Making Capital Investment Decisions

Making Capital Investment Decisions
MBAC 5060 Chapter 6 Making Capital Investment Decisions

We know from Chapter 5: Capital budgeting requires calculating the NPV: Discount future cash flows at the require rate of return But how do you determine the cash flows? And how do you know what discount rate to use? First we’ll look at cash flows (now) Then we’ll look at the discount rate (later) The General Idea: Only use New CFs associated with the project being considered Called Incremental CFs CFs from existing (or previous) operations are not relevant to the decision

Chapter Outline: 6.1 Incremental Cash Flows
6.4 Alternative Definitions of Cash Flow 6.3 Inflation and Capital Budgeting 6.5 Investments of Unequal Lives: The Equivalent Annual Cost Method 6.2 The Baldwin Company: An Example

6.1 Incremental Cash Flows
Use the Stand-Alone Principle Don’t calculate the whole firm’s CFs Calculate CFs with and without the project So calculate the Incremental CFs associated with the project Include all changes in the firm’s CFs that are a direct consequence of the project. These are the Relevant CFs use to calculate NPV

CF from Assets = CF to Creditors + CF to Stockholders
6.1 Incremental Cash Flows Use Cash Flows, not Accounting Income (NI) Net Income (NI) accounts for revenue and costs when an economic event occurs Not necessarily when cash is available for investors Non-Cash Events Include: Sales on account (A/R) Purchases on account (A/P) Inventory not replaced (so money spent last year but counted as COGS this year) Allocation of previous capital costs against this year’s revenue (Depreciation) Calculate CFs available to investors in each year CF from Assets = CF to Creditors + CF to Stockholders

Incremental CFs Only those CFs that result from doing the project
Some Issues and Definitions associated with Identifying Incremental CFs: Sunk Costs A cost already paid or a liability already incurred Opportunity Costs Using an asset the firm already owns How is this different from a sunk cost? You could sell the asset Side Effects Cannibalization or Increased Service Revenues CFs Assoc. with Changes in Working Capital Inventory build-up, customer credit, supplier credit Financing Costs We’ll incorporate the in a later chapter (see why in a minute)

Sunk Costs A Sunk Cost is cost that has already been paid
Or a liability already incurred Any decision about the project will not affect these costs Example: Money spent studying a project before the decision Architectural plans, legal fees concerning zoning… Do not include since this money is spent whether or not the project is accepted Already paying a manager to manage one factory Do not allocate ½ the manager’s salary to the 2nd factory The salary is a sunk cost since you are already paying it So do not included ½ the salary in the 2nd factory CFs

Two More Sunk Cost Examples:
One more $1 slot-machine-pull after loosing $100. Should you consider the past $100 when deciding to the next $1? The $100 loss is not relevant to the decision to bet the next $1 Example 2: We tried to market a red version of our project and that didn’t work Should we try to market a blue version? Should we include the cost of the failed red version when deciding on the blue version? It is often tempting to try to “turn around” a previous bad decision or bad outcome: The only consideration should be changes going forward. Past costs are sunk costs.

Review Question: A firm is deciding whether or not to build a new factory The land will cost $1 million Construction will cost $10 million A road to the factory will cost $2 million It has already spent $500,000 on a feasibility study for the project If these are all the relevant data points, what value should the company use for the initial CF?

Review Answer: CF = $1 + $10 + $2 = $13
Only include costs that will be incurred if the project is approved. Do not include costs that have already been spent. These are sunk costs The land will cost $1 - Include Construction will cost $10 - Include Road will cost $2 - Include Feasibility study $0.5 already spent – Sunk Cost CF = $1 + $10 + $2 = $13

Opportunity Costs If assets are used that the firm already owns:
Account for them at Current Market Value Not the original cost Not the book value The reason: If the assets are not used in the project then they could be sold at Current Market Value

Review Question: A Denver courier company is deciding whether or not to expand to Boulder It owns a currently unused truck which it could employ in the Boulder operation. 8 years ago the company paid $100,000 for the truck The truck has been depreciated to a book value of zero The market value for the truck is $20,000 What cost should the company use when calculating the CFs for the project?

