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Valuation

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

2

• • • • • • • • • • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

The Big Picture: Part II -Valuation

A. Valuation: Free Cash Flow and Risk

Apr 1

Lecture: Valuation of Free Cash Flows Apr 3

Case: Ameritrade B. Valuation: WACC and APV

Apr 8

Lecture: WACC and APV Apr 10

Case: Dixon Corporation Apr 15

Case: Diamond Chemicals C. Project and Company Valuation

Apr 17

Lecture: Real Options Apr 24

Case: MW Petroleum Corporation Apr 29

Lecture: Valuing a Company May 1

Case: Cooper Industries, Inc. May 6

Case: The Southland Corporation

3

Valuation Tools

• →Is project A better than doing nothing? →Is project A better than project B?

→• • for valuation.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

A key task of managers is to undertake valuation exercises in order to allocate capital between mutually exclusive projects:

Is the project’s version A better than its modified version A’?

The process of valuation and ultimately of capital budgeting generally involves many factors, some formal, some not (experience, hard-to-formalize information, politics, etc.). We will focus on financial tools 4

Valuation Tools (cont.)

• • time and risk. • → → Versatility

→ Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

These tools provide managers with numerical techniques to “keep score” and assist in the decision-making process. They build on modern finance theory and deal with cash flows, All rely on (often highly) simplified models of the business:

Technical limitations (less now with computers) Understandability and “communicatibility”

5

How to Value a Project or a Firm?

• → → • → → → • of these.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Look up the price of a comparable project

Arbitrage pricing

More on using comps soon

Calculate NPV:

Estimate the expected cash flows

Estimate the appropriate discount rate for each cash flow Calculate NPV Caveat: Many companies do not use NPV but IRR, payback period, etc. You need to be an educated avoider 6

• firm. • • Plan of Attack:

→ → → • → → Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

The Free Cash Flow (FCF) Approach

FCF: The expected after tax cash flows of an all equity These cash flows ignore the tax savings the firm gets from debt financing (the deductibility of interest expense). Step 1: Estimate the Free Cash Flows.

Step 2: Assess the risk of the free cash flows.

Step 3: Account for the effect of financing on value. Preview of Step 3: Two ways to account for tax shield:

Adjust the discount rate (WACC method). Adjust the cash flow estimate (APV method).

Step 1: Calculating Cash Flows

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

8

Count All incremental , after-tax cash flows allowing for reasonable inflation .

• All:

→ → • • → → Note:

• • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Don’t just look at operating profits in the out years.

If project requires follow-on CAPX or additional working capital, take these into account. After-tax: The rest goes to the IRS.

Be consistent in your treatment of inflation:

Discount nominal cash flows at nominal discount rates. Nominal rates reflect inflation in overall economy, but inflation in cash flows may be different.

In fact, some items in cash flows, e.g., depreciation, may have no inflation.

9

Equivalent Expressions for Free Cash Flows -EBIT t)(1FCF -CAPX -t EBITD t)(1FCF -CAPX -EBIT t)(1FCF ×−= ×+×−= +×−= Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

(see Finance Theory I)

Assets

Net in Change NWC in Change on Depreciati NWC in Change on Depreciati Note:

EBIT = Earnings before interest and taxes

EBITD = Earnings before interest and taxes and depreciation = EBIT + Depreciation Change in NWC is sometimes called Investment in NWC.

Example of Free Cash Flow Calculation

1998 1999 Sales

1,000 1,200 Cost of Goods Sold 700 850 Depreciation

30 35 Interest Expense 40 50 Taxes (38%) 80 90 Profit After taxes 150 175 Capital Expenditures 40 40 Accounts Receivable 50 60 Inventories

50 60 Accounts Payable

20

25

In 1999: FCF = EBIT*(1-t) + Depreciation -CAPX -Change in NWC ĺ EBIT = 1,200 -850 -35 = 315 ĺ t=38%

ĺ Ch. NWC = (60+60-25) -(50+50-20) = 15 ĺ FCF = 315 * (1-.38) + 35 -40 -15 = 175.3

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

10

11

Beware!

• → → • this stage! • → were 100% equity financed.

→ • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Note:

We ignored interest payments We computed taxes on EBIT

Do not take the effect of financing (e.g., interest) into account at Remember our plan:

First, determine the expected cash flows as if the project Later, we will adjust for financing. If you count financing costs in cash flow, you count them twice.

