Making Capital Investment Decisions

Making Capital Investment Decisions

What finance functions add the most to firm value?

General Rules of Discounting
Only cash flows matter Only examine incremental cash flow Be consistent in treatment of inflation Deduct taxes before discounting

Cash Flow are what matter
Cash flow = Dollars receive – Dollars paid Earnings are NOT cash flow Earnings are an ACCOUNTING NUMBER Accountants start with cash flow, but then adjusts for timing, accruals, non-cash items etc. Much of the work in evaluating a project lies in taking accounting numbers and generating cash flows You never write a check for “depreciation”

Incremental Cash Flows
These are cash flows that the firm only incurs if it takes the project Need to consider all incremental cash flows that can be attributed to the project Examples: Project Interactions, Opportunity Costs, Overhead, Depreciation, Taxes (including cap gains tax), and Salvage Values

Interactions (Side Effects)
Affects that the investment has on the cash flows of the firm’s other projects Erosion or Cannibalism (Bad) The new product causes existing customers to demand less of the company’s current products

Erosion in Action Denon is planning on introducing a Blu-Ray player, which will likely hurt the sales of their DVD players. Are all of the sales/profits of the Blu-Ray project incremental? C0 C1 C2 DVD Sales No Blu-Ray 800 1000 DVD Sales With Blu-Ray 500 400 Blu-Ray Sales -200 Blu-Ray Incremental CF

Erosion in Action Denon is planning on introducing a Blu-Ray player, which will likely hurt the sales of their DVD players. Are all of the sales/profits of the Blu-Ray project incremental? C0 C1 C2 DVD Sales No Blu-Ray 800 1000 DVD Sales With Blu-Ray 500 400 Blu-Ray Sales -200 Blu-Ray Incremental CF 100

Erosion in Action Denon is planning on introducing a Blu-Ray player, which will likely hurt the sales of their DVD players. Are all of the sales/profits of the Blu-Ray project incremental? C0 C1 C2 DVD Sales No Blu-Ray 800 1000 DVD Sales With Blu-Ray 500 400 Blu-Ray Sales -200 Blu-Ray Incremental CF 100 200

Working Capital Money the firm has on hand that is necessary for running the business Think of the cash in a register, how effective is the register without the cash in the drawer If a project requires changes in working capital, we need to account for this in our calculations Why???

Opportunity Costs Cash flows that can be realized from putting the assets to use in different projects. What could we be making? Example: When Price Club considers stocking a new product, what is the opportunity costs that it should be considering?

Overhead The ongoing administrative expenses a business incurs, which cannot be attributed to any specific business activity, but are necessary to run the firm. Examples: rent, utilities, and insurance. Accountants allocate overhead across projects Are we concerned about the amount of overhead the account’s will assign to our project?

Overhead NO, we don’t care about accounting numbers
The ongoing administrative expenses a business incurs, which cannot be attributed to any specific business activity, but are necessary to run the firm. Examples: rent, utilities, and insurance. Accountants allocate overhead across projects Are we concerned about the amount of overhead the account’s will assign to our project? NO, we don’t care about accounting numbers We do care about changes in overhead that result from our project

Example A firm has only one division A, with assets of $100m and overhead of $20m. It is planning to add another division B. Division B will have another $50m in assets. Due to the addition of this division, overhead is expected to increase to $27m. The firm allocates overheads for the two divisions based on their assets. What are the allocated overhead expenses? What is the relevant cash flow as far as the decision to add division B?

Example What are the allocated overhead expenses?
A firm has only one division A, with assts of $100m and overhead of $20m. It is planning to add another division B. Division B will have another $50m in assets. Due to the addition of this division, overhead is expected to increase to $27m. The firm allocates overheads for the two divisions based on their assets. What are the allocated overhead expenses? A=(27)*(100/150)=$18m What is the relevant cash flow as far as the decision to add division B?

A firm has only one division A, with assts of $100m and overhead of $20m. It is planning to add another division B. Division B will have another $50m in assets. Due to the addition of this division, overhead is expected to increase to $27m. The firm allocates overheads for the two divisions based on their assets. What are the allocated overhead expenses? A=(27)*(100/150)=$18m, B=(27)*(50/150)=$9m What is the relevant cash flow as far as the decision to add division B?

