Chapte 6 FIN

real discount rate formula

( (1 + Nominal Discount Rate) / (1 + Inflation Rate) ) -1

If a firm's short-term assets are $150,000, its total assets are $320,000, and its short-term liabilities are $80,000, what is its net working capital?

$70,000 Reason: $150,000 - 80,000 = $70,000

(Still rule one) Accountants start with dollars in and dollars out but to obtain accounting income adjust this in two principles way:

1. Capital Expenses - deducts current expenses but does not deduct capital expenses. When calculating NPV, state capital expenditures when they occur, not later when they show up as depreciation. 2. Working Capital Cash outlay to produce goods in period 1 becomes an investment in inventory and then in period 2 when the sale occurs you invest in receivables and pull from inventory investments.

When trying to decide what to discount for both tangible and intangible assets, what should you discount?

1. Discount Cash flows, not profits 2. discount incremental cash flows 3. Treat inflation consistently 4. Separate investment and financing decisions 5. Forecast and deduct taxes

Rule 2: Discount Incremental Cash Flows The value of a project depends on all the additional cash flows that follow from project acceptance.

1. Include All Incidental Effects 1B: It is important to consider a project's effects on the remainder of the firm's business. 2.Do Not Confuse Average with Incremental Payoffs 2B: occasionally, you will encounter turnaround opportunities in which the incremental NPV from investing in a loser is strongly positive. Conversely, it does not always make sense to throw good money after good. A division with an outstanding past profitability record may have run out of good opportunities. 3. Forecast Product Sales but also Recognize After-Sales Cash Flows 3B Many manufacturing companies depend on the revenues that come after their products are sold.For example, the consulting firm Accenture estimates that services and parts typically account for about 25% of revenues and 50% of profits for auto companies.3 4.Include Opportunity Costs --> the cash it could generate for the company if the project were rejected and the resource were sold or put to some other productive use. --> Prompts us to warn you against judging projects on the basis of "before versus after." The proper comparison is "with or without. --> where the resource can be freely traded, its opportunity cost is simply equal to the market price. 5. Forget Sunk Costs Because sunk costs are bygones, they cannot be affected by the decision to accept or reject the project, and so they should be ignored. 6. Beware of Allocated Overhead Costs the accountant's objective is not always the same as the investment analyst's. Now our principle of incremental cash flows says that in investment appraisal we should include only the extra expenses that would result from the project. A project may generate extra overhead expenses; then again, it may not. We should be cautious about assuming that the accountant's allocation of overheads represents the true extra expenses that would be incurred. 7. Remember Salvage Value If the equipment is sold, you must pay tax on the difference between the sale price and the book value of the asset. The salvage value ( net of any taxes) represents a positive cash flow to the firm. Some projects have significant shutdown costs, in which case the final cash flows may be negative

If the nominal discount rate is 4 percent and the annual rate of inflation is 2 percent, what is the real discount rate?

1.96%

Net working capital ( often referred to simply as working capital) is the difference between a company's short-term assets and liabilities.

Accounts receivable and inventories of raw materials, work in progress, and finished goods are the principal short-term assets. The principal short-term liabilities are accounts payable (bills that you have not paid) and taxes that have been incurred but not yet paid.

Using your personal savings to invest in your business is considered to have an ______________ ____________ because you are giving up the use of these funds for other investments or uses, such as, a vacation or paying off a debt.

Blank 1opportunity Blank 2: cost

Rule 1: Discount cash flows, not profits

Cash flow is: the difference between cash recieved and cash paid out. (Common Mistake is confusing this with accounting income.)

Which of the following is given greater importance in capital budgeting problems in corporate finance?

Cash flows

Which of the following should be discounted when determining the feasibility of a capital budgeting project(s)?