Review Answer: Value the asset at its opportunity cost
If the project is not approved, the company can sell the truck for $20,000

Side Effects A new project might have spillover or side effects that must be included Good or Bad side effects A new product might: Cannibalize existing products Generate revenue from servicing the product Generate sales of replacement parts

Review Question: A company that already sells $1 million of blue pens per year wants to sell red pens It believes it can sell $700,000 of red pens It also believes that red-pen sales will cause blue-pen sales to decrease by $100,000 per year. What Incremental or Net Sales value should the company use it’s red-pen capital budgeting analysis?

Review Answer: Addition red-pen sales of $700,000
Less cannibalized blue-pen sales of $100,000 So Incremental sales is $600,000

Net Working Capital = Inv + A/R – A/P
Correcting OCF for Changes in NWC Working Capital Accounts (on the Balance Sheet): Inventory – Asset Stuff you want to sell You have already bought it, but not yet sold it Accounts Receivable (A/R) – Asset The value of stuff you sold on credit So you did not get cash yet Accounts Payable (A/P) – Liability This is stuff you bought or expensed on credit So you did not pay cash yet Simple Model: Net Working Capital = Inv + A/R – A/P

Correcting OCF for Changes in NWC (2)
The Idea: Start with the Working Capital Balance Sheet Accounts at the beginning of the year: Inventory = $60 A/R = $20 A/P = $10 Net Working Capital = Inv + A/R – A/P = $60 + $20 – $10 = $70

Now go to the Income Statement over the year: Sales = $100 COGS = $50 SG&A = $20 So 1st guess of CF = Sales - COGS - SG&A = $100 - $50 - $20 = $30 This is the (almost) CF from operations (OCF)

So 1st guess of CF = Sales - COGS – SG&A = $100 - $50 - $20 = $30 But what if: $20 of the $100 sales were on credit? So $80 in cash and A/R increased by $20 $10 of sold inventory (COGS) was not replaced? So $50 worth sold, but only $40 in cash spent on COGS. So Inventory decreased by $10 $5 of SG&A was on credit? So only $15 in cash spent on SG&A and A/P increased by $5

Sales - COGS - SG&A = $100 - $50 - $20 = $30 $20 of sales on credit So only $80 in cash and A/R increased by $20 $10 of inventory (COGS) was not replaced So only $40 in cash spent on COGS $5 of SG&A was on credit So only $15 in cash spent on SG&A and So 2nd guess of CFs is: $80 - $40 - $15 = $25 Is there another way to get the $25 CF? 

Now back to the Balance Sheet for the End of the Year Sales of $100, but $20 on credit A/R = $20 + $20 = $40 Sold $50, replaced only $40 Inventory = $60 - $50 + $40 = $50 SG&A Expenses of $20, but only paid $15 A/P = $10 + $5 = $15 Net Working Capital = Inv + A/R – A/P = $50 + $40 – $15 = $75 Change in NWC = New – Old = $75 - $70 = $5

Recall OCF = Sales - COGS – SG&A = $100 - $50 - $20 = $30 $20 of Sales not a cash inflow So cash inflow is $20 less than $100 So A/R increased by $20 $10 of COGS expense not a cash outflow Since only $40 of inventory was replaced So the COGS cash outflow was $10 less than $50 So Inventory decreased by $10 $5 of SG&A expense not a cash outflow Since only $15 was paid So A/P increased by $5 Change in NWC = $20 + (-$10) - $5 = $5 Actual CF = $30 - Change in NWC = $30 – $5 = $25

Review: Correcting OCF for Changes in NWC
A new project might require new inventory Pay cash for inventory? That is a cash outflow Borrow the money from suppliers (trade credit)? A/P increases but there is no cash outflow Sales in Cash or Credit (A/R)? If credit sales, then no CF until payment received Projected expenses in Cash or on Account (A/P)? If on account, then no CF until payment is made Also consider Working Cap changes at the project’s end: Built-up Inventories sold A/R and A/P settled Do they return to zero? Assuming they do is a simplifying assumption

Review Question: A company expects sales of $5 million next year
$4 million in cash and $1 million on credit Its COGS will be $3 million But it will replace only $2 million of the inventory sold Of the $2 million paid to replace inventory, only $1 million will be in cash, the rest will be on credit At the beginning of the year, its Work Cap accounts are: A/R = $1.5, Inv = $2.5 and A/P = $0.5 Calculate the ending values for the working capital accounts.