A firm has only one division A, with assts of $100m and overhead of $20m. It is planning to add another division B. Division B will have another $50m in assets. Due to the addition of this division, overhead is expected to increase to $27m. The firm allocates overheads for the two divisions based on their assets. What are the allocated overhead expenses? A=(27)*(100/150)=$18m, B=(27)*(50/150)=$9m What is the relevant cash flow as far as the decision to add division B? Relevant overhead is $7m

Depreciation Allocates the cost of an asset over its expected life, for accounting and tax purposes Accounts for the decline in asset value because of wear and tear or obsolescence Depreciation is based on the asset’s expected life, not on the life of the project LAND DOES NOT DEPRECIATE

Why do we care about Depreciation
Depreciation is a non-cash expense, an accounting number, so why do we care about it? Depreciation is tax deductible, and taxes are a LARGE cash expense

The Two Depreciations Book (Accounting) Depreciation is what appears on financial statements Ex. Straight line depreciation Tax Depreciation is used to determine the firms tax bill This determines the Tax Shield

The Two EBT’s EBDT -Book Dep -Tax Dep EBT (Book) EBT (Tax) -Taxes Paid
Tax Rate Taxes Paid Net Income = Book EBT – Taxes Paid

Book Depreciation This type of depreciation is used to calculate a company’s Net Income Straight line Depreciation: (Investment – Salvage Value) / Expected life Investment: Salvage Value:

Book Depreciation This type of depreciation is used to calculate a company’s Net Income Straight line Depreciation: (Investment – Salvage Value) / Expected life Investment: what did we pay for it Salvage Value:

Book Depreciation This type of depreciation is used to calculate a company’s Net Income Straight line Depreciation: (Investment – Salvage Value) / Expected life Investment: what did we pay for it Salvage Value: asset value at end of it’s life What can we sell it for?

Tax Depreciation Tax Depreciation is calculated using the Modified Accelerated Cost Recovery System Tax depreciation ignores salvage value MACRS allows for more depreciation early How will this affect the PV of the tax shield? Tax Shield = (Tax Depreciation * tax rate) What is the Tax Shield?

Tax Depreciation Tax Depreciation is calculated using the Modified Accelerated Cost Recovery System Tax depreciation ignores salvage value MACRS allows for more depreciation early How will this affect the PV of the tax shield? Tax Shield = (Tax Depreciation * tax rate) What is the Tax Shield? The money that now goes to investors instead of the government

Acct & Tax Dep. Example Purchase an asset costing $1m, which has a 5 year expected life. After 5 years you can sell it for scrap, $100k. What is the yearly accounting (straight line) and tax depreciation? Year 1 Year 2 Year 3 Year 4 Year 5 Accting Tax

Acct & Tax Dep. Example Purchase an asset costing $1m, which has a 5 year expected life. After 5 years you can sell it for scrape, $100k. What is the yearly accounting and tax depreciation? Straight line (1,000,000 – 100,000)/5 = 180,000 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Acct 180,000 Tax

Acct & Tax Dep. Example Purchase an asset costing $1m, which has a 5 year expected life. After 5 years you can sell it for scrape, $100k. What is the yearly accounting and tax depreciation? Straight line (1,000,000 – 100,000)/5 = 180,000 Tax 1,000,000 * schedule percent = Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Acct 180,000 Tax 200,000

Acct & Tax Dep. Example Purchase an asset costing $1m, which has a 5 year expected life. After 5 years you can sell it for scrape, $100k. What is the yearly accounting and tax depreciation? Straight line (1,000,000 – 100,000)/5 = 180,000 Tax 1,000,000 * schedule percent = Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Acct 180,000 Tax 200,000 320,000

Acct & Tax Dep. Example Purchase an asset costing $1m, which has a 5 year expected life. After 5 years you can sell it for scrape, $100k. What is the yearly accounting and tax depreciation? Straight line (1,000,000 – 100,000)/5 = 180,000 Tax 1,000,000 * schedule percent = Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Acct 180,000 Tax 200,000 320,000 192,000

Acct & Tax Dep. Example Purchase an asset costing $1m, which has a 5 year expected life. After 5 years you can sell it for scrape, $100k. What is the yearly accounting and tax depreciation? Straight line (1,000,000 – 100,000)/5 = 180,000 Tax 1,000,000 * schedule percent = Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Acct 180,000 Tax 200,000 320,000 192,000 115,200

