator sell the company? Why? LO 5
Solution:
The NPV of each choice is: NPV1 = $700,000 / (1.12)1 = $625,000 NPV2 = $1,000,000 / (1.12)2 = $797,194 NPV3 = $1,200,000 / (1.12)3 = $854,136 NPV4 = $1,300,000 / (1.12)4 = $826,174 Selling the company in 3 years provides the highest NPV.
11.24 Replace an existing asset: Bell Mountain Vineyards is considering updating its current
manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. The Bell Mountain’s opportunity cost of capital is 10 percent, and the costs and values of investments made at different times in the future are as follows: Year
Cost
Value of Future Savings (at time of purchase)
28
0
$5,000
$7,000
1
4,500
7,000
2
4,000
7,000
3
3,600
7,000
4
3,300
7,000
5
3,100
7,000
When should Bell Mountain buy the new accounting system? LO 4
Solution:
The NPV of each choice is: NPV0 = Future savings – savings – Cost Cost = $7,000 - $5,000 = $2,000 NPV1 = $2,500 / (1.1)1 = $2,275 NPV2 = $3,000 / (1.1)2 =$ 2,479 NPV3 = $3,400 /(1.1)3 =$2,554 NPV4 = $3,700 / (1.1)4 = $2,527 NPV5 = $3,900 / (1.1)5 = $2,422 Therefore the company should purchase the system in year 3.
11.25 Replace an existing asset: You have a 1993 Nissan that is expected to run for another three
years, but you are considering buying a new Hyundai before the Nissan wears out. You will donate the Nissan to Goodwill when you buy the new car. The annual maintenance cost is $1,500 per year for the Nissan and $200 for the Hyundai. The price of your favorite Hyundai
29
model is $18,000, and it is expected to run for 15 years. Your opportunity cost of capital is 3 percent. Ignore taxes. When should you buy the new Hyundai? LO 4
Solution:
NPV of cost of the new car is:
NPVHyundai
1 1 15 (1.03) $18,000 ( $200) $20,387.59 0.03
EAC of the new car is: EACHyundai
(1 k )t k NPVt t (1 k ) 1 (1.03)15 (0.03)( $20, 38 $1, 70 387.59) 707.80 (1.03)15 1
Since the EAC of the new car is $1,707.8 and exceeds that of the Nissan( $1,500), you should drive the 1993 Nissan for three more years and then buy a new Hyundai.
11.26 Replace an existing asset: Assume that you are considering replacing your old Nissan with a
new Hyundai, as in the previous problem. However, the annual maintenance cost of the old Nissan increases as time goes by. It is $1,200 in the first year, $1,500 in the second year, and $1,800 in the third year. When should you replace it with the new Hyundai in this case? LO 4
Solution:
30
(1 k )t EACHyundai k NPVt t (1 k ) 1 (1.03)15 (0.03)( $20, 38 $1, 70 387.59) 707.80 (1.03)15 1 The EAC of the Hyundai remains at $1,707.80, as calculated above. Comparing this amount with the annual maintenance costs of the Nissan and you will see that in year 2 it is cheaper to drive the Nissan, but in year 3 it is cheaper to drive the Hyundai. Therefore, the optimal time to replace the old car ca r is at the end of year 2.
11.27 When to harvest an existing asset: Anaconda Manufacturing Company currently own a mine
that is known to contain a known amount of gold. Since Anaconda does not have any goldmining expertise, the company plans to sell the entire mine and base the selling price on a fixed multiple of the spot price for gold at the time of the sale. Analysts at Anaconda have forecast the price spot for gold and have determined that the price p rice will increase by 14 percent, 12 percent, 9 percent, and 6 percent during the next one, two, three, and four years, respectively. If Anaconda’s If Anaconda’s opportunity cost of capital is 10 percent, what is the optimal time for Anaconda to sell the mine? LO 5
Solution:
The rate of gold price appreciation ap preciation is greater than the opportunity cost of capital ca pital for the next two years and then it drops below b elow the opportunity cost of capital. Therefore, Anaconda should sell the gold at the beginning of the third year (or at the end of the second year).
