Fin 305

Capital spending at the time of project inception (i.e., the "initial outlay")

+ purchase price of the new asset - selling price of the asset replaced (if applicable) + costs of site preparation, setup, and startup +/- increase (decrease) in tax liability due to sale of old asset at other than book value = net capital spending

Payback period problem Year 0: -500 Year 1: 100 Year 2: 200 Year 3: 500 Initial Cost = 500

100 + 200 + 300 = 800 800 - 500 = 300 Total - initial cost 500 - 300 = 200 Year 3 cash flow - 300 from above 200/500 = .4 200 from above/year 3 cash flow 2 years + .4 = 2.4 year payback period OR -500 + 100 + 200 = -200 -200/500 = .4 + 2 = 2.4

Year Cash Flow 0 -$ 18,800 1 11,100 2 10,000 3 6,500 What is the profitability index for the set of cash flows if the relevant discount rate is 21 percent?

11,100/1.21 + 10,000/1.21^2 + 6500/1.21^3 = 19673 19673/18800 = 1.05 (PI) the higher the discount rate the lower the PI

A project that provides annual cash flows of $17,200 for eight years costs $78,000 today. What is the NPV for the project if the required return is 7 percent?

17200*(1-(1/1.07^8))/.07 1.7182 --->(1.07^8) .582--->(1/1.7182) .418-->(1-.582) 5.9714--->(.418/.07) 102,708.5714--->(5.9714*172000) -78,000 + 102,708.5714 = 24706 NPV

Other key points

2 like ch. 10 problems Final Cash flows given (chapter 9 kind of question where you have the Free Cash Flows), 2 Mutually Exclusive Projects Best worst case scenario based on these ranges of values Graph/Crossover Point (determine NPV's at an R of 0, label crossover point, IRR's)

2. You are evaluating a project that will generate positive cash flows as follows: for 5 years, you will see cost savings of $40,000 per year; for 6 years after that, you will see cost savings of $20,000 per year; forever after that you will see cost savings of $10,000 per year. Your required return on this type of project is 15%. The tax rate is 25%. What is the maximum price you are willing to pay to undergo this project?

40,000(.75)=30,000 20,000(.75)=15,000 10,000(.75)=7,500 (30,000/.15) (1-1/1.15^5) + (15,000/.15) (1-1/1.15^6)/1.15^5 + (7500/.15)/1.15^11 100,560 + 28,224 + 50k/4.6524

An investment project has annual cash inflows of $4,000, $4,900, $6,100, and $5,300, and a discount rate of 13 percent. A) What is the discounted payback period for these cash flows if the initial cost is $6,700? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Discounted payback period_____ years B) What is the discounted payback period for these cash flows if the initial cost is $8,800? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Discounted payback period____years C) What is the discounted payback period for these cash flows if the initial cost is $11,800?

4000/1.13 + 4900/1.13^2 + 6100/1.13^3 + 5300/1.13^4 = After first 2 years you have surpassed 6700 ($7377 total) 4900/1.13^2 = 3837.41 A) 7377.24 - 6700 = 677.24 cash required in year 2 = 3837.41 - 677.24 = 3160.17 time required in year 2 = 3160.17 / 3837.41 = 0.82 Discounted payback period = year 1 + 0.82 = 1.82 years B) initial cost = 8800 This time first 3 years covers the payment (4000/1.13 + 4900/1.13^2 + 6100/1.13^3) = 11,604.85 6100/1.13^3 = 4227.6 11604.85 - 8800 = 2804.85 cash required in year 3 = 4227.60 - 2804.85 = 1422.75 time required in year 3 = 1422.75 / 4227.60 = 0.34 Discounted payback period = year 1 + year 2 + 0.34 = 2.34 years C) initial cost = 11800 This time it will take you full 4 years 5300/1.13^4 = 3250.59 14855.44 - 8800 = 3055.44 cash required in year 4 = 3250.59 - 3055.44 = 195.15 time required in year 4 = 195.15 / 3250.59 = 0.06 Discounted payback period = year 1 + year 2 + year 3 + 0.06 = 3.06 years