Review Answer: $1 in credit sales COGS is $3 but only $2 replaced
A/R = $1.5 + $1 = $2.5 COGS is $3 but only $2 replaced Inventory = $2.5 – $1 = $1.5 $2 in replaced inventory, but only $1 in cash A/P = $0.5 + $1 = $1.5

Review Question: Calculate the CF for the firm
A company expects Sales of $5 million next year Its COGS will be $3 million Working Cap accounts at the beginning of the year are: A/R = $1.5, Inv = $2.5 and A/P = $0.5 Working Cap accounts at the end of the year will be: A/R = $2.5, Inv = $1.5 and A/P = $1.5 Calculate the CF for the firm Hint: Calculate beginning NWC, ending NWC and then change in NWC

Review Answer: Operating CF = Sales – COGS = $5 - $3 = $2
Beginning NWC = A/R + Inv – A/P = $1.5 + $2.5 – $0.5 = $3.5 Ending NWC = A/R + Inv – A/P = $2.5 + $1.5 – $1.5 = $2.5 Change in NWC = $2.5 – $3.5 = -$1 CF = OCF – Change in NWC = $2 – (-$1) = $3

Extra Explanation: Operating CF = Sales – COGS = $5 - $3 = $2
Credit Sales means the Operating CF is too high by $1 A/R increases $1 Only $2 of inventory replaced means the Operating CF is too high by another $1 Inv decreases $1 But since only $1 of the inventory that is replaced is paid for in cash, it means the Operating CF is too low by $1 A/P increase $1 The net result is only $4 was collected and only $1 was paid The easy way to calculate this is to calculate the Change in NWC (which is equal to -$1) CF = Operating CF – DNWC = $2 – (-$1) = $3

CFs from Assets = CFs to Creditors + CFs Stkhldrs
Financing Costs We will not included Financing Costs: Dividends Paid and Interest Expense Why? We are interested in the CFs generated by the project’s assets Not interested in CFs to investors creditors (aka bond holders) and stockholders Recall from Chapter 2: CFs from Assets = CFs to Creditors + CFs Stkhldrs This equation shows the allocation of CFs from Assets: Some to creditors, some to stockholders We care about the CFs from Assets How CFs from assets is allocated is a question for later For now: Compare PV of the project’s CFs to the project’s costs

Pro Forma Financial Statements
Pro Forma – Latin: “as a matter of form” The words “Pro Forma” have two main uses in business: Pro Forma Earnings: Produced by companies as an addendum to GAAP earnings It usually shows current earnings excluding non-recurring or other extraordinary (unusual) expenses Restructuring cost, inventory write-offs, asset write-offs… Companies do it to show what a “regular quarter would have looked like” without the bad stuff that happened only this once Pro Forma Financial Statements: Created in advance of the actual project Created as part of a business plan Projected Income Statements, Balance Sheets and Cash Flow Projections This is what we will be doing and how we will use the term “pro forma”

Pro Forma Financial Statements
Used to calculate CFs for a proposed project Total CF in any period is Operating Cash Flows (OCF) Less the Change in Net Working Capital (DNWC) Less Net Capital Spending (NCS) CF = OCF – DNWC – NCS We will use Pro Form financial statements to estimate the CFs for a proposed project

Pro Forma Financial Statements:
Example: Sell cans of soup Need to estimate: Units sold: 50,000 cans per year for 3 years Selling Price: $4.00 per can Variable Costs: $2.50 per can Fixed Costs: $12,000 per year Costs of Machinery: $90,000 Depreciated at Straight-line to zero over three years Any machinery residual value will equal disposal costs These are simplifying assumptions Investment in Net Working Capital: $20,000 New inventory, short term borrowing,… The tax rate is 34% Required Return is 20% Produce a Pro Forma Income Statement for this Project 