12

→ → → •

→ → •

→ → → • •

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Turbo Widget Example

XYZ, a profitable widget producer (0M annual after-tax profit) contemplates introducing new Turbo Widgets (TWs), developed in its labs at an R&D cost of M over the past 3 years.

New plant to produce TW would cost M today

last 10 years with salvage value of M

be depreciated to

Valuation

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

2

• • • • • • • • • • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

The Big Picture: Part II -Valuation

A. Valuation: Free Cash Flow and Risk

Apr 1

Lecture: Valuation of Free Cash Flows Apr 3

Case: Ameritrade B. Valuation: WACC and APV

Apr 8

Lecture: WACC and APV Apr 10

Case: Dixon Corporation Apr 15

Case: Diamond Chemicals C. Project and Company Valuation

Apr 17

Lecture: Real Options Apr 24

Case: MW Petroleum Corporation Apr 29

Lecture: Valuing a Company May 1

Case: Cooper Industries, Inc. May 6

Case: The Southland Corporation

3

Valuation Tools

• →Is project A better than doing nothing? →Is project A better than project B?

→• • for valuation.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

A key task of managers is to undertake valuation exercises in order to allocate capital between mutually exclusive projects:

Is the project’s version A better than its modified version A’?

The process of valuation and ultimately of capital budgeting generally involves many factors, some formal, some not (experience, hard-to-formalize information, politics, etc.). We will focus on financial tools 4

Valuation Tools (cont.)

• • time and risk. • → → Versatility

→ Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

These tools provide managers with numerical techniques to “keep score” and assist in the decision-making process. They build on modern finance theory and deal with cash flows, All rely on (often highly) simplified models of the business:

Technical limitations (less now with computers) Understandability and “communicatibility”

5

How to Value a Project or a Firm?

• → → • → → → • of these.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Look up the price of a comparable project

Arbitrage pricing

More on using comps soon

Calculate NPV:

Estimate the expected cash flows

Estimate the appropriate discount rate for each cash flow Calculate NPV Caveat: Many companies do not use NPV but IRR, payback period, etc. You need to be an educated avoider 6

• firm. • • Plan of Attack:

→ → → • → → Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

The Free Cash Flow (FCF) Approach

FCF: The expected after tax cash flows of an all equity These cash flows ignore the tax savings the firm gets from debt financing (the deductibility of interest expense). Step 1: Estimate the Free Cash Flows.

Step 2: Assess the risk of the free cash flows.

Step 3: Account for the effect of financing on value. Preview of Step 3: Two ways to account for tax shield:

Adjust the discount rate (WACC method). Adjust the cash flow estimate (APV method).

Step 1: Calculating Cash Flows

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

8

Count All incremental , after-tax cash flows allowing for reasonable inflation .

• All:

→ → • • → → Note:

• • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Don’t just look at operating profits in the out years.

If project requires follow-on CAPX or additional working capital, take these into account. After-tax: The rest goes to the IRS.

Be consistent in your treatment of inflation:

Discount nominal cash flows at nominal discount rates. Nominal rates reflect inflation in overall economy, but inflation in cash flows may be different.

In fact, some items in cash flows, e.g., depreciation, may have no inflation.

9

Equivalent Expressions for Free Cash Flows -EBIT t)(1FCF -CAPX -t EBITD t)(1FCF -CAPX -EBIT t)(1FCF ×−= ×+×−= +×−= Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

(see Finance Theory I)

Assets

Net in Change NWC in Change on Depreciati NWC in Change on Depreciati Note:

EBIT = Earnings before interest and taxes

EBITD = Earnings before interest and taxes and depreciation = EBIT + Depreciation Change in NWC is sometimes called Investment in NWC.

Example of Free Cash Flow Calculation

1998 1999 Sales

1,000 1,200 Cost of Goods Sold 700 850 Depreciation

30 35 Interest Expense 40 50 Taxes (38%) 80 90 Profit After taxes 150 175 Capital Expenditures 40 40 Accounts Receivable 50 60 Inventories

50 60 Accounts Payable

20

25

In 1999: FCF = EBIT*(1-t) + Depreciation -CAPX -Change in NWC ĺ EBIT = 1,200 -850 -35 = 315 ĺ t=38%

ĺ Ch. NWC = (60+60-25) -(50+50-20) = 15 ĺ FCF = 315 * (1-.38) + 35 -40 -15 = 175.3

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

10

11

Beware!