Market Value - Book Value

= Gain (or loss)

Net capital spending

= change in net fixed assets + depreciation Sale price at end of 5 years + (book - sales price)* tax rate

Suppose we are asked to decide whether or a new consumer product should be launched. Based on projected sales/costs, we expect that the cash flows over the 5 year life of the project will be: $2000 in the first 2 years $4000 in the next 2 years $5000 in the last year Will cost $10,000 to begin production We use 10% discount rate

=(2000/1.1) + (2000/1.1^2) + (4000/1.1^3) + (4000/1.13^4) + (5000/1.1^5)= $12,313 NPV = 12,313 - 10,000 = 2,313 GOOD PROJECT

A firm evaluates all of its projects by applying the NPV decision rule. A project under consideration has the following cash flows: Year Cash Flow 0: - 28,100 1: 12,100 2: 15,100 3: 11,100 What is the NPV for the project if the required return is 12 percent? What is the NPV for the project if the required return is 24%?

A) 12,100/1.12 + 15,100/1.12^2 + 11,100/1.12^3 = 30,741.96 30,741.96 - 28,100 = 2641.96 (NPV) Since NPV is positive you ACCEPT project B) 12,100/1.24 + 15,100/1.24^2 + 11,100/1.24^3 = 25400.37 25,400 - 28,100 = -2699.62 (NPV) Since it is negative you REJECT project

A project requires an initial investment of $1,000,000 and is depreciated straight-line to zero salvage over its 10-year life. The project produces items that sell for $1,000 each, with variable costs of $700 per unit. Fixed costs are $350,000 per year. What is the accounting break-even quantity, operating cash flow at accounting break-even, and DOL at that output level?

Accounting break-even: Q = (FC + D) / (P - V) = ($350,000 + $100,000) / ($1,000 - $700) = 1,500 units OCF = ( S - VC - FC - D) + D = (1,500 x $1,000 - 1,500 x $700 - $350,000 - $100,000) + $100,000 = $100,000 DOL = 1 + (FC / OCF) = 1 + ($350,000 / 100,000) = 4.5 1M/10 = 100k depreciation = D

Break even measures (ignore taxes)

Accounting break-even: sales volume at which NI = 0 Q = (FC + D)/(P - v) Cash break-even: sales volume at which OCF = 0 Q = (FC + OCF)/(P - v) Financial break-even: sales volume at which NPV = 0

Take gain (or loss) x (marginal tax rate) =

After tax Salvage

#5

Annual Depreciation = 490000/7 = 70000 Depreciation for 5 Years = 70000*5 = 350000 Book Value at the End of 5 Years = 490000 - 350000 = 140000 Gain on Sale of Asset = 165000 - 140000 = 25000 After Tax Cash Flow = 165000 - (25000)*.34 = 156500 Answer is 156500.

Year Cash Flow (A) Cash Flow (B) 0 -$ 29,700 -$ 29,700 1 15,100 4,650 2 13,000 10,150 3 9,550 15,900 4 5,450 17,500

At what rate would the company be indifferent between these two projects? 29700 - 29700 = 0 15,100 - 4650 = 10450 13,000 - 10,150 = 2850 9550 - 15,900 = -6350 5450 - 17500 = -12050 Take IRR of (0, 10450, 2850, -6350, -12050) = 14.25%

Avg/marginal cost

Average Cost TC / # of units Will decrease as # of units increases Marginal Cost The cost to produce one more unit Same as variable cost per unit

How to calculate OCF

Bottom-Up Approach Works only when there is no interest expense OCF = NI + depreciation Top-Down Approach OCF = Sales - Costs - Taxes Don't subtract non-cash deductions Tax Shield Approach OCF = (Sales - Costs)(1 - T) + Depreciation*T OCF = EBIT + depreciation - taxes

New Machine Initial cost = 150,000 5-year life Salvage in 5 years = 0 Cost savings = 50,000 per year 3-year MACRS depreciation Required return = 10% Tax rate = 40% Original Machine Initial cost = 100,000 Annual depreciation = 9,000 Purchased 5 years ago Book Value = 55,000 Salvage today = 65,000 Salvage in 5 years = 10,000

