making capital investment decisions. what finance functions add the most to firm value? 2

Making Capital Investment Decisions

What finance functions add the most to firm value?

2

3

General Rules of Discounting

1. Only cash flows matter

2. Only examine incremental cash flow

3. Be consistent in treatment of inflation

4. Deduct taxes before discounting

4

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”

5

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

6

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

7

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 -200 400 800

Blu-Ray Incremental CF

8

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 -200 400 800

Blu-Ray Incremental CF -200

9

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 -200 400 800

Blu-Ray Incremental CF -200 100

10

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 -200 400 800

Blu-Ray Incremental CF -200 100 200

11

Working Capital

Money the firm has on hand that is necessary for running the businessThink 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 calculationsWhy???

12

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?

13

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?

14

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?

NO, we don’t care about accounting numbers

We do care about changes in overhead that result from our project

15

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?

16

Example

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?

17

Example

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?

18

Example

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

19

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 obsolescenceDepreciation is based on the asset’s expected life,

not on the life of the project LAND DOES NOT DEPRECIATE

20

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

21

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 billThis determines the Tax Shield

22

The Two EBT’sEBDT

EBT (Tax)

EBT (Book)

-Tax Dep -Book Dep

Taxes Paid

-Taxes Paid

Net Income =Book EBT – Taxes Paid

Tax Rate

23

Book Depreciation

This type of depreciation is used to calculate a company’s Net Income

Straight line Depreciation: (Investment – Salvage Value) / Expected lifeInvestment:Salvage Value:

24

Book Depreciation

This type of depreciation is used to calculate a company’s Net Income

Straight line Depreciation: (Investment – Salvage Value) / Expected lifeInvestment: what did we pay for itSalvage Value:

25

Book Depreciation

This type of depreciation is used to calculate a company’s Net Income

Straight line Depreciation: (Investment – Salvage Value) / Expected lifeInvestment: what did we pay for itSalvage Value: asset value at end of it’s life

What can we sell it for?

26

Tax Depreciation Tax Depreciation is calculated using the

Modified Accelerated Cost Recovery SystemTax 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?

27

Tax Depreciation Tax Depreciation is calculated using the

Modified Accelerated Cost Recovery SystemTax 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

28

Tax Depreciation Schedules by Recovery-Period Class

Year(s) 3-Year 5-Year 7-Year 10-Year

1 33.33 20.00 14.29 10.00 2 44.45 32.00 24.49 18.00 3 14.81 19.20 17.49 14.40 4 7.41 11.52 12.49 11.52 5 11.52 8.93 9.22 6 5.76 8.93 7.37 7 8.93 6.55 8 4.45 6.55 9 6.55 10 6.55 11 3.29

29

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

30

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 180,000 180,000 180,000 180,000 180,000

Tax

31

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 180,000 180,000 180,000 180,000 180,000

Tax 200,000

32

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 180,000 180,000 180,000 180,000 180,000

Tax 200,000 320,000

33

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 180,000 180,000 180,000 180,000 180,000

Tax 200,000 320,000 192,000

34

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 180,000 180,000 180,000 180,000 180,000

Tax 200,000 320,000 192,000 115,200

35

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 180,000 180,000 180,000 180,000 180,000

Tax 200,000 320,000 192,000 115,200 115,200

36

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 180,000 180,000 180,000 180,000 180,000

Tax 200,000 320,000 192,000 115,200 115,200 57,600

37

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

38

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?

39

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?

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:

40

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?

Initial investment: 1,500,000; 5 years Tax Dep: 20%, 32%, 19.2%

Year 3 BV: 1,500,000 * (1-0.2-0.32-0.192)=432,000

Profit:

41

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?

Initial investment: 1,500,000; 5 years Tax Dep: 20%, 32%, 19.2%

Year 3 BV: 1,500,000 * (1-0.2-0.32-0.192)=432,000 Profit: 600,000 - 432,000=168,000 Capital Gains Tax owed:

42

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?

Initial investment: 1,500,000; 5 years Tax Dep: 20%, 32%, 19.2%

Year 3 BV: 1,500,000 * (1-0.2-0.32-0.192)=432,000 Profit: 600,000 - 432,000=168,000 Capital Gains Tax owed 0.20 * 168,000=

$33,600

43

Inflation and Capital Budgeting

Inflation: general increase in the price of goodsAlternative: the general decline in the purchasing

power of moneyHershey 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.