31
11.28 Replace an existing asset: You are thinking about delivering pizzas in your spare time. Since
you must use your own car c ar to deliver the pizzas, you will wear out your current car one on e year earlier, which is one year from today, than if you did not take on the delivery job. You estimate that when you purchase a new car, regardless of when that occurs, you will pay $20,000 for the car and it will last you five years. If your opportunity cost of capital is 7 percent, what is the opportunity cost of using your car to deliver pizzas? LO 4
Solution:
0.07))5 (1 0.07 EAC New CAr 0.07 $20, 000 5 $4, 877.81 ( 1 0 . 0 7 ) 1 Therefore, the opportunity cost of wearing out your car a year earlier is
NPVUsing your car $4,877.81 $4,877.81// (1.07)1 $4,558, $4,558, 70
ADVANCED
®
SlimBod y, Inc., a retailer of the exercise machine Slimbody6 and 11.29 You are the CFO of SlimBody, related accessories. Your firm is considering opening up a new n ew store in Los Angeles. The store will have a life of 20 years. It will generate annual sales of 5,000 exercise ex ercise machines, and the price of each machine is $2,500. The annual sales of accessories will be $600,000, and the operating expenses of running the store, including labor and rent, will amount to 50 percent of the revenues from the exercise machines. The initial investment in the store will equal $30 32
million and will be fully depreciated on a straight-line basis over the 20-year life of the store. Your firm will need to invest $2 million in additional working capital immediately, and recover it at the end of the th e investment. Your firm’s marginal tax rate is 30 percent. The opportunity cost of opening up the store is 10 percent. What are the incremental increm ental cash flows from this project at the beginning of the project p roject as well as in years 1-19 and 20? Should you approve it? LO 1
Solution:
Step One: Initial outlay = $30,000,000 + $2,000,000 (WC requirement) = $32,000,000 Step Two: ΔNR for years 11- 20: $2,500 × 5,000 machines = $12,500,000 plus $600,000 = $13,100,000 Step Three: ΔOpExp for years 11- 20: $1,250 × 5,000 machines = $6,250,000 Step Four: ΔD&A for years 11- 20: $30,000,000 / 20 years = $1,500,000 / year Step Five: Plug information into the text book template as below. Step Six: Yr 20 recapture of WC requirements that were funded in year 0.
Yrs 1-19 1
ΔNR Δ
O
Δ
E
Δ
D
Δ
E
(
1
p
B
E
t
T
I
,
-
D
A
6
A
B
-
x
I
&
3
5
6
,
-
T
1
2
8
1
,
0
5
5
5
3
0
0
0
0
5
,
,
0
0
,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
)
Δ
N
O
Δ
D
&
Δ
C
F
Δ
C
a
Δ
A
W
Δ
F
C
Yr 20
0
P
A
T
3
A
O
p
E
x
-
3
C
F
-
-
3
,
7
4
5
,
0
.
0
1
3
,
-
6
6
,
-
5
1
2
8
1
,
0
5
5
5
3
0
0
0
0
5
,
,
0
0
,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
3
,
7
4
5
,
0
.