• → → • this stage! • → were 100% equity financed.

→ • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Note:

We ignored interest payments We computed taxes on EBIT

Do not take the effect of financing (e.g., interest) into account at Remember our plan:

First, determine the expected cash flows as if the project Later, we will adjust for financing. If you count financing costs in cash flow, you count them twice.

12

→ → → •

→ → •

→ → → • •

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Turbo Widget Example

XYZ, a profitable widget producer (0M annual after-tax profit) contemplates introducing new Turbo Widgets (TWs), developed in its labs at an R&D cost of M over the past 3 years.

New plant to produce TW would cost M today

last 10 years with salvage value of M

be depreciated to

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over 5 years using straight-line depreciation TWs need painting: Use 40% of the capacity of a painting machine currently owned and used by XYZ at 30% capacity

with maintenance costs of 0,000 (regardless of capacity used) Annual

operating costs: 0,000

operating income generated: M

operating income from sales of regular widgets would decrease by M Working capital (WC): M needed over the life of the project Corporate tax rate 36%

13

Calculate Incremental Cash Flows:

• • → ¾ → ¾ → ¾ Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

We want to compare firm value with and without the project:

V(project) = V(firm w/ project) -V(firm w/o project) Use only cash flows (in and out) attributable to the project.

Sunk costs should be ignored

They are spent w/ or w/o the project (bygones are bygones). Opportunity costs should be accounted for

A project might exclude good alternatives (e.g., use of land). Accounting illusions should be avoided

e.g. the project might be “charged” for a fraction of expenses that would be incurred anyway.

14

• • • • • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

TW Example (cont.)

Which of the following items are relevant to evaluate the project? 0M after-tax profit

R&D cost of M over the past three years The plant’s M cost

Machine’s 0K maintenance cost

Operating income from regular widgets decreases by M

15

• • • • → → • → → 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0

2

2

2

2

2

2

2

2

2

2

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

TW Example (cont.)

Ignore the 0M after-tax profit and focus on incremental cash flows R&D cost of M over the past three years: Sunk cost ==> Ignore it The plant’s M cost: It’s a CAPX ==> Count it

Machine’s 0K maintenance cost: Not incremental ==> Ignore it

Incurred with or without TW production

True even if accounting charges TW production a fraction of these Operating income from widgets decreases by M due to cannibalization

Would not occur without TW production It is an opportunity cost ==> Count it

Year 10

CAPX

20 RW Income decrease

16

Use After-tax Cash Flows

• • etc. • → → → → Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

These are what you have left after paying for your costs (COGS and other costs), and after paying the IRS. Make sure to count the tax benefits of expensing, depreciation, CAPX and Depreciation:

Tax treatment of CAPX depends on depreciation CAPX is not directly subtracted from taxable income

Instead, each year’s depreciation “expense” is subtracted from that year’s taxable income

As far as taxes are concerned, everything is as if there was no CAPX and a cost equal to depreciation was incurred each year.

17

• → → • • 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 0

5

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

TW Example (cont.)

Depreciation:

Straight line depreciation: Flat annual depreciation Accelerated depreciation: Decreasing M CAPX is depreciated linearly over 5 years, down to zero.

D = (20 -0) / 5 = M Salvage value of M is fully taxable since book value is zero.

Year 10

CAPX 20 Depreciation

Salv age Value

TW Example (cont.)

Year 0 1 2 3 4 5 6 7 8 9 10 CAPX 20.0 ----------Income

-42.0 42.0 42.0 42.0 42.0 42.0 42.0 42.0 42.0 42.0 RW Income decrease - 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 Incremental income -40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 Incremental cost -0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 Salvage value ---------- 5.0

Incremental profit -39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 44.6 Depreciation - 4.0 4.0 4.0 4.0 4.0 -----EBIT

-35.6 35.6 35.6

35.6 35.6 39.6 39.6 39.6 39.6 44.6 Incremental taxes (36%) -12.8 12.8 12.8 12.8 12.8 14.3 14.3 14.3 14.3 16.1

