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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

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.

  [环球时报综合报道]俄罗斯和土耳其就叙利亚问题达成协议,美国被晾在一边。22日晚,俄土两国总统签署“历史性协议”,主要内容是由两国接管此前被库尔德武装控制的叙利亚东北部地区。一向埋怨“打仗太花钱”的美国总统川普对这一安排似乎很满意,23日发推特称:“土叙边界取得巨大成功!安全区已创建,停火已执行……库尔德人很安全……”23日中午他宣布将对土耳其取消制裁,称土政府已承诺停火。然而,美国媒体显然无法接受华盛顿在地区领导权的旁落。“美国成为最大输家”,美国有线电视新闻网(CNN)23日哀叹,“普京和埃尔多安跃升为该地区主要的地缘力量经纪人”,“美国在塑造叙利亚的未来方面将没有一席之地”。目前,奉总统之命撤出叙利亚的美军处境确实尴尬。23日,伊拉克防长下逐客令说,这批撤到伊拉克的美军“必须在四周内离境”。

  “俄土协议可能使地区形势发生新的改观”,埃及《黎明报》23日称,这一“历史性协议”使在地区博弈的各方力量此消彼长,俄罗斯的地位和影响力将进一步上升,而美国则由于抛弃库尔德盟友、关键时刻又撤军到伊拉克境内而遭到蔑视。土俄协议中规定的联合巡逻、150小时的新期限等,保证了俄土叙的利益,库尔德武装也因为时间的宽限而变得比以前更容易接受现实,“惟一失分和受损的是美国”。文章称,美国因为自私及其中东政策的失误、前后不连贯而成了“孤家寡人”,其撤离的军队在途经库尔德人聚居的村镇时,还受到库尔德人砸扔土豆的“隆重欢送场面”,到了伊拉克西北部之后,伊拉克强调他们只能“过境”,“没有获得任何停留和驻扎权”。23日,伊拉克防长希姆马里在巴格达与来访的美国防长埃斯珀会晤后称,从叙利亚“过境”伊拉克的美军“将在不超过四个星期的时间内”前往科威特、卡塔尔或美国,他还说,将美军运出伊拉克的飞机已经抵达。

  23日,俄媒纷纷称赞索契峰会是“俄罗斯和土耳其的共同外交胜利”。俄政治研究所所长马尔科夫表示,这一协议签署意味着俄罗斯在具有重要战略意义的地中海将拥有永久军事基地,同时将恢复与叙利亚的经济合同,而“叙利亚正在接近和平”。

  俄土领导人会晤后,普京与叙利亚总统巴沙尔通电话。巴沙尔向普京表示感谢,表达对俄土领导人会晤成果的全面支持。巴沙尔还表示准备派遣叙利亚边防部队与俄罗斯宪兵一起前往叙土边界,继续进行政治监管。与普京通话后,巴沙尔22日赴叙利亚西北部的伊德利卜省视察,看望前线士兵,并谴责土耳其“和平之泉”的军事行动是“侵略”。中东媒体评论称,巴沙尔此前很少公开讲话,这次他的底气来自俄罗斯的支持。

  不过,眼下叙利亚的局势依然不太平。据“阿拉比亚”电视台23日报道,当天在叙利亚北部的阿勒颇,支持土耳其的一些武装派别与库尔德武装分子发生激战,双方使用了中型和重型武器,导致至少4人死亡。

  [环球时报驻埃及、美国特派特约记者 黄培昭 温燕 柳玉鹏 环球时报记者 赵雨笙] 

。 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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