Acct & Tax Dep. Example Purchase an asset costing $1m, which has a 5 year expected life. After 5 years you can sell it for scrape, $100k. What is the yearly accounting and tax depreciation? Straight line (1,000,000 – 100,000)/5 = 180,000 Tax 1,000,000 * schedule percent = Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Acct 180,000 Tax 200,000 320,000 192,000 115,200 57,600

Proceeds from Sale and Capital Gains Tax
When a company sells an asset, if the price is above the tax book value, it is subject to capital gains Capital Gains Tax Obligation = (Price- Tax Book Value) * Capital Gains Tax Rate

Capital Gains Tax Example
You purchase a machine that will cost your company $1.5m, that has a life of 5 years. You plan to use the project for 3 years and then sell the machine for $600k, at the end of 5 years the machine is worth $50k. The capital gains rate is 20%. What is the tax obligation resulting from the sale?

You purchase a machine that will cost your company $1.5m, that has a life of 5 years. You plan to use the project for 3 years and then sell the machine for $600k, at the end of 5 years the machine is worth $50k. The capital gains rate is 20%. What is the tax obligation resulting from the sale? First what is the book value of the machine? Initial investment: 1,500,000; 5 years Tax Dep: 20%, 32%, 19.2% Year 3 BV:

You purchase a machine that will cost your company $1.5m, that has a life of 5 years. You plan to use the project for 3 years and then sell the machine for $600k, at the end of 5 years the machine is worth $50k. The capital gains rate is 20%. What is the tax obligation resulting from the sale? Initial investment: 1,500,000; 5 years Tax Dep: 20%, 32%, 19.2% Year 3 BV: 1,500,000 * ( )=432,000 Profit:

You purchase a machine that will cost your company $1.5m, that has a life of 5 years. You plan to use the project for 3 years and then sell the machine for $600k, at the end of 5 years the machine is worth $50k. The capital gains rate is 20%. What is the tax obligation resulting from the sale? Initial investment: 1,500,000; 5 years Tax Dep: 20%, 32%, 19.2% Year 3 BV: 1,500,000 * ( )=432,000 Profit: 600, ,000=168,000 Capital Gains Tax owed:

You purchase a machine that will cost your company $1.5m, that has a life of 5 years. You plan to use the project for 3 years and then sell the machine for $600k, at the end of 5 years the machine is worth $50k. The capital gains rate is 20%. What is the tax obligation resulting from the sale? Initial investment: 1,500,000; 5 years Tax Dep: 20%, 32%, 19.2% Year 3 BV: 1,500,000 * ( )=432,000 Profit: 600, ,000=168,000 Capital Gains Tax owed 0.20 * 168,000= $33,600

Inflation and Capital Budgeting
Inflation: general increase in the price of goods Alternative: the general decline in the purchasing power of money Hershey Nickel Bar: In 1930 bar was 2 oz In 1968 bar was ¾ oz Inflation is an important fact of economic life and must be considered in capital budgeting.

Dealing with Inflation
KEY: Keep everything in either real or nominal terms Real Cash Flows → Real Discount Rate Nominal Cash Flows → Nominal Discount Rate As long as we are consistent in our treatment of inflation we will get the same NPV

Real vs. Nominal Nominal dollars: Real dollars: Nominal rate:
Real rate:

Real vs. Nominal Nominal dollars are the dollars we have in our wallets Real dollars Nominal rate Real rate

Real vs. Nominal Nominal dollars are the dollars we have in our wallets Real dollars refer to a dollar’s purchasing power at a specific point in time Nominal rate Real rate

Real vs. Nominal Nominal dollars are the dollars we have in our wallets Real dollars refer to a dollar’s purchasing power at a specific point in time Nominal rate is the “total” rate of interest Accounts for what you should earn & inflation Real rate

Real vs. Nominal Real rate is want an investment should earn
Nominal dollars are the dollars we have in our wallets Real dollars refer to a dollar’s purchasing power at a specific point in time Nominal rate is the “total” rate of interest Accounts for what you should earn & inflation Real rate is want an investment should earn Ignores inflation

Inflation and Discount rate
The relationship between interest rates and inflation is known as the Fisher Equation (1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate)

Real vs. Nominal Rate Example 1
If you invest $10,000 at a nominal rate of 12% APR, how much will you have in 30 years? How much will you have in real terms if the rate of inflation is 4% per year?