44

Dealing with Inflation

KEY: Keep everything in either real or nominal termsReal Cash Flows → Real Discount RateNominal Cash Flows → Nominal Discount Rate

As long as we are consistent in our treatment of inflation we will get the same NPV

45

Real vs. Nominal

Nominal dollars: Real dollars: Nominal rate: Real rate:

46

Real vs. Nominal

Nominal dollars are the dollars we have in our wallets

Real dollars Nominal rate Real rate

47

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

48

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 interestAccounts for what you should earn & inflation

Real rate

49

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 is want an investment should earnIgnores inflation

50

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)

51

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?

52

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?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?

53

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?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 ≈1.07692307692N= 30, I/Y = 7.069, PV= 10,000, PMT = 0, FV= ????FV = $92,372.03, this is the Future Real Dollar

Value

54

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?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 ≈1.07692307692N = 30, I/Y = 7.069, PV= 10,000, PMT = 0, FV= ????FV = $92,372.03

ORN= 30, I/Y = 4, PV=????, PMT = 0, FV= 299,599.22PV = $92,372.03, this is the Future Real Dollar Value

55

Real vs. Nominal Rate Example 2 Nominal Rate is 15%, inflation is 10%

What is the real discount rate? What are the nominal cash flows?

Year 0 1 2 3

Real CF -10 10 11 12

Nominal CF -10

56

Real vs. Nominal Rate Example 2 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 0 1 2 3

Real CF -10 10 11 12

Nominal CF -10

57

Real vs. Nominal Rate Example 2 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 0 1 2 3

Real CF -10 10 11 12

Nominal CF -10 10*1.1=

11

58

Real vs. Nominal Rate Example 2 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 0 1 2 3

Real CF -10 10 11 12

Nominal CF -10 10*1.1=

11

11*1.12=

13.31

59

Real vs. Nominal Rate Example 2 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 0 1 2 3

Real CF -10 10 11 12

Nominal CF -10 10*1.1=

11

11*1.12=

13.31

12*1.13=

15.97

60

Depreciation & Inflation

Depreciation is always given in nominal termsSo, 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

61

Costs we Do NOT Care About Sunk Costs: are expenses that have already been

paidAlready paid so NOT INCREMENTAL to projectEx: 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.

62

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

63

Estimating Cash Flows

Cash Flow from OperationsRecall that:

OCF = EBIT – Taxes + Depreciation

64

Other Methods for Computing OCF Bottom-Up Approach

Works only when there is no interest expenseOCF = NI + depreciation

Top-Down ApproachOCF = Sales – Costs – TaxesDo not subtract non-cash deductions

Tax Shield ApproachOCF = (Sales – Costs)(1 – τ) + Depreciation* τ

65

Interest Expense

For now, assume that debt is independent of the projectInterest expense is not influenced by the

project Later we will deal with the impact that

debt has on firm value

66

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%

67

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 1.00 1.00 0.00

68

Big Example 1: OperationsDenon 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 1.00 1.00

EBDT 2.60 3.00 3.40

Book Dep 1.00 1.00 1.00

EBT 1.60 2.00 2.40

69

Big Example 1: Corp TaxesDenon 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

70

Big Example 1: Capital GainsDenon 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

71

Big Example 1: Op 2, Net IncomeDenon 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 1.00 1.00

EBDT 2.60 3.00 3.40

Book Dep 1.00 1.00 1.00

EBT 1.60 2.00 2.40

Tax 0.56 0.49 0.85

Net Income 1.04 1.51 1.55

72

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 0.00 1.00

Net Income 1.04 1.51 1.55

Book Dep 1.00 1.00 1.00

Sale Proceeds 2.00

Capital Gains (0.11)

Lost CD Sales (1.00) (1.00) (1.00)

Net Cash Flow (6.00) 1.04 1.51 4.44

NPV (0.47)

73

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%.

74

Other Tricks with NPV

Optimal Timing of a Project Choosing between equipment with different

lives Replacing an Existing Machine Cost of Excess Capacity

75

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%

76

Teak Farm Example

When do we harvest the trees?

Why

Year 0 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 $124.18 $123.16

77

Teak Farm Example

When do we harvest the trees? Either in year 5 or 6

Why?