0
7
0
1
,
5
0
0
,
0
0
0
1
,
5
0
0
,
0
0
0
5
,
2
4
5
,
0
0
0
5
,
2
4
5
,
0
0
0
0
,
0
0
0
,
0
0
0
0
2
,
0
0
0
,
0
0
0
0
2
,
0
0
0
,
0
0
0
2
,
0
0
0
,
0
0
0
0
7
,
2
4
5
,
0
0
0
5
,
2
4
5
,
0
0
0
Therefore the NPV of the project is:
33
1 1 (1.10)19 NPV $32,000,000 $32, 000,000 $5, $5, 245 245,, 000 0.10 $12,950,928.97
1 7, 245,, 000 7,245 (1.10)20
You should approve the project since it has a positive NPV. Alternative Solution:
Incremental cash flows in year 0 is: FCF0
= -$30,000,000-$2,000,000= -$32,000,000
Annual incremental cash flows through the life of the investment are: FCFt
= ($2,500 ×$2,500+$600,000) × (1-0.3)+0.3 ×$1,500,000 = $5,245,000
Additional incremental cash flows at the end of the project are: $2,000,000 Therefore the NPV of the project is:
1 1 (1.10)19 NPV $32,000,000 $32, 000,000 $5, $5, 245 245,, 000 0.10 $12,950,928.97
1 7, 245,, 000 7,245 (1.10)20
You should approve the project since it has a positive NPV.
11.30 Merton Shovel Corporation has decided to bid for a contract to supply shovels to the
Honduran Army. The Honduran Army intends to buy 1000 shovels shovels per year for the next three years. To supply these shovels, Merton Merton will have to acquire manufacturing manufacturing equipment at a cost of $150,000. This equipment will be depreciated on a straight-line basis over its its fiveyear lifetime. At the end of the third year year Merton can sell the equipment for exactly its book value ($60,000). Additional fixed costs will be $36,000 per year and variable costs will will be $3.00 per shovel. An additional investment of $25,000 in net working capital will be required required when the project is initiated. This investment will be recovered at the end of the third year.
34
Merton Shovel has a 35% marginal tax rate and a 17% required rate of return on the project. What is the lowest possible per shove bid price that Merton can submit for the contract? LO 1
Solution
Year 0 cash flow = Cap Exp + Add WC = -$150,000 – -$150,000 – $25,000 $25,000 = -$175,000 Year 3: Cap Exp + Add WC = $60,000 + $25,000 = $85,000 We can’t directly solve for CF Opns since revenue depends on what we are going to charge per shovel. Since CF Opns must be the same in years 1, 2, and 3 of the project this is a three year annuity and we can solve for the total value of CF Opns as: Present value of CF Opns = CF Opns × [(1-1/(1.17)3)/.17] NPV of the shovel contract = -$175,000 + $85,000/(1.17)3 + OCF [(1-1/(1.17)3)/.17] Set NPV = 0 and solve for CF Opns: CF Opns = $55,181 Now solve CF Opns formula for the price of each shovel (P): CF Opns = [Revenue – [Revenue – OpEx OpEx – – D&A) D&A) × (1 – (1 – t )] )] + D&A $55,181 = [(P × 1000) – 1000) – ($3.00 ($3.00 × 1000) – 1000) – $36,000 $36,000 - $30,000] × (1-0.35) + $30,000 P = $107.74 This is the minimum bid price for a shovel. If Merton Shovel charges less than this per shovel the NPV of the contract will be less than zero.
11.31 Rocky Mountain Lumber, Inc., is considering purchasing a new wood saw that costs $50,000.
The saw will generate revenues of $100,000 per year for five years. The cost of materials and labor needed to generate these revenues will total $60,000 per year, and other cash expenses will be $10,000 per year. The machine is expected to sell for $1,000 at the end of its five-year life and will be depreciated on a straight-line basis over over five years to zero. Rocky Mountain’s tax rate is 34 percent, and its opportunity cost of capital is 10 percent. Should the company purchase the saw? Explain why or why not.
35
LO 1
Solution:
Step One: Initial outlay = $50,000 Step Two: ΔNR for years 11- 5: $100,000 Step Three: ΔOpExp for years 11- 5: $60,000 + $10,000 = $70,000 Step Four: ΔD&A for years 11- 5: $50,000 / 5 years = $10,000 / year Step Five: Plug into the text book template as below. Step Six: Yr 5: Capital recovery = $1,000 $ 1,000 – – (0.34 (0.34 × 1,000 gain on sale) = $660.