If you invest $10,000 at a nominal rate of 12% APR, how much will you have in 30 years? N = 30, I/Y = 12, PV= 10,000, PMT = 0, FV= ???? FV = $299,599.22 How much will you have in real terms if the rate of inflation is 4% per year?

If you invest $10,000 at a nominal rate of 12% APR, how much will you have in 30 years? N = 30, I/Y = 12, PV= 10,000, PMT = 0, FV= ???? FV = $299,599.22 How much will you have in real terms if the rate of inflation is 4% per year? 1+Real = 1.12/1.04 ≈ N = 30, I/Y = 7.069, PV= 10,000, PMT = 0, FV= ???? FV = $92,372.03, this is the Future Real Dollar Value

If you invest $10,000 at a nominal rate of 12% APR, how much will you have in 30 years? N = 30, I/Y = 12, PV= 10,000, PMT = 0, FV= ???? FV = $299,599.22 How much will you have in real terms if the rate of inflation is 4% per year? 1+Real = 1.12/1.04 ≈ N = 30, I/Y = 7.069, PV= 10,000, PMT = 0, FV= ???? FV = $92,372.03 OR N = 30, I/Y = 4, PV=????, PMT = 0, FV= 299,599.22 PV = $92,372.03, this is the Future Real Dollar Value

Nominal Rate is 15%, inflation is 10% What is the real discount rate? What are the nominal cash flows? Year 1 2 3 Real CF -10 10 11 12 Nominal CF

Nominal Rate is 15%, inflation is 10% What is the real discount rate? (1.15 / 1.10) - 1= 4.55% What are the nominal cash flows? Year 1 2 3 Real CF -10 10 11 12 Nominal CF

Nominal Rate is 15%, inflation is 10% What is the real discount rate? (1.15 / 1.10) - 1= 4.55% What are the nominal cash flows? Year 1 2 3 Real CF -10 10 11 12 Nominal CF 10*1.1=

Nominal Rate is 15%, inflation is 10% What is the real discount rate? (1.15 / 1.10) - 1= 4.55% What are the nominal cash flows? Year 1 2 3 Real CF -10 10 11 12 Nominal CF 10*1.1= 11*1.12= 13.31

Nominal Rate is 15%, inflation is 10% What is the real discount rate? (1.15 / 1.10) - 1= 4.55% What are the nominal cash flows? Either way, Real & Real or Nominal & Nominal NPV is $20.13 Year 1 2 3 Real CF -10 10 11 12 Nominal CF 10*1.1= 11*1.12= 13.31 12*1.13= 15.97

Depreciation & Inflation
Depreciation is always given in nominal terms So, if using real cash flow and discount rates you will need to convert nominal depreciation into real depreciation Generally it’s simpler to use nominal cash flows and the nominal discount rate

Costs we Do NOT Care About
Sunk Costs: are expenses that have already been paid Already paid so NOT INCREMENTAL to project Ex: Feasibility study, R&D expenses, test marketing, etc. Each of theses is an independent projects, subject to NPV Just because “we have come this far” does not mean that we should continue to throw good money after bad.

Cost Categories When determining whether a cost is relevant in NPV analysis, you need to classify it Incremental costs, We care about these Opportunity costs, We care about these Sunk costs, We do NOT care about these

Estimating Cash Flows Cash Flow from Operations Recall that:
OCF = EBIT – Taxes + Depreciation

Other Methods for Computing OCF
Bottom-Up Approach Works only when there is no interest expense OCF = NI + depreciation Top-Down Approach OCF = Sales – Costs – Taxes Do not subtract non-cash deductions Tax Shield Approach OCF = (Sales – Costs)(1 – τ) + Depreciation* τ

Interest Expense For now, assume that debt is independent of the project Interest expense is not influenced by the project Later we will deal with the impact that debt has on firm value

Big Example 1 Denon is planning to introduce a DVD player. It seeks your advice on whether this project should be taken up. The details are given below: The initial investment in plant and machinery is 5 million. The project also requires an initial Net Working Capital of 1 million which will be recouped entirely when the project is sold off at the end of year 3. The revenues from the DVD player is expected to be 9, 10 and 11 million in the first three years. Variable cost are expected to be 60% of sales. Fixed costs are expected to be 1 million each year. For simplicity, assume all assets have a life of 5 years, and assets have no salvage value. The firm expects to sell off the assets after 3 years for $2m. DVD player sales are expected to cannibalize $1million from CD player sales Corporate tax rate is 35%. Capital gains tax rate is 20%. Discount rate = 10%