Year 0 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 $124.18 $123.16

78

Teak Farm Example

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

Year 0 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 $124.18 $123.16

79

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) = 614.46 + 4,000 = $4,614.46 Cheap: N = 5, I/Y = 10, PV=????, PMT = 500, FV=0

PV(costs) = 1,895.39 + 1,000 = $2,895.39 Cheap PV(Costs) is lower, so it has a higher NPV

Doesn’t account for Cadillac’s longer life

80

Comparing Investments with Different Expected Lives

1. Replacement Chain Repeat projects until they begin and end at

the same time. Compute NPV for the “repeated projects.”

2. The Equivalent Annual Cost Method

81

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

82

Replacement Chain ApproachThe Cadillac cleaner time line of cash flows:

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

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

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Replacement Chain ApproachThe Cadillac cleaner time line of cash flows:

-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100

0 1 2 3 4 5 6 7 8 9 10

-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500

0 1 2 3 4 5 6 7 8 9 10

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

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Replacement Chain ApproachThe Cadillac cleaner time line of cash flows:

-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100

0 1 2 3 4 5 6 7 8 9 10

-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500

0 1 2 3 4 5 6 7 8 9 10

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

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Replacement Chain ApproachThe Cadillac cleaner time line of cash flows:

-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100

0 1 2 3 4 5 6 7 8 9 10

-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500

0 1 2 3 4 5 6 7 8 9 10

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

PV(Costs) = $4,693.20 =$2,895.39 + $2,895.39 / (1.15)

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Equivalent Annual Cost (EAC) Spread the cost of buying and maintaining a

machine over its expect life, while accounting for time value of moneyThe payments that an annuity with the same PV and

lifeUsed when the only difference is the costsPick the machine with the lower EAC

Pick the machine with the lower EACThe EAC for the Cadillac is ($4,614.46)?The EAC for the Cheapskate is ($2,895.39)?

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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 (750.98 < 763.80)

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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 = 15.16 + 20 = $35.16 (B) N = 3, I/Y = 10, PV=???, PMT = 5, FV=0 :: Op PV=12.43 (B) Total PV = 12.43 + 15 = $27.4

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EAC Solution (Given)PVA EACA EACA EACA EACA EACA |-----------|----------|----------|----------|----------| 0 1 2 3 4 5 PVB EACB EACB EACB |-----------|----------|----------| 0 1 2 3

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

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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 = 40.13 +30.42 = $70.55m

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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 = 45.88+38.03 = $83.91m

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Replacement Chain Pick One (Given)

So which machine do we invest in?A $70.55, or B $ 83.91Choose A

Does it matter if we use EAC or Equal Horizons?It does not matter whether we use the

replacement chain or the EAC

93

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?

94

Equivalent Annual Revenue (EAR) The EAR is the payment of an annuity with the

same PV and life as the investmentUsed when the different projects produce different

revenue streamsSpreads 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

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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.

96

Machines EAR

NPVnew = NPVold =

EARnew = EARold =

Do we replace the machine? Why?

97

New Machine NPV PV of cash flows

N = 3, I/Y = 6, PV=???, PMT = 8,000, FV=0 PV = 21,384.1

98

New Machine PV of cash flows = $21,384.1 NPV = -15,000 + 21,384.1 = 6,384.1

99

New Machine PV of cash flows = $21,384.1 NPV = -15,000 + 21,380 = 6,384.1 EAR: N = 3, I/Y = 6, PV=6,384.1, PMT

= ???, FV=0PMT = $2,388.35

New Machine’s EAR is $2,388.35

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Old Machine PV of cash flows

N = 2, I/Y = 6, PV=???, PMT = 4,000, FV=0PV = 7,333.58

101

Old Machine PV of cash flows = $7,333.58 NPV = -0 + 7,333.58 = 7,333.58

102

Old Machine PV of cash flows = $7,333.58 NPV = -0 + 7,333.58 = 7,333.58 EAR: N = 2, I/Y = 6, PV=7,333.58, PMT

= ???, FV=0PMT = $4,000

Old Machine’s EAR is $4,000

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Machines EAR

NPVnew = $6,380 NPVold = $7,333.58

EARnew = $2,387 EARold = $4,000

Do we replace the machine? Why?

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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.

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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?