Yrs 1-4 1
ΔNR Δ
O
Δ
E
Δ
D
Δ
E
(
1
p
B
E
I
&
t
T
-
D
I
0
7
A
3
A
B
-
x
0
-
T
0
N
O
Δ
D
&
Δ
C
F
Δ
C
a
Δ
A
W
Δ
F
C
0
0
0
0
0
0
,
0
0
0
0
0
0
,
0
0
0
6
6
0
0
0
0
)
Δ
,
0
1
2
Yr 5
0
P
A
T
1
A
O
p
E
x
-
5
0
,
0
0
C
F
-
5
0
,
0
0
3
,
.
2
0
-
0
7
3
-
,
0
0
1
2
,
0
0
,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
6
0
0
0
1
3
,
.
2
1
0
,
0
0
0
1
0
,
0
0
0
2
3
,
2
0
0
2
3
,
2
0
0
6
6
0
0
0
0
0
0
1
2
3
,
2
0
0
0
2
3
,
8
6
0
Therefore, NPV of investment is:
NPV $50, $50, 000
$23 $23,200 $23 $23, 200 200 $23 $23, 200 200 $23 $23,200 $23 $23,860 ,860 (1.10) (1.10) 2 (1.10)3 (1.10)4 (1.10)5
$38,356 Since NPV > 0, the company should buy the machine.
Alternatively:
The annual operating cash flows from year 1 to 5 are: ($100,000-$60,000-$10,000) ×1-0.34) + 0.34 ×10,000=$23,200 The after-tax terminal value in year 5 is: $1,000 - (0.34)($1,000-$0) = $660 36
Therefore, NPV of investment is: NPV $50,000
$23 $23,200 $23 $23,200 $23 $23,200 $23 $23,200 $23 $23,860 ,860 2 3 4 (1.10) (1.10) (1.10) (1.10) (1.10)5
$38,356 Therefore the company should buy the machine.
11.32 A beauty product company is developing a new fragrance named Happy Forever. There is a
probability of 0.5 that consumers will love Happy Forever, and in this case, annual sales will be 1 million bottles; a probability of 0.4 that consumers will find find the smell acceptable and annual sales will be 200,000 bottles; and a probability of 0.1 that consumers co nsumers will find the smell weird and annual sales will be only onl y 50,000 bottles. The selling price is $38, $38 , and the variable cost is $8 per bottle. There is a fixed production cost of $1 million per year, and depreciation will be $1.2 million. Assume that the marginal tax rate is 40 percent. What are the expected annual incremental incremen tal cash flows from the new fragrance? LO 1
Solution:
Step One: Expected sales units: (0.5) ×1,000,000 + (0.4) ×200,000 + (0.1) ×50,000 = 585,000 units Step Two: ΔNR: 585,000 units × $38 = $22,230,000 Step Three: ΔOpExp: 585,000 units x $8 + $1,000,000 = $5,680,000 Step Four: ΔD&A: $1,200,000 Step Five: Plug into the text book template as below.