Big Example 1: Investment
Denon is planning to introduce a DVD player. It seeks your advice on whether this project should be taken up. The details are given below: The initial investment in plant and machinery is 5 million. The project also requires an initial Net Working Capital of 1 million which will be recouped entirely when the project is sold off at the end of year 3. Year 0 Year 1 Year 2 Year 3 Total Investment Plant & Machinery 5.00 Net Working Capital 1.00 0.00

Big Example 1: Operations
Denon is planning to introduce a DVD player. It seeks your advice on whether this project should be taken up. The details are given below: The revenues from the DVD player is expected to be 9, 10 and 11 million in the first three years. Variable cost are expected to be 60% of sales. Fixed costs are expected to be 1 million each year. For simplicity, assume all assets have a life of 5 years, and assets have no salvage value. Year 0 Year 1 Year 2 Year 3 Profit / Loss Accounts Sales 9.00 10.00 11.00 Variable Costs (60% Sale) 5.40 6.00 6.60 Fixed Costs 1.00 EBDT 2.60 3.00 3.40 Book Dep EBT 1.60 2.00 2.40

Big Example 1: Corp Taxes
Denon is planning to introduce a DVD player. It seeks your advice on whether this project should be taken up. The details are given below: For simplicity, assume all assets have a life of 5 years, and assets have no salvage value. Corporate tax rate is 35%. Capital gains tax rate is 20%. Discount rate = 10% Year 0 Year 1 Year 2 Year 3 Corp Tax EBDT 2.60 3.00 3.40 Tax Dep % 20.0% 32.0% 19.2% Tax Dep 1.00 1.60 0.96 EBT (Tax) 1.6 1.40 2.44 Tax (35%) 0.56 0.49 0.85

Big Example 1: Capital Gains
Denon is planning to introduce a DVD player. It seeks your advice on whether this project should be taken up. The details are given below: The firm expects to sell off the assets after 3 years for $2m The assets has a life of 5 years, and assets have no salvage value. Corporate tax rate is 35%. Capital gains tax rate is 20%. Discount rate = 10% Year 0 Year 1 Year 2 Year 3 Capital Gains Tax Proceeds from sale 2.00 Tax Dep 1.00 1.60 0.96 BV of asset 5.00 4.00 2.40 1.44 Profit 0.56 Capital Gains Tax (20%) 0.11

Big Example 1: Op 2, Net Income
Denon is planning to introduce a DVD player. It seeks your advice on whether this project should be taken up. The details are given below: Year 0 Year 1 Year 2 Year 3 Profit / Loss Accounts Sales 9.00 10.00 11.00 Variable Costs (60% Sale) 5.40 6.00 6.60 Fixed Costs 1.00 EBDT 2.60 3.00 3.40 Book Dep EBT 1.60 2.00 2.40 Tax 0.56 0.49 0.85 Net Income 1.04 1.51 1.55

Big Example 1: C F Summary
Year 0 Year 1 Year 2 Year 3 Investments (5.00) Change in Working Capital (1.00) 0.00 1.00 Net Income 1.04 1.51 1.55 Book Dep Sale Proceeds 2.00 Capital Gains (0.11) Lost CD Sales Net Cash Flow (6.00) 4.44 NPV (0.47)

Big Example 2: (In-Class 1, Given)
Your R&D department has come up with a innovative product. Your firm had spent $2m as R&D expenses for this project. You are now wondering whether this product introduction will increase shareholder wealth? Investment of $6.0m is required immediately and another $4.0m is required at the end of year 1. The factory can start manufacturing only after this second investment is made. Assume all assets have a life of 5 years, and depreciation starts after manufacturing begins. You expect to sell 1m units in the first year of production, 1.5m units in the next four years. You plan to sell the factory after that and you expect it to fetch $1m. Selling price is expected to be $10/unit in the first year of goods sold and is expected to increase at 5% p.a. Cost of goods sold is $6/unit in the first year of production and is expected to increase at 4% p.a. Assume the level of net working capital to be $1.0m in the first year of production. Afterwards, it will increase by $1.0m each year. In the last year, the firm will be able to liquidate its entire NWC without loss in value. Assume corporate income tax rate to be 35% and capital gains tax rate of 20%. This project requires a nominal discount rate of 10%.