Buy new machine, sell old machine What are the cash flow consequences of selling the old machine today instead of in 5 years? Year 0 -Cost of new machine = 150,000 (outflow) -After-tax salvage on old machine = 65,000 - .4(65,000 - 55,000) = 61,000 (inflow) (salvage - tax(salvage-book))= AT salvage -Incremental net capital spending = 150,000 - 61,000 = 89,000 (outflow) (Initial cost - AT salvage) = NCS Year 5 -After-tax salvage on old machine = 10,000 - .4(10,000 - 10,000) = 10,000 (outflow because we no longer receive this)

CHAPTER 9

CHAPTER 9

Textbook Problem

Cash revenues =20k per year Cash costs (including taxes) = 14k per year Will wind down the business in = 8 years PPE = 2000 as salvage after 8 years Project costs 30k to launch We use 15% discount rate There are 1000 shares of stock outstanding, what will be the effect on price per share for taking this investment Total PV = 6000 (1 - (1/1.15^8)/.15 + 2000/1.15^8 = $27,578 Compare this to 30k estimated cost NPV = -30k + 27,578 = -$2,422 With 1000 shares outstanding, our best estimate of the impact would be 2422/1000 = $2.42 (loss of value per share)

Chapter 9 HW

Ch. 9 hw

Ch. 10 HW

Chapter 10

Purchase equipment for 100k, costs 10k to have it installed/delivered You believe you can sell it for 17,000 when you are done with it in 6 years Marginal tax rate = 40%

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 Market Selling Price = $17,000 Book Value at year 6: $17,000 Capital gain/loss = 0 Taxes paid on gain/loss = ($0).40 = $0 After-tax salvage value: 17,000 - .40 (17,000 - 17,000) = $17,000

Straight -line depreciation's formula is Straight -line depreciation's formula is

D = (Initial cost - salvage) / number of years

NPV

Difference between investments market value and its cost How much value is created or added today by undertaking an investment Much easier to estimate when you can compare it to other investments Capital budgeting becomes much more difficult when we cannot observe the market price for at least roughly comparable investments

4/13

EXAM 4 REVIEW

DCF

Estimate future cash flows, apply basic discounted cash flow procedure to estimate present value of these cash flows. Once we have this estimate, we estimate the NPV as the difference between PV of the future cash flows and the cost of the investment

Accounting B/E problem: A new product requires an initial investment of $5 million and will be depreciated to an expected salvage of zero over 5 years The price of the new product is expected to be $25,000, and the variable cost per unit is $15,000 The fixed cost is $1 million

Find Acct B/E each year Depreciation = 5,000,000 / 5 = 1,000,000 Q = (1,000,000 + 1,000,000)/(25,000 - 15,000) = 200 units Q = (FC + D) / (P - v)

Financial B/E Assume a required return of 18% Accounting break-even = 200 Cash break-even = 100

Find Financial B/E (NPV=0) What OCF (or payment) makes NPV = 0? N = 5; PV = 5,000,000; I/Y = 18; CPT PMT = 1,598,889 = OCF Q = (1,000,000 + 1,598,889) / (25,000 - 15,000) = 260 units (FC + OCF/ P - V) The question now becomes: Can we sell at least 260 units per year? 5 years above, initial investment 5million, required return of 18%, FV=0, Solve for PMT

Ch. 11

KNOW WHAT THEY ARE BUT DON'T HAVE TO DO IT Sensitivity Analysis Scenario Analysis B/E analysis -Accounting -Cash -Financial DOL - How sensitive OCF is to change in quantity (Degree of Operating Leverage)

NPV vs. Payback period Long Short Year 0: -250 -250 Year 1: 100 100 Year 2: 100 200 Year 3: 100 0 Year 4: 100 0

Long payback = 2.5 years Short payback = 1.75 years 2 + (50/100) = 2.5 1 + (150/200) = 1.75 Payback favors shorter project NPV (short) = -250 + (100/1.15) + (200/1.15^2) = -11.81 NPV(long)= -250 + (100*[1-1/1.15^4)]/.15) = 35.50