Pro Forma Income Statement:
Sales (50,000 units at $4.00/unit) $200,000 Variable Costs ($2.50/unit) ,000 Fixed costs ,000 Depreciation Exp ($90,000/3) ,000 Taxable Income ,000 Taxes (34%) ,220 Net Income $21,780 OCF = NI + Dep $51,780 (Note: No interest expense. Account for this as a financing cost.) Pro Forma Statement of Projected Capital Requirements 

Really looks like this:
Since estimates are the same each year: Year 1 Year 2 Year 3 Sales $200, $200, $200,000 VC , , ,000 Fixed costs , , ,000 Depreciation , , ,000 Taxable Income , , ,000 Tax Exp , , ,220 NI $21, $21, $21,780 OCF $51, $51, $51,780 OCF1 = $51,780 OCF2 = $51,780 OCF3 = $51,780 (Later we will have different estimates for each year)

Projected NWC and NCS: Spend $20,000 at time zero on Working Capital (inventory…) DNWC0 = $20,000 Spend $90,000 at time zero on Fixed Assets (Machines) Net Capital Spending = NCS0 = $90,000 Get $20,000 in working capital back at time 3 when the project ends DNWC3 = -$20,000 (Sell all the inventory, collect all the A/R, pay all A/P) This is a simple example: Sales are the same in each year Should they increase over time? Inventory (part of working capital) is constant Usually increase gradually and sell it off as project nears end Will company collect all A/R? Now Create a Pro Form CF Statement 1 2 3 Net Working Capital 20,000 DNWC -20,000 Net Capital Spending 90,000

Pro Forma Cash Flow Statement:
CFs at each period = OCF - DNWC - Net Capital Spending Why do we add $20,000 to Year 3 OCF to get CF? We subtracted $20,000 in COGs when we calculated OCF But since the inventory was not replaced, the cash was not spent When was that cash spent on Inventory? Time zero. And we reduced CF0 by $20k 1 2 3 OCF 51,780 ΔNWC 20,000 -20,000 NCS 90,000 CF = OCF – ΔNWC - NCS -110,000 71,780

Calculate NPV using Pro-Forma IS:
Calculate the NPV using the CFs and R = 20% CF0 = -110,000 CF1 = 51,780 CF2 = 51,780 CF3 = 71,780 NPV = $10,684 > 0 so accept the project 1 2 3 OCF 51,780 ΔNWC 20,000 -20,000 NCS 90,000 CF = OCF – ΔNWC - NCS -110,000 71,780

OCF = (Sales – VC – FC)(1 – T) + Dep x T
6.4 Other Methods of Computing OCF The Tax Shield Approach to OCF A slightly different way to calculate OCF The idea is to see how much of OCF can be attributed to the depreciation method Depreciation is an expense that “shields the firm from taxes” So come up with a formula to calculate OCF that isolates the tax savings from Depreciation OCF = (Sales – VC – FC)(1 – T) + Dep x T We’ll also use this as an opportunity to talk about Depreciation and Net Salvage Value

The Tax Shield Approach to OCF
Before we calculated OCF = NI + Dep: NI = Sales – VC – FC – Dep – Tax Exp Tax Exp = (Sales – VC – FC – Dep)T So Sub for Tax Exp and simplify: NI = (Sales – VC – FC – Dep) – (Sales – VC – FC – Dep)T NI = (Sales – VC – FC – Dep)(1 – T) NI = ($200 – $125 – $12 – $30)(1 – 0.34) = $21.78 Same as NI on slide #35

The Tax Shield Approach to OCF Now:
OCF = (Sales – VC – FC)(1 – T) + Dep x T Dep x T is the tax savings for the amount of depreciation expense OCF = ($200 – $125 – $12)(1 – 0.34) + $30(0.34) OCF = ($63)(0.66) + $30(0.34) OCF = $ $10.20 = $51.78 Same as OCF on slide #35

The Tax Shield Approach to OCF
Same value but we can break OCF in to 2 components: The OCF with no depreciation ($41.58) This year’s tax savings from this years depreciation ($10.20) The tax savings is the “tax shield” So separate depreciation to see how different depreciation schedules change OCF Using the Tax Shield Approach: Calculate OCF if this years depreciation is $40 instead of $30: OCF = (Sales – VC – FC)(1 – T) + Dep x T OCF = ($63)(0.66) + $40(0.34) = $55.18 Why a bigger OCF? ($55.18 > $51.78) Larger Deprecation means lower taxes

Review Question: For a new project, a firm expects annual sales of $15, VC of $3 and FC of $8 The Depreciation Expense will be $3 per year The Marginal tax rate is 35% Calculate the annual Depreciation Tax Shield and the annual OCF for the project.