Other Tricks with NPV Optimal Timing of a Project
Choosing between equipment with different lives Replacing an Existing Machine Cost of Excess Capacity

Optimal Timing NPV can be used to determine the optimal time to undertake a project Ex: You have a teak farm and you have to decide when to harvest. The longer you wait, the bigger the trees, and hence higher the value. However, after the initial growth phase, the trees grow slower and slower. The opportunity cost of capital is 10%

Teak Farm Example When do we harvest the trees? Why Year 1 2 3 4 5 6 7
1 2 3 4 5 6 7 Value 100 120 140 160 180 200 220 240 Yr % 20% 16.7% 14.3% 12.5% 11.1% 10% 9.1% PV $109.10 $115.70 $120.21 $122.94 $124.18 $123.16 When do we harvest the trees? Why

Teak Farm Example When do we harvest the trees? Either in year 5 or 6
1 2 3 4 5 6 7 Value 100 120 140 160 180 200 220 240 Yrly % 20% 16.7% 14.3% 12.5% 11.1% 10% 9.1% PV $109.10 $115.70 $120.21 $122.94 $124.18 $123.16 When do we harvest the trees? Either in year 5 or 6 Why?

Teak Farm Example When do we harvest the trees? Either in year 5 or 6
1 2 3 4 5 6 7 Value 100 120 140 160 180 200 220 240 Yrly % 20% 16.7% 14.3% 12.5% 11.1% 10% 9.1% PV $109.10 $115.70 $120.21 $122.94 $124.18 $123.16 When do we harvest the trees? Either in year 5 or 6 Why Same NPV → Equally Valuable Before 5 yield was greater than cost of capital, after 6 yield is less

Investments of Unequal Lives
There are times when application of the NPV rule can lead to the wrong decision. Consider a factory that must have an air cleaner that is mandated by law. Discount rate is 10% There are two choices: The “Cadillac cleaner” costs $4,000 today, has annual operating costs of $100, and lasts 10 years. The “Cheapskate cleaner” costs $1,000 today, has annual operating costs of $500, and lasts 5 years. Cadillac: N = 10, I/Y = 10, PV=????, PMT = 100, FV=0 PV(costs) = ,000 = $4,614.46 Cheap: N = 5, I/Y = 10, PV=????, PMT = 500, FV=0 PV(costs) = 1, ,000 = $2,895.39 Cheap PV(Costs) is lower, so it has a higher NPV Doesn’t account for Cadillac’s longer life

Comparing Investments with Different Expected Lives
Replacement Chain Repeat projects until they begin and end at the same time. Compute NPV for the “repeated projects.” The Equivalent Annual Cost Method

Replacement Chain Approach
The Cadillac last 10 years The Cheapskate last 5 years What is the minimum time span over, which we can fairly compare these two? 10 years, the life of 1 Cadillac, and 2 Cheapstakes

The Cadillac cleaner time line of cash flows: The Cheapskate cleaner time line of cash flows over ten years:

The Cadillac cleaner time line of cash flows: -$4,000 – The Cheapskate cleaner time line of cash flows over ten years: -$1,000 – ,

The Cadillac cleaner time line of cash flows: -$4,000 – PV(Costs) = $4,614.46 The Cheapskate cleaner time line of cash flows over ten years: -$1,000 – ,

The Cadillac cleaner time line of cash flows: -$4,000 – PV(Costs) = $4,614.46 The Cheapskate cleaner time line of cash flows over ten years: -$1,000 – , PV(Costs) = $4, =$2, $2, / (1.15)

Equivalent Annual Cost (EAC)
Spread the cost of buying and maintaining a machine over its expect life, while accounting for time value of money The payments that an annuity with the same PV and life Used when the only difference is the costs Pick the machine with the lower EAC The EAC for the Cadillac is ($4,614.46)? The EAC for the Cheapskate is ($2,895.39)?