Total

-20.0 26.8 26.8 26.8 26.8 26.8 25.3 25.3 25.3 25.3 28.5

Note: We do as if entire EBIT is taxable ==> We ignore (for now) the

fact that interest payments are not taxable.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

18

19

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

So far (but we’re not done yet):

Example: We could have computed the CF in year 1 as

(1 -36%) * 39.6 + 36% * 4 -0 = .8M

CF

= Incr. Profit = Incr. Profit –Taxes –CAPX

= Incr. Profit = Incr. Profit –t * (Incr. Profit t * (Incr. Profit –Depr.)–CAPX = (1–t) * Incr. Profit + t * Depr.t) * Incr. Profit + t * Depr. –CAPX

20

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Changes in (Net) Working Capital:

Working Capital = Inventory + A/R -A/P

Remark 1:

• Many projects need some capital to be tied up (working capital) which constitutes an opportunity cost.

We need the Change in Working Capital implied by the project. Remark 2:

• Accounting measure of earnings are based on:

Sales -Cost of Goods Sold

• But: Income and expense are reported when a sale is declared.

→ COGS in 2000 includes the costs of items sold in 2000 even if the cost was incurred in 1999 or hasn’t been incurred yet. → Sales in 2000 include the income from items sold in 2000 even if the payment has not been received yet.

TW Example (cont.)

Year 0 1 2 3 4 5 6 7 8 9 10 CAPX

20.0 ----------Incremental profit

-39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 44.6 Incremental taxes (36%) -12.8 12.8 12.8 12.8 12.8 14.3 14.3 14.3 14.3 16.1 NWC

2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 -Change in NWC 2.0 ----------2.0 Total

-22.0 26.8 26.8 26.8 26.8 26.8 25.3 25.3 25.3 25.3 30.5

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

22

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Putting It All Together

FCF = (1FCF = (1 –t) * Incr. Profit + t * Depr.t) * Incr. Profit + t * Depr. –CAPX –∆NWC This can also be rewritten as:

FCF = (1FCF = (1 –t) * EBIT + Depr.t) * EBIT + Depr. –CAPX –∆NWC

21

23

Finding the Value of the Cash Flows

• → →→ → Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

What now?

We know how to find the expected Free Cash Flows We want to calculate the present value of the cash flows: We need to account for the tax benefit of interest payments

Adjust the discount rate (WACC method). Adjust the cash flow estimate (APV method). We need to account for the risk of the project

Calculate a risk-adjusted discount rate:

What expected rate of return do outside investors require to invest into the project?

24

Calculating a risk-adjusted discount rate:

• • free cash flows:

• r Assets = r f • [] [] ( ) [] ( )

... 111 3

3 2 21 + + + + + + +

= Assets Assets Assets r r r Cash V Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Ignore the tax benefits of debt for now, i.e. assume the project is 100% equity financed. Then the firm’s or project’s value is the present value of the future Expected Return = Cost of Capital = + Risk Premium The risk premium for an investment is the required rate of return of

the investment minus the risk free rate.

C E C E C E

25

Risk Premium

• • → • → the market return to get the asset beta.

→ asset betas.

→ [ ] [ ]( )

f m a f Assets A r r r −+== β Finance Theory II (15.402) – Sprin

g 2003 – Dirk Jenter

How do we find the Risk Premium? CAPM is one method:

Get risk premium from beta & market premium How do you estimate asset betas?

For an all-equity firm (project), simply regress past stock returns on

For levered firms, regress past stock returns on the market return to get equity betas, then unlever the estimated equity betas to arrive at Find comparable firms with similar risk, estimate their asset betas and average across comparables.

r E r E 26

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Appendix

27

Computing the CAPM asset beta:

• project. • on all of the financial claims on the assets:

• )()()( Equity Debt Assets E

D E

E D D + + + =

[

]

[

]

f market Equity f Equity f market Debt f Debt r r r r −⋅+= −⋅+= )()( )()( β β Finance Theory II (15.402) – Sprin

g 2003 – Dirk Jenter

Definition: Measure of the systematic risk of the cash flows of the firm or Note: The expected return on the assets must equal the expected return The CAPM is a general asset-pricing model that can price any type of

asset. Hence the CAPM specifies the expected returns for both the debt and equity claims:

r E r E r E r E

r E r E

r E 28

Cont.:

• • • Equity

Debt Assets E

D E

E D D βββ + + + =

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Substituting the CAPM equations above into the formula for the expected

return on the assets, we see that the asset beta is just a weighted average of the debt and equity betas:

Hence we need an estimate of each term on the right-hand side of this

equation. Typically, we start by estimating equity betas from a regression of equity returns on stock market returns. Problem: Sometimes we need to use the betas on “comparable” firms,

either because there is insufficient data on the project available, or

because we try to improve the precision of the estimate in that way. This “comparable firms” procedure for the estimation of asset betas is explained on the next slide.