Review Answer: For a new project, a firm expects annual sales of $15, VC of $3 and FC of $8 The Depreciation Expense will be $3 per year The Marginal tax rate is 35% Depreciation Tax Shield = Dep x T = $3 x 0.35 = $1.05 OCF = (Sales – VC – FC)(1 – T) + Dep x T = ($15 – $3 – $8)(1 – 0.35) + ($3 x 0.35) = $2.6 + $1.05 = $3.65

More About Depreciation:
Depreciation as a Tax Shield: You buy a $100k truck today that will last 4 years The ONLY cash outflow is right now (CF0 = -$100k) But GAAP allows charging a portion of the cost against sales over each of the next four years This lowers taxes in each of the next four years So when calculating the CFs for each of the next four years, calculate depreciation expense We can think about the Depreciation Expense as a Tax Shield Note: I am using a truck for this example. Generally trucks do not qualify for the depreciation schedule used in this example.

Depreciation as a Tax Shield (2):
Previous example OCF = (Sales – VC – FC)(1 – T) + Dep x T Sales = $200, VC = $125, FC = $12, Dep = $30 and T = 34% Sales – VC – FC = $200 - $125 - $12 = $63 We only keep 66% of $63. The rest is paid in taxes: $63( ) = $41.58 Tax Shield from Dep = $30 x 0.34 = $10.2 We keep this extra $10.2 since taxable income was $30k lower So the cost of the truck is an outflow only at time 0 (CF0) But depreciation lowers taxes in the following years

Assume we buy a $100k truck (CF0 =-$100) We use it 4 years Sales = $75, Costs = $30, T = 34% All sales are cash, all costs are cash so no DNWC Assume Straight-Line Dep: $25 per year CF = OCF = (Sales – Costs)(1 – T) + Dep x T CF = ($75 - $30)(1 – 0.34) + ($25)(0.34) = $ $8.50 = $38.20 So CF0 = -$100, CF1 through CF4 = $38.20 If R = 20% then NPV = -$1.11  reject

Now assume we can depreciate a little quicker Use the MACRS schedule Still expense the $100 over 4 years: What is the effect in years 1 & 2? Higher depreciation expense - higher than $25 So Lower Taxable Income means Lower Taxes So Higher CF Year 1 Year 2 Year 3 Year 4 Total Straight-Line $25.00 $100 MACRS $33.33 $44.44 $14.82 $7.41

CF = OCF = (Sales – Costs)(1 – T) + Dep x T (Sales – Costs)(1 – T) = ($75 - $30)(1 – 0.34) = $29.70 (in all yrs) Dep1 x T = $33.33(0.34) = $  CF1 = $ Dep2 x T = $44.44(0.34) = $  CF2 = $ Dep3 x T = $14.82(0.34) = $  CF3 = $ Dep4 x T = $7.41(0.34) = $  CF4 = $ 20% = $0.953 > 0 The accelerated depreciation increased the NPV

Here is the Same Example:

So CF timing changes the NPV
Notice Under Either Depreciation Schedule: Total Taxable income over the 4 years is $80 Total Tax Expense over the 4 years is $27.20 34% of $80 = $27.20 Total CFs over the 4 years is $152.80 The depreciation schedule just changes the timing of the CFs: Higher CFs sooner, Lower CFs later So CF timing changes the NPV

Total Taxable Income over the 4 years is $80
Total Tax Expense over the 4 years is $27.20 Total CFs over the 4 years is $152.80 So only the timing of the CFS change Which changes the NPV from -$1.11 to $0.95