Cash flows Reason: Cash flows should be discounted when determining the feasibility of a capital budgeting project. Earnings are accrual-based, so they do not give an accurate representation of project value

Rule 3: Treat Inflation Consistently

Discount nominal cash flows at a nominal discount rate. Discount real cash flows at a real rate. Never mix real cash flows with nominal discount rates or nominal flows with real rates. Investors take inflation into account when they decide what is an acceptable rate of interest. If the discount rate is stated in nominal terms, then consistency requires that cash flows should also be estimated in nominal terms, taking account of trends in selling price, labor and materials costs, and so on. This calls for more than simply applying a single assumed inflation rate to all components of cash flow. Labor costs per hour of work, for example, normally increase at a faster rate than the consumer price index because of improvements in productivity. Tax savings from depreciation do not increase with inflation; they are constant in nominal terms because tax law in most countries allows only the original cost of assets to be depreciated. Of course, there is nothing wrong with discounting real cash flows at a real discount rate. In fact, this is standard procedure in countries with high and volatile inflation. If Given Real Cash Flows: It would be inconsistent to discount these real cash flows at the 15% nominal rate. You have two alternatives: Either restate the cash flows in nominal terms and discount at 15%, or restate the discount rate in real terms and use it to discount the real cash flows. --> Example: Assume that inflation is projected at 10% a year. Then the cash flow for year 1, which is $35,000 in current dollars, will be35,000 x 1.10 = $38,500 in year-I dollars.

Ms. T. Potts, the treasurer of Ideal China, has a problem. The company has just ordered a new kiln for $400,000. Of this sum, $50,000 is described by the supplier as an installation cost. Ms. Potts does not know whether the company will need to treat this cost as a tax-deductible current expense or as a capital investment. In the latter case, the company could depreciate the $50,000 straight-line over five years.How will the tax authority's decision affect the after-tax cost of the kiln? The tax rate is 25%, and the opportunity cost of capital is 5%. (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)

Explanation If the $50,000 installation cost is expensed at the end of year 1, the value of the tax shield is:PV = ($50,000 × 0.25) / (1 + 0.05)PV = $11,905If the $50,000 cost is capitalized and then depreciated using a five-year straight-line depreciation, the value of the tax shield is:PV = ($10,000 × 0.25) × ((1 / 0.05) − {1 / [0.05 × (1 + 0.05)5]})PV = $10,824If the installation cost can be expensed, then the tax shield is larger, which means the after-tax cost is smaller.

Which of the following should be treated as incremental cash flows when deciding whether to invest in a new manufacturing plant? The site is already owned by the company, but existing buildings would need to be demolished.

Explanation The cost of a new access road put in last year is a sunk cost. A proportion of the cost of leasing the president's jet airplane is an overhead cost. Future depreciation of the new plant is a non-cash expense. Money already spent on engineering design of the new plant is a sunk cost. check all that apply 2 Lost earnings on other products due to executive time spent on the new facility. checked The reduction in the corporation's tax bill resulting from tax depreciation of the new plant. checked The market value of the site and existing buildings. checked Money already spent on engineering design of the new plant. unchecked The initial investment in inventories of raw materials. checked Future depreciation of the new plant. unchecked The cost of a new access road put in last year. unchecked Demolition costs and site clearance.checked A proportion of the cost of leasing the president's jet airplane .unchecked

As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $50,000. Its operating costs are $20,000 a year, but at the end of five years, the machine will require a $20,000 overhaul (which is tax deductible). Thereafter, operating costs will be $30,000 until the machine is finally sold in year 10 for $5,000.The older machine could be sold today for $25,000. If it is kept, it will need an immediate $20,000 (tax-deductible) overhaul. Thereafter, operating costs will be $30,000 a year until the machine is finally sold in year 5 for $5,000.Both machines are fully depreciated for tax purposes. The company pays tax at 21%. Cash flows have been forecasted in real terms. The real cost of capital is 12%.a. Calculate the equivalent annual costs for selling the new machine and for selling the old machine. B. Which machine should United Automation sell?

Explanation a.In order to solve this problem, we calculate the equivalent annual cost for each of the two alternatives.Alternative 1—Sell the new machine: If we sell the new machine, we receive the after-tax cash flow from the sale of the new machine, pay the costs associated with keeping the old machine, and receive the after-tax proceeds from the sale of the old machine at the end of year 5.NPV1 = [$50,000 − $20,000 − $30,000 × ((1 / 0.12) − {1 / [0.12(1 + 0.12)5]}) + $5,000 / (1 + 0.12)5] × (1 − 0.21)NPV1 = −$59,491.86EAC1 = −1 × (−$59,491.86/ ((1 / 0.12) − {1 / [0.12(1 + 0.12)5]}))EAC1 = $16,503.62 Alternative 2—Sell the old machine: If we sell the old machine, we receive the after-tax cash flow from the sale of the old machine, pay the costs associated with keeping the new machine, and receive the after-tax proceeds from selling the new machine at the end of year 10.NPV2 = [$25,000 − $20,000 × ((1 / 0.12) − {1 / [0.12(1 + 0.12)5]}) − $20,000 / (1 + 0.12)5 − ($30,000 × ((1 / 0.12) − {1 / (0.12(1 + 0.12)5]}) / (1 + 0.12)5) + [$5,000 / (1 + 0.12)10]] × (1 − 0.21)NPV2 = −$93,376.10EAC2 = −1 × (−$93,376.10/ ((1 / 0.12) − {1 / [0.12(1 + 0.12)10]})EAC2 = $16,526.09 b.Thus, the least-expensive alternative is to sell the new machine and keep the old machine because this alternative has the lowest equivalent annual cost (but not by much). One key assumption underlying this result is that, whenever the machines have to be replaced, the replacement will be a machine that is as efficient to operate as the machine being replaced.