After-tax Salvage =

Market Value - taxes paid

Accounting B/E

NI = (Sales - VC - FC - D)(1 - T) = 0 QP - vQ - FC - D = 0 Q(P - v) = FC + D Q = (FC + D) / (Price - variable cost) More interested in cash flow than accounting numbers If a firm just breaks even on an accounting basis, cash flow = depreciation If a firm just breaks even on an accounting basis, NPV will generally be < $0

Ch. 9

NPV IRR --> Some problems 1. If we don't have conventional cash flows it could result in multiple IRR's 2. If we are comparing mutually exclusive projects, and we choose the one with the higher IRR, we could be choosing wrong project AIRR/MIRR--> Alleviates conventional cash flow problem (know general idea, convert cash flows to conventional cash flows and you don't have multiple IRR, you must choose discount rate and you could manipulate result by choosing one to get the answer you want). Payback Period -->Favors shorter projects, does not take into account TVM Discounted Payback period-->Find PV of the cash flows, Factors in TVM, still favors shorter projects PI (Profitability Index) - When deciding if a project is good or bad, gives us the same answer as NPV. If we compare mutually exclusive projects, could still choose wrong project. Favors smaller projects, because size of project is indicated in the initial cost (year 0 cash flow) so it gives you an idea of the size of the project, so when you divide by that, you're going to end up favoring much smaller projects Know Crossover Rate Graph Any 2 projects that are mutually exclusive that have conventional cash flows, we will prefer one project at one discount rate, and another project at another discount rate At all discount rates, lower than crossover point we prefer project B, but at all discount rates higher than that we prefer project A (has the higher IRR). Which project you use depends on what discount rate you use to find NPV.

NPV/IRR will give same answer except when...

Nonconventional cash flows - cash flow signs change more than once Mutually exclusive projects Initial investments are substantially different (issue of scale) Timing of cash flows is substantially different IRR is unreliable with nonconventional cash flows or mutually exclusive projects

B/e problem w/ taxes

OCF = [(P - v)Q - FC - D](1 - T) + D Use a tax rate = 40% and rework the Wettways example from the book: Need 1170 in OCF to break-even on a financial basis OCF = [(40 - 20)(Q) - 500 - 700](1 - .4) + 700 = 1170 Q = 99.2 You end up with a new quantity of 100 units. The firm must sell an additional 16 units to offset the effects of taxes.

Cash B/E (Same problem as above)

OCF = [(P-v)Q - FC - D] + D = (P-v)Q - FC Q = (OCF + FC) / (P - v) Q = (0 + 1,000,000) / (25,000 - 15,000) = 100 units Need to find value where OCF = 0 so set it equal to zero in the equation

Project A (Project B) $ - 353,000 -$ 48,500 1 --> 42,000 23,700 2 -->62,000 21,700 3--> 62,000 19,200 4 -->437,000 14,300 What is the payback period for each project?

Payback A: 3.43 (-353,000)+42,000+62,000+62,000+437,000 -353,000 + 42,000 = - 311,000 -312,000 + 62,000 = - 249,000 249,000 + 62,000 = -187,000 -187,000 + 437,000 = 250,000 187/437 = .43 --->(3+.43 = 3.43) Payback B: 2.16 (-48,500) + 23,700 + 21,700 + 19,200 + 14,300 = 30,400 (-48,500) + 23,700 = -24,800 (1 year) -24,800 + 21,700 = -3100 (2 years) - 3100 + 19,200 = 16,100 -3100/19,200 = .16 (2+.16=2.16) CHOOSE PROJECT B

Pay taxes on a gain

Receive a tax benefit on a loss

If IRR< Required Return

Reject Project

Ch. 10

Relevant/Incremental Cash Flows (only occur cause you do the project) -Sunk costs not relevant -Opportunity Costs ARE relevant -Spillover Effects ARE relevant -Actual project cash flows themselves ARE relevant: ---(Project OCF, Change in NWC, NCS, FCF for each year) Equivalent Annual Cost-for comparing machines with different life times. NO FORMULA, there is a process. Find NPV of operating for both machines? Then convert that into EAC Finding Bid price (Find financial B/E price meaning NPV=0)

DOL

Sales/Operating cash flow relationship The higher the DOL, the greater the variability in operating cash flow The higher the fixed costs, the higher the DOL DOL depends on the sales level you are starting from. DOL = 1 + (FC / OCF)

MIRR

Step 1: Take the Cash flows to the end of the project and add them up; this is labeled the "terminal value". Step 2: Find the rate of return that equates the cost with the terminal value for the life of the project. This is the MIRR.