29

An approach for estimating the asset beta:

1) 2) 3) above:

i. stock returns on market returns.

ii. iii. 4) Calculate the asset beta for our firm as the average of the asset betas

of the comparable firms.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Recognize that all firms that generate cash flow streams with the same

risk will have the same asset beta.

Identify firms that are likely to have cash flow streams that have similar

risk. These are the “comparable” firms.

Estimate asset betas for the comparable firms using the formula

Estimate equity betas for each comparable firm by regressing

Estimate debt betas for each comparable firm in the same

manner. Usually, you won’t have data to do this. In practice, it is common to assume that debt is risk free (debt beta of zero), or to assume debt betas between 0.1 and 0.3, which come from

empirical studies of corporate debt returns. We need to be more careful if leverage is high.

Estimate the market value (D+E) of the firm as the sum of the

market values of the debt and equity of the firm. If market value of debt (D) is not available, proxy with book value of debt.

  中新经纬客户端2月4日电 美东时间周一,美国三大股指集体收高,道指涨超140点。特斯拉大涨近20%,股价创历史新高。

美国三大股指分时走势图 来源:Wind美国三大股指分时走势图 来源:Wind

  截至收盘,道指上涨143.78点,涨幅0.51%,报28399.81点;纳指涨122.47点,涨幅1.34%,报9273.40点;标普500指数涨23.40点,涨幅0.73%,报3248.92点

  美国大型科技股涨跌不一,苹果跌0.27%,亚马逊跌0.23%,奈飞涨3.74%,谷歌母公司涨3.48%,Facebook涨1.13%,微软涨2.44%。

  热门中概股集体上涨,阿里巴巴涨2.84%,京东涨4.01%,百度涨5.61%;惠普森医药涨94.32%,爱奇艺涨7.24%,微博涨3.5%,拼多多涨1.62%,蔚来汽车涨7.14%,网易涨2.72%。

  个股方面,特斯拉收盘大涨近20%,股价报780美元创历史新高。

  经济数据方面,周一美国供应管理协会(ISM)报告称,美国1月ISM制造业PMI指数为50.9,市场预期值为48.5,12月PMI指数为47.2。数据显示,美国制造业新订单指数创2019年5月以来新高。

  欧股方面,欧洲三大股指3日全线收涨。英国《金融时报》100种股票平均价格指数3日报收7326.31点,比前一交易日上涨40.30点,涨幅为0.55%。法国CAC40指数3日报收于5832.51点,较前一交易日上涨26.17点,涨幅为0.45%。德国DAX指数3日上涨63.22点,涨幅为0.49%,报收于13045.19点。

  国际金价3日下跌,纽约商品交易所黄金期货市场交投最活跃的4月黄金期价3日比前一交易日下跌5.5美元,收于每盎司1582.4美元,跌幅为0.35%。

  国际油价3日下跌。纽约商品交易所3月交割的西德克萨斯中质原油(WTI)期货价格下跌1.45美元,跌幅为2.8%,收于每桶50.11美元。伦敦洲际交易所3月布伦特原油期货价格下跌2.21美元,跌幅为3.9%,收于每桶54.41美元。(中新经纬APP)

。 over 5 years using straight-line depreciation TWs need painting: Use 40% of the capacity of a painting machine currently owned and used by XYZ at 30% capacity

with maintenance costs of 0,000 (regardless of capacity used) Annual

operating costs: 0,000

operating income generated: M

operating income from sales of regular widgets would decrease by M Working capital (WC): M needed over the life of the project Corporate tax rate 36%

13

Calculate Incremental Cash Flows:

• • → ¾ → ¾ → ¾ Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

We want to compare firm value with and without the project:

V(project) = V(firm w/ project) -V(firm w/o project) Use only cash flows (in and out) attributable to the project.