Modified Accelerated Cost Recovery System
Rules showing you how to depreciate assets Assets classified as 3, 5, 7, 10, 15 or 20 years Theory: Assets are Most Valuable when new So expense a higher percentage early Example: Three-Year assets: Depreciation expense in four years The idea is that you buy it in the middle of the 1st year So you get ½ of the 1st year’s use year 1 and ½ of the 1st year’s use in year 2 The last half of the 3rd year’s use is in year 4 So three-year assets are depreciated over 4 periods

MACRS Schedules See Page 181 for a discussion on classifying assets.
For our purposes, Recovery Class Period is Given. (Table 6.3 Page 176)

Depreciation and Net Salvage Value
Example: Buy a $100,000 truck, use it for four years, then sell it Depreciate it using Five-Year MACRS (so expense it over 6 periods) Sale price at time 4 is $30,000. So cash inflow of $30,000 But what are the tax consequences of the sale? How much depreciation have we taken on the truck by time 4? The Depreciation schedule for the $100k truck is: After 4 years, Total Depreciation = $82,720 and Book Value = $17,280

Example Continued: So the book value at time 4 is $17,280
But the truck was just sold for $30,000 This means the truck was over-depreciated by: $30,000 - $17,280 = $12,720 This means we expensed to much over the past four years! Or: We lowered our taxable income by too much Or: We paid too little in taxes: We should have paid and extra $12,720 x 0.34 = $4,324.80 So we’ll add that back in the year the truck is sold Do this by including the sale price as we would income on the pro forma income statement Call this “Recaptured Excess Depreciation” Not a capital gain A capital gain happens if we sell the truck for more than $100k Say $120k Then we owe taxes on two different amounts: $100,000 - $17,280 = $82,720 in Recaptured Excess Depreciation $120,000 - $100,000 = $20,00 in capital gains

NSV = Sale Price + (Book Value - Sale Price) x T
More About Net Salvage Value The Formula: NSV = Sale Price + (Book Value - Sale Price) x T An Example: An asset costs $100 at Time 0 Depreciated straight-line over ten years So Depreciation is $10 per year Sell it for $50 at time 4 The tax rate is 30% Calculate the After-Tax CF from the sale This is called the Net Salvage Value And is the NCS at Time 4

Net Salvage Value Example Continued:
Cost is $100, Sell it for $50 at time 4, Dep is $10 per year, T = 30% Calculate the After-Tax CF from the sale: Calculate the Book Value at time 4: Accumulated depreciation is 4 x $10 = $40 Book Value is $100 - $40 = $60 Plug into the formula: Net Salvage Value = Sale Price + (Book Value - Sale Price) x T = $50 + ($60 - $50)(0.30) = $50 + ($10)(0.30) = $50 + $3 = $53 Net Capital Spending = -$53 So why do you net $53 when the sale price is only $50?

Why do you net $53 when the sale price is only $50? The actual value of the machine after 4 years (as shown by its market sale price) is $50. You have it on your books for $60. This means that you should have depreciated it an additional $10 over the last 4 years. That additional $10 of depreciation would have saved you $3 in taxes (given the 30% tax rate). So you get that $3 in tax savings when you sell the machine at time 4. So add the additional tax savings of $3 to the sale price and you get $53.

What if you sold it for $70 (not $50) at time 4? Same formula: Net Salvage Value = Sale Price + (Book Value - Sale Price) x T = $70 + ($60 - $70)(0.30) = $70 + (-$10)(0.30) = $70 - $3 = $67 Note that the book value ($60) does not change (Why?) Net Capital Spending = -$67 So why do you only net $67 when the sale price is $70?

Why do you only net $67 if the sale price is $70? The actual value of the machine after 4 years (as shown by its market sale price) is $70. You have it on your books for $60. This means that you depreciated an extra $10 over the last 4 years that you should not have depreciated That extra $10 of depreciation saved you $3 in taxes (given the 30% tax rate). So you have to pay that $3 in taxes when you sell the machine at time 4. So subtract the additional taxes $3 from the sale price and you get $67

Review Question: A company with a 35% tax rate is interested in starting a delivery service which it will operate for 4 years. It will buy truck for $100,000 and depreciate it straight-line over a 5 year period. The company believes it can sell the truck for $30,000 at time 4. Calculate the Net Capital Spending at time 0 and time 4.