Machines A and B are mutually exclusive and are expected to produce the following real cash flows: The real opportunity cost of capital is 10%.a. Calculate the NPV of each machine. b. Calculate the equivalent annual cash flow from each machine.

Explanation a.NPVA = −$100,000 + $110,000 / (1 + 0.10) + $121,000 / (1 + 0.10)2NPVA = $100,000 NPVB = −$120,000 + $110,000 / (1 + 0.10) + $121,000 / (1 + 0.10)2 + $133,000 / (1 + 0.10) 3NPVB = $179,925 b.EACFA = $100,000 / ((1 / 0.10) − {1 / [0.10 × (1 + 0.10)2]}) EACFA = $57,619 EACFB = $179,925 / ((1 / 0.10) − {1 / [0.10 × (1 + 0.10)3]})EACFB = $72,350 c.Select Machine B because it has the higher equivalent annual cash flow.

What is the real interest rate if the nominal annual interest rate is 10 percent and the annual inflation rate is 4 percent?

Reason: (1.10/1.04) - 1 = 5.77% Correct Answer 5.77%

The Borstal Company has to choose between two machines that do the same job but have different lives. The two machines have the following costs: YearMachine AMachine B 0 $40,000 $50,000 1. 10,000 8,000 2. 10,000 8,000 3 10,000+ replace. 8,000 4 Machine B 8,000+ replace These costs are expressed in real terms. Suppose you are Borstal's financial manager. If you had to buy one or the other machine and rent it to the production manager for that machine's economic life, what annual rental payment would you have to charge? Assume a 6% real discount rate and ignore taxes. b. Which machine should Borstal buy? C. If there is steady 8% per year inflation, what will be the annual rental payment for machine B for the second year?

Explanation a.PVA = −$40,000 + (−$10,000) / (1 + 0.06) + (−$10,000) / (1 + 0.06)2 + (−$10,000) / (1 + 0.06)3PVA = −$66,730.12 EACA = −1 × [−$66,730.12 / ((1 / 0.06) − {1 / [0.06 × (1 + 0.06)3]})]EACA = $24,964.39PVB = −$50,000 + (−$8,000) / (1 + 0.06) + (−$8,000) / (1 + 0.06)2 + (−$8,000) / (1 + 0.06)3 + (−$8,000) / (1 + 0.06)4PVB = −$77,720.84EACB = −1 × [−$77,720.84 / ((1 / 0.06) − {1 / [0.06 × (1 + 0.06)4]})]EACB = $22,429.57 Annual rental is $24,964.39 for Machine A and $22,429.57 for Machine B. b.Borstal should buy Machine B.c.The payments would increase by 8 percent per year.For example, for Machine B, rent for the first year would be $22,429.57; rent for the second year would be ($22,429.57 × 1.08) = $24,223.94.

Rule 4: Separate Investment and Financing Decisions

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 on the debt as cash outflows. Regardless of the actual financing, you should view the project as if it were all-equity-financed, treating all cash outflows required for the project as coming from stockholders and all cash inflows as going to them.

Calculate the equivalent annual cash flow from each machine

Must be done with real rates

Machine B is expected to produce the following real cash flows: Cash Flows ($ thousands)Machine Machine C was purchased five years ago for $200,000 and produces an annual real cash flow of $80,000. It has no salvage value but is expected to last another five years. The company can replace machine C with machine B either now or at the end of five years.The real opportunity cost of capital is 10%.When should the company replace machine C?