Sunk costs should be ignored

They are spent w/ or w/o the project (bygones are bygones). Opportunity costs should be accounted for

A project might exclude good alternatives (e.g., use of land). Accounting illusions should be avoided

e.g. the project might be “charged” for a fraction of expenses that would be incurred anyway.

14

• • • • • Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

TW Example (cont.)

Which of the following items are relevant to evaluate the project? 0M after-tax profit

R&D cost of M over the past three years The plant’s M cost

Machine’s 0K maintenance cost

Operating income from regular widgets decreases by M

15

• • • • → → • → → 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0

2

2

2

2

2

2

2

2

2

2

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

TW Example (cont.)

Ignore the 0M after-tax profit and focus on incremental cash flows R&D cost of M over the past three years: Sunk cost ==> Ignore it The plant’s M cost: It’s a CAPX ==> Count it

Machine’s 0K maintenance cost: Not incremental ==> Ignore it

Incurred with or without TW production

True even if accounting charges TW production a fraction of these Operating income from widgets decreases by M due to cannibalization

Would not occur without TW production It is an opportunity cost ==> Count it

Year 10

CAPX

20 RW Income decrease

16

Use After-tax Cash Flows

• • etc. • → → → → Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

These are what you have left after paying for your costs (COGS and other costs), and after paying the IRS. Make sure to count the tax benefits of expensing, depreciation, CAPX and Depreciation:

Tax treatment of CAPX depends on depreciation CAPX is not directly subtracted from taxable income

Instead, each year’s depreciation “expense” is subtracted from that year’s taxable income

As far as taxes are concerned, everything is as if there was no CAPX and a cost equal to depreciation was incurred each year.

17

• → → • • 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 0

5

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

TW Example (cont.)

Depreciation:

Straight line depreciation: Flat annual depreciation Accelerated depreciation: Decreasing M CAPX is depreciated linearly over 5 years, down to zero.

D = (20 -0) / 5 = M Salvage value of M is fully taxable since book value is zero.

Year 10

CAPX 20 Depreciation

Salv age Value

TW Example (cont.)

Year 0 1 2 3 4 5 6 7 8 9 10 CAPX 20.0 ----------Income

-42.0 42.0 42.0 42.0 42.0 42.0 42.0 42.0 42.0 42.0 RW Income decrease - 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 Incremental income -40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 Incremental cost -0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 Salvage value ---------- 5.0

Incremental profit -39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 44.6 Depreciation - 4.0 4.0 4.0 4.0 4.0 -----EBIT

-35.6 35.6 35.6

35.6 35.6 39.6 39.6 39.6 39.6 44.6 Incremental taxes (36%) -12.8 12.8 12.8 12.8 12.8 14.3 14.3 14.3 14.3 16.1

Total

-20.0 26.8 26.8 26.8 26.8 26.8 25.3 25.3 25.3 25.3 28.5

Note: We do as if entire EBIT is taxable ==> We ignore (for now) the

fact that interest payments are not taxable.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

18

19

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

So far (but we’re not done yet):

Example: We could have computed the CF in year 1 as

(1 -36%) * 39.6 + 36% * 4 -0 = .8M

CF

= Incr. Profit = Incr. Profit –Taxes –CAPX

= Incr. Profit = Incr. Profit –t * (Incr. Profit t * (Incr. Profit –Depr.)–CAPX = (1–t) * Incr. Profit + t * Depr.t) * Incr. Profit + t * Depr. –CAPX

20

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Changes in (Net) Working Capital:

Working Capital = Inventory + A/R -A/P

Remark 1:

• Many projects need some capital to be tied up (working capital) which constitutes an opportunity cost.

We need the Change in Working Capital implied by the project. Remark 2:

• Accounting measure of earnings are based on:

Sales -Cost of Goods Sold

• But: Income and expense are reported when a sale is declared.

→ COGS in 2000 includes the costs of items sold in 2000 even if the cost was incurred in 1999 or hasn’t been incurred yet. → Sales in 2000 include the income from items sold in 2000 even if the payment has not been received yet.

TW Example (cont.)