Review Answer: Net Capital Spending at time 0 = $100 (an outflow) ($100 is spent. This is subtracted from OCF to the Total CF.) Net Salv Val = Sale Price + (Book Value - Sale Price) x T Sale Price = $30 Annual Depreciation = $100/5 = $20 Book Value at time 4 = $100 – 4($20) = $20 T = 35% Net Salv Val = $30 + ($20 - $30) x 0.35 = $26.50 Net Capital Spending at time 4 = -$ (an inflow) The company took an extra $10 of depreciation (and therefore saved an extra $3.50 in taxes. It has to pay that $3.50 at the time of the sale.

Review Question: Same company, same truck, but now salvage value (sale price) at time 4 is zero. Calculate the Net Capital Spending at time 0 and time 4. T = 35% Book Value at time 4 = $20

Review Answer: Net Capital Spending at time 0 = $100 (an outflow) ($100 is spent. This is subtracted from OCF to the Total CF.) Net Salv Val = Sale Price + (Book Value - Sale Price) x T Sale Price = $0 Book Value at time 4 = $20 T = 35% Net Salv Val = $0 + ($20 - $0) x 0.35 = $7.00 Net Capital Spending at time 4 = -$7.00 (an inflow) The company did not depreciate enough. It should have taken an extra $20 of depreciation (and therefore saved an extra $7.00 in taxes. It gets to save that $7.00 at the time of the sale.

Example: Replace an Old Machine. We have an old machine
Example: Replace an Old Machine? We have an old machine. Replace it now while it’s still worth some thing in salvage value? Or use it for another 5 years? Also get cost savings from a new, more efficient machine Old Machine Initial cost = 100,000 Annual Dep = $9,000 Purchased 5 years ago Book Value = $55,000 Salvage today = $65,000 Salvage in 5 years = $10,000 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%

Replacement Example Continued:
Old machine will last another 5 years Should we replace it now instead? Calculate INCREMENTAL CFs if replaced now: Annual costs savings ($50k/yr) Depreciation Differences (MACRS vs. S-L) The cost of the new machine ($150K) Salvage value of the old machine now ($65k) Book value of old machine now ($55k) Book Val = Cost – Accumulated Dep = $100k – 5($9) = $55k Pay tax on Salvage – Book Val = $10 (excess depreciation) Salvage value of the old machine in 5 years ($10k) Salvage value of the new machine in 5 years ($0)

First: Look at Incremental Depreciation:
Calculate Annual Depreciation for the new machine: Cost ($150k) 3 year MACRS schedule Calculate Incremental Dep from replacement: Old Machine Depreciation = S-L at $9k per year Incremental = New – Old Only 4 years of depreciation (3-yr MACRS) even though we expect 5 years of use. Is that okay? Yes. That’s the rule.

Next: Look at the Annual change in OCF:
Cost savings increases taxable income and taxes Increased Depreciation decreases taxable income and taxes So calculate cost savings less new taxes: Incremental CF1 = NI + Incremental Dep = $5.7 + $40.5 = $46.2 Incremental CF1 = Cost Savings - Incremental Tax = $50 - $3.8 = $46.2 Negative Incremental Tax in year 2 due to Incremental Dep > Cost savings Incremental Taxes are lower in year 2 Taxes are higher in every other year due to cost savings of $50k

Next: Look at Purchase and Salvage:
Need to look at time 0 and time 5 CFs from: Buying the new machine now $150k outflow Selling the old machine now $65k inflow Paying taxes on the over-depreciated portion of the old machine Sale Price – Book Value = $65 - $55 = $10 Not receiving the salvage value of the old machine in 5 years Forgoing $10k Same as a cash outflow Not paying taxes on the over-depreciated portion of the old machine Book Value in 5 more years = Book Value after 10 years of ownership Price – Accumulated Depreciation = $100k – 10($9k) = $10k Sale price = Book Value so no tax consequences from the sale If we happen to sell it for more than $10k, then we’ll owe some tax. Talk about that later