Incremental Relevant Cash Flows explained

Sunk Cost: A college student purchased a computer for $1,500 while in high school. A better computer is now available that also costs $1,500. The relevant factors to the decision are what benefits would be provided by the better computer to justify the purchase price. The cost of the original computer is irrelevant Opportunity costs - the classic example of an opportunity cost is the use of land or plant that is already owned. It is important to point out that this is 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. A good example of a positive side effect is when you will establish a new distribution system with this project that can be used for existing or future projects. The benefit provided to those projects needs to be considered. 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. A good real-world example is McDonald's introduction of the Arch Deluxe sandwich. Instead of generating all new sales, it primarily reduced sales in the Big Mac and the Quarter Pounder. Additional examples are provided in a Lecture Tip in the IM. It is important to consider changes in NWC. We need to remember that operating cash flow derived from the income statement assumes all sales are cash sales and that the COGS was actually paid in cash during that period. By looking at changes in NWC specifically, we can adjust for the difference in cash flow that results from accounting conventions. Most projects will require an increase in NWC initially as we build inventory and receivables. Then, we recover NWC at the end of the project. We do not include financing costs. Students often have difficulty understanding why when it appears that we will only raise capital if we take the project. It is important to point out that because of economies of scale, companies generally do not finance individual projects. Instead, they finance the entire portfolio of projects at one time. Taxes will change as the firm's taxable income changes. Consequently, we have to consider cash flows on an after-tax basis.

Important Point

The important point is that we DO NOT use IRR to choose between projects regardless of whether or not we have limited capital.

VC/FC

Total variable costs = quantity * cost per unit Fixed costs are constant, regardless of output, over some time period Total costs = fixed + variable = FC + vQ

DOL problem

Use previous example Suppose sales are 300 units This meets all three break-even measures What is the DOL at this sales level? OCF = (25,000 - 15,000)*300 - 1,000,000 = $2,000,000 (P - V)*Q- FC DOL = 1 + 1,000,000 / 2,000,000 = 1.5 What will happen to OCF if unit sales increases by 20%? 1.5(.2) = .3 or 30% OCF would increase to: 2,000,000(1.3) = $2,600,000 Thus, if unit sales increases by 20%, then the Operating Cash Flow (OCF) would increase by not 20% but 30% demonstrating the effect of operating leverage. A small change in sales yields a much bigger change in OCF.

Sensitivity

What happens to NPV when we change one variable at a time?

Market Salvage =

What the asset could be sold for

An investment under consideration has a payback of eight years and a cost of $871,000. Assume the cash flows are conventional. If the required return is 10 percent, what is the worst-case NPV

Worst case NPV = (-464,672) 871,000/1.1^8 = 406327 406327 - 871,000 = -464,672

#4

http://www.chegg.com/homework-help/questions-and-answers/piece-newly-purchased-industrial-equipment-costs-975-000-classified-seven-year-property-ma-q5091894

NPV of 0

indifferent

Book Value =

initial cost - accumulated depreciation Company intends to use machine for 5 years Accum Dep = (900,000/10 years)= 90,000 5*90k = 450,000 = Book Salvage

After Tax Salvage

salvage - T*(salvage - book value at time of sale) Market salvage*(1-tax rate)

As quantity increases

total fixed costs remain constant, but, on a per unit basis, they decrease with increasing volume. And, as quantity increases, total cost per unit approaches variable cost per unit. If a company expects a high unit sales volume, the company may desire to exploit the possible economies of scale by investing more in fixed costs in an effort to lower variable cost per unit. However, this could create future financial problems if sales expectations fail to materialize.