37
= = x = + = =
ΔNR ΔOpEx ΔEBITDA ΔD&A ΔEBIT (1-t) ΔNOPAT ΔD&A ΔCFO ΔCapEx ΔAWC ΔFCF
22,230,000 -5,680,000 16,550,000 -1,200,000 15,350,000 0.60 9,210,000 1,200,000 10,410,000 0 0 10,410,000
Alternatively, the expected annual incremental cash flows are:
(((0.5 ×1,000,000+0.4 ×200,000+0.1 ×50,000) × ($38-$8)) -1,000,000) × (1 - 0.4)
+1,200,000 ×0.4 = $10,410,000
11.33 Great Fit, Inc., is a company that makes clothing. The company has a product line that
produces women’s tops of regular sizes. The same machine could be used to produce petite sizes as well. However, the life of the machines will be reduced from four more years to two more years if the petite size production is added. The cost of identical ide ntical machines with a life of eight years is $2 million. Assume the opportunity cost of capital is 8 percent. What is the opportunity cost of adding petite sizes? LO 4
Solution:
The opportunity cost is the incremental costs of the machine in year 3 and year 4 if petite sizes are in production. The EAC of the machine is:
38
(1 k )t EACA k NPVt t (1 k ) 1 (1.08)8 (0.08)( $2, 00 $348, 02 000, 00 000) 029.52 (1.08)8 1
The present value of such cost in year 3 and year 4 is:
NPV
$348,029 $348,029.5 .52 2 (1.08)3
$348,029 $348,029.52 .52 (1.08) 4
$532,089.14
11.34 Biotech Partners LLC has been farming a new strain of radioactive-material-eating bacteria
that the electrical utility industry can use to help d ispose of its nuclear waste. Two opposing effects are affecting Biotech’s decision of when to harvest the bacteria. The bacteria are currently growing at a 22 percent annual rate, but due to known competition from other top firms, Biotech analysts estimate that the price for the bacteria will fluctuate according to the scale below. If the opportunity cost of capital is 10 percent, then when should shou ld Biotech harvest the entire bacteria colony at one time? Year
Change in Price Due to Competition (5)
1
5%
2
-2
3
-8
4
-10
5
-15
6
-25
LO 5
39
Solution:
Change in revenue: Yr 1
(1.05)(1.22) = 1.2810 or 28.1%
Yr 2
(0.98)(1.22) = 1.1956 or 19.56%
Yr 3
(0.92)(1.22) = 1.1224 or 12.24%
Yr 4
(0.9)(1.22) = 1.0980 or 9.80%
Yr 5
(0.85)(1.22) = 1.037 or 3.70%
Yr 6
(0.75)(1.22) =- 0.9150 or -8.50%
Since the change in revenue is higher for the first two years, Biotech should shoul d sell its bacteria colony at the beginning of the third year or at the end of the second year.
ex isting production line with a new line 11.35 ACME manufacturing is considering replacing an existing that has a greater output capacity and operates with less labor than the existing line. The new line would cost $1 million, have a five-year life, and would be depreciated using MACRS over three years. At the end of five years, the new line could be sold as scrap for $200,000 (in year 5 dollars). Because the new line is more automated, it would require fewer operators, resulting in a saving of $40,000 per year before tax and unadjusted for inflation (in today’s dollars). Additional sales with the new machine are expected ex pected to result in additional net cash inflows, before tax, of $60,000 per year (in year (in today’s dollars). If ACME invests in the new line, a one-time investment of $10,000 in additional working capital will be required. The tax rate is 35 percent, the opportunity cost of capital is 10 percent, and the annual rate of inflation is 3 percent. What is the NPV of the new production line? 40
LO 4
Solution: t =
0.35
rate =
0.1
Buy the New Line 0
1
2
3
4
5
(Revenue Op Exp)(1-t)
$66,950
$68,959
$71,027
$73,158
plus Tax x Deprec
$116,655
$155,575
$51,835
$25,935
minus Cap Exp
$1,000,000
$75,353
$(200,000)
$(70,000)
plus tax on Salvage
minus Add WC
$10,000
Net Cash Flows
$(1,010,000)
$183,605
$224,534
$122,862
$99,093
$215,353
PV of Net Cash Flows
$(1,010,000)
$166,914
$185,565
$92,308
$67,682
$133,717
Net Present Value
$(10,000)
$(363,814)
11.36 The alternative to investing in the new production line in Problem 11.31 is to overhaul the
existing line, which currently has both a book value and a salvage value of $0. It would cost $300,000 to overhaul the existing line, but this expenditure would extend its useful life to five 41
years. The line would have a $0 salvage value at the end of five years. The overhaul outlay would be capitalized and depreciated using MACRS over three years. Should ACME replace or renovate the existing line? LO 4 t =
0.35
rate =
0.1
Renovate Old Line 0
1
2
3
4
$34,997
$46,673
$15,551
$7,781
5
(Revenue Op Ex)(1-t )
plus Tax × Deprec
minus Cap Exp
$300,000
plus tax on Salvage
minus Add WC
Net Cash Flows
$(300,000)
$34,997
$46,673
$15,551
$7,781
$0
PV of Net Cash Flows
$(300,000)
$31,815
$38,572
$11,683
$5,314
$0
Net Present Value
$(212,615)
NPVnew - NVPold
$(151,199)
Renovating the old line is less costly. 42
CF A Pr oble oblems ms
11.37. FITCO is considering considering the purchase of new equipment. The equipment costs $350,000, and an additional $110,000 is needed to install it. The equipment will be depreciated straight-line to zero over a five-year life. The equipment will generate additional annual revenues of $265,000, and it will have annual cash operating expenses of $83,000. The equipment will be sold for $85,000 after five years. An inventory inventor y investment of $73,000 is required during the life of the investment. FITCO is in the 40 percent tax bracket and its cost of capital is 10 percent. What is the project NPV?