Incremental CF at Time 0 Could have done it this way:
Cost of New Machine -$150,000 Sale Price of Old Machine $65,000 Book Value of Old Machine $55,000 Taxable Amount $10,000 Taxable Expense (40%) $4,000 Net Proceeds from old Machine $61,000 Net CF $89,000 Could have done it this way: CF0 = Cost + Sale Price – T(Sale Price - Book) = -$150 + $ ($65 - $55) = -$89

Incremental CF at Time 5 So in addition to the Incremental OCFs
Forgone Salvage of old Machine -$10,000 Sale Price of Old Machine $10,000 Book Value of Old Machine $10,000 Taxable Amount $0 Taxable Expense (40%) $0 Net Forgone Proceeds $10,000 Net CF $10,000 So in addition to the Incremental OCFs Add the Net Capital Spending: Include outflow of $89k at time 0 Include outflow of $10k at time 5 Note that the $10 at time 5 is not really an outflow, but a forgone inflow We would have sold the old machine for net $10 at time 5 Instead we are selling it now for net $61 This helps offset the $150 cost of the new machine Implicit Assumption: There is no change in New Working Capital.

So Replace the Machine Now or in 5 Years?
We have calculated all the relevant incremental CFs. Just calculate the NPV of the CFs: 10% = $54,812 > 0 so accept the project So replace the machine now!

6.5 Projects with Different Lives
To compare mutually exclusive projects of different lives: Determine the annual annuity CF that is equivalent to the projects CFs Compare each projects’ Annuity CFs Called the Equivalent Annual Cost (EAC) Or the Equivalent Annual Payment

EAC You need an air cleaner for your factory
Calculate the NPV of each with a 10% discount rate: NPVLong: =PV(.1,10,100)-4000 = -4,614.46 NPVShort: =PV(.1,5,500)-1000 = -2,895.39 Calculate the Equivalent Annual Cost (EAC): The EAC is the annuity payment with the same PV as the original set of cash flows. EACLong: =PMT(.1,10, ) = EACShort: =PMT(.1,5, ) = EACLong < EACShort Long Lived Short Lived Initial Cost -$4,000 -$1,000 Annual Operating Cost -$100 -$500 Expected Life 10 5

Equivalent Annual Payment
Two Mutually Exclusive Machines But replace the machine as it fails - forever NPVA > NPVB BUT we are not considering the different lives Machine A: Pay $100 every three years Get $60 every year. Machine B: Pay $300 every two years Get $200 every year. A B Initial Cost -$100 -$300 Annual CF $60 $200 Expected Life 3 2 10% $49.21 $47.11

Recall: =-PMT(rate, nper, pv, [fv], [type]) =-PMT(.1,3,49.21) = $19.79
Machine A: Pay $100 every 3 yrs, get $60 every yr, NPV = $49.21 Machine B: Pay $300 every 2 yrs, get $200 every yr, NPV = $47.11 What equal annual payments each year are equivalent to Machine A’s CFs? =-PMT(rate, nper, pv, [fv], [type]) =-PMT(.1,3,49.21) = $19.79 So getting $19.79 is equivalent to Machine A’s CFs What equal annual payments each year are equivalent to Machine B’s CFs? =-PMT(.1,2,47.77) = $27.14 So getting $27.14 is equivalent to Machine B’s CFs

Check This: Time Net CFA DCFA Net CFB DCFB -100.00 -300.00 1 60.00
1 60.00 54.55 200.00 181.82 2 49.59 -82.64 3 -40.00 -30.05 150.26 4 40.98 -68.30 5 37.26 124.18 6 -22.58 -56.45 7 30.79 102.63 8 27.99 -46.65 9 -16.96 84.82 10 23.13 -38.55 11 21.03 70.10 12 19.12 63.73 Sum = NPV 134.83 184.94 EAP 19.79 27.14

We tweak our assumptions
Where do we go from here? We tweak our assumptions We see how our assumption affect the results How sensitive are the NPV calculations to our estimates? Change one variable at time Called Sensitivity Analysis Change many variables together Called Scenario Analysis Discuss Real options

Making Capital Investment Decisions

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