Cadillac versus Cheapskate
The EAC for Cadillac is ($4,614.46)? N = 10, I/Y = 10, PV=4,614.46, PMT = ???, FV=0 PMT = $750.98 The EAC for Cheapskate is ($2,895.39)? N = 5, I/Y = 10, PV=2,895.39, PMT = ???, FV=0 PMT = $763.80 Buy the Cadillac Cleaner ( < )

Different Lives Example (Given)
There are two machines, A and B. Both machines have the same capacity and produce identical goods. However, while machine A has a life of 5 years, machine B has a life of 3 years. The initial investments are $20m and $15m respectively. There is no salvage value for either machine. The operating costs are $4m and $5m per year respectively. Assume that the discount rate is 10%. Which one should you choose? Find the Present Value of each machines total costs (A) N = 5, I/Y = 10, PV=???, PMT = 4, FV=0:: Op PV=15.16 (A) Total PV = = $35.16 (B) N = 3, I/Y = 10, PV=???, PMT = 5, FV=0 :: Op PV=12.43 (B) Total PV = = $27.4

EAC Solution (Given) PVA = 35.16; EACA = N = 5, I/Y = 10, PV=35.16, PMT = ???, FV=0:: PMT = $9.28 PVB = ; EACB = N = 3, I/Y = 10, PV=27.43, PMT = ???, FV=0:: PMT = $11.03 Choose Machine A (9.28 < 11.03)

Replacement Chain Machine A (Given)
How often will machine A be replaced? 2 In year 5, and again in year 10 PVA (Investment)=20 +20/(1.15)+20/(1.110) = 40.13 PVA (Operating Costs) = N=15, I/Y=10, PV=???, PMT=4m, FV=0::PV= $30.42m PVA = = $70.55m

Replacement Chain Machine B (Given)
How often will machine B be replaced? 4 In years 3, 6, 9, 12 PVB (Investment) = 15+15/(1.13)+15/(1.16)+15/(1.19)+15/(1.112) = 45.88 PVB (Operating Costs) = N = 15, I/Y=10, PV=???, PMT=5m,FV=0::PV= $38.03m PVB = = $83.91m

Replacement Chain Pick One (Given)
So which machine do we invest in? A $70.55, or B $ 83.91 Choose A Does it matter if we use EAC or Equal Horizons? It does not matter whether we use the replacement chain or the EAC

Twist Now, if the machines also vary in the revenue that they will produce (possible because of quality variations) how will we modify our methods?

Equivalent Annual Revenue (EAR)
The EAR is the payment of an annuity with the same PV and life as the investment Used when the different projects produce different revenue streams Spreads the machines revenue evenly over it’s life Get the EAR just like the EAC, but now we are using revenue so we want to pick the machine with the higher EAR

Replacing an Existing Machine
The existing machine will last for 2 years. It will produce a cash inflow of $4,000 in year 1 and $4,000 in year 2. You can replace this with a new machine that costs $15,000 but will produce cash inflows of $8,000 a year for three years. Do you go for the new machine or stay with the old one? Assume a 6% discount rate.

Machines EAR NPVnew = NPVold = EARnew = EARold =
Do we replace the machine? Why?

New Machine NPV PV of cash flows
N = 3, I/Y = 6, PV=???, PMT = 8,000, FV=0 PV = 21,384.1

New Machine PV of cash flows = $21,384.1
NPV = -15, ,384.1 = 6,384.1

New Machine PV of cash flows = $21,384.1
NPV = -15, ,380 = 6,384.1 EAR: N = 3, I/Y = 6, PV=6,384.1, PMT = ???, FV=0 PMT = $2,388.35 New Machine’s EAR is $2,388.35

Old Machine PV of cash flows N = 2, I/Y = 6, PV=???, PMT = 4,000, FV=0

Old Machine PV of cash flows = $7,333.58
NPV = , = 7,333.58

Old Machine PV of cash flows = $7,333.58
NPV = , = 7,333.58 EAR: N = 2, I/Y = 6, PV=7,333.58, PMT = ???, FV=0 PMT = $4,000 Old Machine’s EAR is $4,000

Machines EAR NPVnew = $6,380 NPVold = $7,333.58
EARnew = $2,387 EARold = $4,000 Do we replace the machine? Why?

Machines EAR NPVnew = $6,380 NPVold = $7,333.58
EARnew = $2,387 EARold = $4,000 Do we replace the machine? Why? NO, the old machine has a higher EAR than the new machine.

Quick Quiz How do we determine if cash flows are relevant to the capital budgeting decision? What are the different methods for computing operating cash flow, and when are they important? How should cash flows and discount rates be matched when inflation is present? What is equivalent annual cost, and when should it be used?

Making Capital Investment Decisions

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Making Capital Investment Decisions

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