a.
$47,818
b.
$63,658
c.
$80,189
d.
$97,449
LO 4 Solution:
d is correct.
Outlay = FCInv + NWCInv – NWCInv – Sal0 Sal0 + T × (Sal0 – (Sal0 – B0) B0) Outlay = (350,000 + 110,000) + 73,000 – 73,000 – 0 0 + 0 = $533,000 The installed cost is $350,000 + $110,000 = $460,000, so the annual depreciation is $460,000/5 = $92,000. The annual after-tax operating cash flow for Years 1 – 5 is CF = (S – (S – C C – D)(1 – D)(1 – – T) T) + D = (265,000 – (265,000 – 83,000 83,000 – – 92,000)(1 92,000)(1 – – 0.40) 0.40) + 92,000 CF = $146,000
The terminal year after-tax non-operating cash flow in Year 5 is TNOCF = Sal5 + NWCInv – NWCInv – T(Sal5 T(Sal5 – – B5) B5) = 85,000 + 73,000 – 73,000 – 0.40(85,000 0.40(85,000 – – 0) 0) TNOCF = $124,000 The NPV is 43
NPV 533, 533, 000
5
t 1
146,00 146,000 0 124,00 124,000 0 1.10t
1.105 = $97,449
11.38. After estimating a project’s NPV, the analyst is advised that the fixed capital capital outlay will be revised upward by $100,000. The fixed capital outlay is depreciated straight-line over an eight-year life. The tax rate is 40 percent and the required rate of return is 10 1 0 percent. No changes in cash operating revenues, cash operating expenses, or salvage value are expected. What is the effect on the project NPV?
a.
$100,000 decrease
b.
$73,325 decrease
C.
$59,988 decrease
d.
No change
LO 4 Solution:
B is correct. The additional annual depreciation is $100,000/8 = $12,500. The depreciation tax savings is 0.40 ($12,500) = $5,000. The change in project NPV is 8
100, 000 t 1
5,000 000 26, 67 675 $73, 325 100, 00 (1.10)t
11.39. When assembling the cash flows to calculate an NPV or IRR, the project’s after -tax -tax interest expenses should be subtracted from the cash flows for
a.
the NPV calculation, but not the IRR calculation.
b.
the IRR calculation, but not the NPV calculation.
c.
both the NPV calculation and the IRR calculation.
44
d.
neither the NPV calculation nor the IRR calculation.
LO 1 Solution:
D is correct. Financing costs are not subtracted from the cash flows for either the NPV or the IRR. The effects of financing costs are captured in the discount rate used.
Sample Test Problems
11.1
You purchased 100 shares of stocks of an oil company, Texas Energy, Inc., at $50 per share. The company has 1 million shares outstanding. Ten days later, Texas Energy announced an investment in an oil field in east Texas. Tex as. The probability of the investment being successful and generating NPV of $10 million is 0.2; the probability of the investment will be a failure and generate a negative NPV of negative $1 million is 0.8. How would you expect the stock price to change upon the company’s announcement of the investment?