NPVB = −$120,000 + $110,000 / (1 + 0.10) + $121,000 / (1 + 0.10)2 + $133,000 / (1 + 0.10)3NPVB = $179,925 EACFB = $179,925 / ((1 / 0.10) − {1 / [0.10 × (1 + 0.10)3]}) EACFB = $72,350In this problem, we must ignore the sunk costs and past real cash flows and focus on future cash flows.Machine C is expected to last another five years and produces a real annual cash flow of $80,000.Since Machine C's real annual cash flow exceeds Machine B's equivalent annual cash flow, the company should wait and replace Machine C at the end of five years.

What is the difference between nominal cash flow and real cash flow? Multiple choice question.

Nominal cash flow is the actual dollars to be received. Real cash flow refers to the cash flow's purchasing power.

Mr. Art Deco will be paid $100,000 one year hence. This is a nominal flow, which he discounts at an 8% nominal discount rate:PV = $100,000 / 1.08 = $92,593The inflation rate is 4%.Calculate the PV of Mr. Deco's payment using the equivalent real cash flow and real discount rate. (

Real cash flow = $100,000 / (1 + 0.04) = $96,154r = (1 + 0.08) / (1 + 0.04) - 1 = 0.03846, or 3.846%PV = $96,154 / (1 + 0.03846) = $92,593

Opportunity costs are classified as ____ costs in project analysis.

Reason: A sunk cost is a cost that has already been made and can't be recovered. Opportunity costs are the costs of an alternative investment. While opportunity costs are not shown in accounting, they are relevant and should be considered in analyzing a project. Correct Answer relevant

True or false: It is inappropriate to ignore all incidental effects that a project has on the firm's existing business.

Reason: All incidental effects should be taken into consideration when calculating incremental cash flows. Correct Answer True

True or false: Corporate finance techniques emphasize the importance of cash flows rather than accounting income.

Reason: Financial models use cash flows rather than accounting income. Accounting income is often based on numbers that can be easily manipulated. Correct Answer True

Which of the following is an example of an opportunity cost?

Rental income likely to be lost by using a vacant building for an upcoming project Money spent on advertising to take advantage of opportunities in the market Reason: Money spent on advertising is not an opportunity cost. It is an actual cash flow associated with the product(s) being advertised. Lowering taxes by increasing depreciation expenses Reason: This is an actual cash flow, not an opportunity cost. Correct Answer Rental income likely to be lost by using a vacant building for an upcoming project

What is net working capital?

Short-term assets minus short-term liabilities

Rule 5: Remember to Deduct Taxes

Taxes are an expense just like wages and raw materials. Therefore, cash flows should be estimated on an after-tax basis. Subtract cash outflows for taxes from pretax cash flows and discount the net amount.

True or false: NPV will be the different regardless of whether nominal or real cash flows are used.

True Reason: As long as nominal cash flows are discounted at the nominal rate and real cash flows are discounted at the real rate, the NPV will be the same. False Reason: As long as nominal cash flows are discounted at the nominal rate and real cash flows are discounted at the real rate, the NPV will be the same. Correct Answer False

True or false: Discounting involves determining the future value of present cash flow.

True Reason: Discounting involves determining the present value of future cash flows. False Correct Answer False

Incremental cash flows of a project are changes in a firm's cash flows that occur as a direct consequence of ____. Multiple choice question.

accepting a project Reason: Incremental cash flows of a project are changes in a firm's cash flows that occur as a direct consequence of accepting a project.

The three most important components of working capital are:

accounts payable accounts receivable inventory

The three most important components of working capital are

accounts payable inventory accounts receivable

The three most important components of working capital are all of the following except: Multiple choice question.

depreciation Reason: working capital only includes short term assets and liabilities

6.4 In Textbook Pg 152 4 Hard mutually exclusive NPV project options.

•Problem 1 The investment timing problem. Should you invest now or wait and think about it again next year? (Here, today's investment is competing with possible future investments.) ••Problem 2 The choice between long- and short-lived equipment. Should the company save money today by choosing cheaper machinery that will not last as long? (Here, today's decision would accelerate a later investment in machine replacement.) ••Problem 3 The replacement problem. When should existing machinery be replaced? (Using it another year could delay investment in more modern equipment.) ••Problem 4 The cost of excess capacity. What is the cost of using equipment that is temporarily not being used? (Increasing use of the equipment may bring forward the date at which additional capacity is required.)