Year 0 1 2 3 4 5 6 7 8 9 10 CAPX

20.0 ----------Incremental profit

-39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 39.6 44.6 Incremental taxes (36%) -12.8 12.8 12.8 12.8 12.8 14.3 14.3 14.3 14.3 16.1 NWC

2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 -Change in NWC 2.0 ----------2.0 Total

-22.0 26.8 26.8 26.8 26.8 26.8 25.3 25.3 25.3 25.3 30.5

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

22

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Putting It All Together

FCF = (1FCF = (1 –t) * Incr. Profit + t * Depr.t) * Incr. Profit + t * Depr. –CAPX –∆NWC This can also be rewritten as:

FCF = (1FCF = (1 –t) * EBIT + Depr.t) * EBIT + Depr. –CAPX –∆NWC

21

23

Finding the Value of the Cash Flows

• → →→ → Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

What now?

We know how to find the expected Free Cash Flows We want to calculate the present value of the cash flows: We need to account for the tax benefit of interest payments

Adjust the discount rate (WACC method). Adjust the cash flow estimate (APV method). We need to account for the risk of the project

Calculate a risk-adjusted discount rate:

What expected rate of return do outside investors require to invest into the project?

24

Calculating a risk-adjusted discount rate:

• • free cash flows:

• r Assets = r f • [] [] ( ) [] ( )

... 111 3

3 2 21 + + + + + + +

= Assets Assets Assets r r r Cash V Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Ignore the tax benefits of debt for now, i.e. assume the project is 100% equity financed. Then the firm’s or project’s value is the present value of the future Expected Return = Cost of Capital = + Risk Premium The risk premium for an investment is the required rate of return of

the investment minus the risk free rate.

C E C E C E

25

Risk Premium

• • → • → the market return to get the asset beta.

→ asset betas.

→ [ ] [ ]( )

f m a f Assets A r r r −+== β Finance Theory II (15.402) – Sprin

g 2003 – Dirk Jenter

How do we find the Risk Premium? CAPM is one method:

Get risk premium from beta & market premium How do you estimate asset betas?

For an all-equity firm (project), simply regress past stock returns on

For levered firms, regress past stock returns on the market return to get equity betas, then unlever the estimated equity betas to arrive at Find comparable firms with similar risk, estimate their asset betas and average across comparables.

r E r E 26

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Appendix

27

Computing the CAPM asset beta:

• project. • on all of the financial claims on the assets:

• )()()( Equity Debt Assets E

D E

E D D + + + =

[

]

[

]

f market Equity f Equity f market Debt f Debt r r r r −⋅+= −⋅+= )()( )()( β β Finance Theory II (15.402) – Sprin

g 2003 – Dirk Jenter

Definition: Measure of the systematic risk of the cash flows of the firm or Note: The expected return on the assets must equal the expected return The CAPM is a general asset-pricing model that can price any type of

asset. Hence the CAPM specifies the expected returns for both the debt and equity claims:

r E r E r E r E

r E r E

r E 28

Cont.:

• • • Equity

Debt Assets E

D E

E D D βββ + + + =

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Substituting the CAPM equations above into the formula for the expected

return on the assets, we see that the asset beta is just a weighted average of the debt and equity betas:

Hence we need an estimate of each term on the right-hand side of this

equation. Typically, we start by estimating equity betas from a regression of equity returns on stock market returns. Problem: Sometimes we need to use the betas on “comparable” firms,

either because there is insufficient data on the project available, or

because we try to improve the precision of the estimate in that way. This “comparable firms” procedure for the estimation of asset betas is explained on the next slide.

29

An approach for estimating the asset beta:

1) 2) 3) above:

i. stock returns on market returns.

ii. iii. 4) Calculate the asset beta for our firm as the average of the asset betas

of the comparable firms.

Finance Theory II (15.402) – Spring 2003 – Dirk Jenter

Recognize that all firms that generate cash flow streams with the same

risk will have the same asset beta.

Identify firms that are likely to have cash flow streams that have similar

risk. These are the “comparable” firms.

Estimate asset betas for the comparable firms using the formula

Estimate equity betas for each comparable firm by regressing

Estimate debt betas for each comparable firm in the same

manner. Usually, you won’t have data to do this. In practice, it is common to assume that debt is risk free (debt beta of zero), or to assume debt betas between 0.1 and 0.3, which come from

empirical studies of corporate debt returns. We need to be more careful if leverage is high.

Estimate the market value (D+E) of the firm as the sum of the

market values of the debt and equity of the firm. If market value of debt (D) is not available, proxy with book value of debt.

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