Solution:
The expected change in the stock price should be equal to the expected NPV of the project divided by the number of shares outstanding. The expected NPV of the project is 0.2 ×10,000,000 + 0.8 × ( – – 1,000,000), 1,000,000), such that: Change in stock price = (0.2 ×10,000,000 + 0.8 ×(-1,000,000)) / 1,000,000 shares = $1.2/share Stock price of Texas Energy, Inc., will increase by $1.20 upon the announcement of the investment.
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11.2
A chemical company is considering buying bu ying a magic fan for its plant. The magic fan is expected to work forever and to help cool the machines in the plant and hence reduce their maintenance costs by $4,000 per year. The cost of the fan is $30,000. The appropriate discount rate is 10 percent, and the marginal tax rate is 40 percent. Should the company buy the magic fan?
Solution:
The after-tax saving of maintenance costs is: $4,000 $4,0 00 × (1 – (1 – 40%) 40%) / 10% = $24,000, which is less than the cost. Therefore the company should not buy the fan. If one fails to take into consideration the tax effect on maintenance costs, the opposite conclusion will be made. Therefore it is important to remember our Rule 5 for incremental cash flow calculations: Include only after-tax cash flows.
11.3
Hogvertz Elvin Catering (HEC) is considering switching from its old food maker to a new Wonder Food Maker. Both food makers will remain useful for the next ten years, but the new option will generate a depreciation expense of $5,000 per year while the old food maker will generate a depreciation expense exp ense of $4,000 per year. What is the after-tax cash flow effect from deprecation of switching to the new food maker for HEC if the firm’s marginal tax rate is 40 percent and the correct discount rate is 12 percent?
Solution:
Without the benefit of other information required in the cash flow calculation table, we must isolate the cash flow effect of depreciation for a firm. We therefore find that we have a
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deduction of D&A above the tax calculation line and an addition of D&A below the tax calculation line. This means that the net yearly after-tax effect of depreciation and amortization can be simplified to:
D & A 1 – t D & A
– D&A
D & A t D & A D & A t
Using that result, we find that the net yearly effect of depreciation and amortization of cash flow is: (D&A) × t = ($5,000 – ($5,000 – $4,000) $4,000) × 0.4 = $400 and so the present value of the total after-tax cash flow effect from depreciation can be found as follows: $400 × (((1.12)10 - 1) / ((1.12)10 × 0.12)) = $400 × 5.650223 = $2,260.09
11.4
The Long-Term Financing Company Compan y has identified an alternative project that is similar to a project currently under consideration in all respects except one. That is, the new project will reduce the need for working capital by $10,000 during the 30-year life of the project. The firm’s cost of capital is 18 18 percent, and the marginal corporate tax rate for the firm is 34 percent. What is the after-tax present value of this new alternative project?
Solution:
Because working capital has no effect on the income statement of the firm, there are a re no tax effects from the two cash flows associated with the working capital change. Therefore, the after-tax present value of the alternative is: $10,000 – $10,000 – $10,000 $10,000 × (1.18)-30 = $10,000 – $10,000 – ($10,000) ($10,000) × 0.006975 = $9,930.25
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11.5
Choice Masters must choose between two projects of unequal lives. Project 1 has a NPV of $50,000 and will be viable for five years. The discount rate for project 1 and project 2 is 10 percent. Project 2 will be viable for seven years. In order for Choice Master to be indifferent between the two projects, what must the NPV of project 2 be?
Solution:
The EAC for project 1 is:
1 0.15 0.1 $50, 000 $13,189.87 5 1 0.1 1 which means that project 2 must also a lso generate cash flow of $13,189.87 per year for seven years. Therefore, the NPV of project 2 must be
1 1 1 $64, 213.83 7 0.1 1 0.1
$13,189.87
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