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This version 11/9/2001. Includes WORD tables. Lecture: Valuing Companies and Investment Projects. Copyright K. Cuthbertson and D. Nitzsche. TOPICS . Basic Ideas Compounding/Terminal Value Discounted Present Value DPV \ Discounted Cash Flow DCF

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This version 11/9/2001. Includes WORD tables

Lecture: Valuing Companies and

Investment Projects

Copyright K. Cuthbertson and D. Nitzsche

TOPICS

Basic Ideas

Compounding/Terminal Value

Discounted Present Value DPV \ Discounted Cash Flow DCF

Investment ( Project) Appraisal, Internal Rate Of Return,

Valuation Of The Firm: Enterprise Vale and Equity

~ choice of discount rate

~ valuation in practice: EBITD, Depreciation, FCF etc.

Complementary Valuation Techniques: EP, EVA,APV

Self Study: Other Investment Appraisal Methods

Copyright K. Cuthbertson and D. Nitzsche

READING

Investments:Spot and Derivative Markets, K.Cuthbertson and D.Nitzsche

Chapter 3

Discounted Present Value DPV \ Discounted Cash Flow DCF

Internal Rate Of Return, IRR

Investment ( Project) Appraisal

Valuation Of The Firm And The Firm’s Equity (Incl. Continuing Value).

Valuation In Practice: EBITD, Depreciaiton, FCF etc

Other Investment Appraisal Methods

Chapter 11

Economic Profit, Economic Value Added, Adjusted Present Value

P. 342-346.

Copyright K. Cuthbertson and D. Nitzsche

BASIC IDEASCompounding/Terminal ValueDiscounted Present Value DPV Discounted Cash Flow DCF Internal Rate of Return Investment/ Project Appraisal

Copyright K. Cuthbertson and D. Nitzsche

Compounding/ Terminal Value

Assume zero inflation+cash flows known with certainty

Vo = value today ($1000), r = interest rate (0.10)

Value in 1,2 years time

V1 = (1.1) 1000 = $1100

V2 = (1.1) 1100 = (1.1) 2 1000 = $1210

Terminal Value after n-years: Vn = Ao (1 + r)n

We could ‘move all payments forward’ to time n=10 years and then add them - but we do not do this

Copyright K. Cuthbertson and D. Nitzsche

Discounting

‘Bring all payments back’ to t=0 and then add.

Value today of V2 = $1210 payable in 2 yrs ?

DPV =

Hence “ DPV of $1210 is $1000”

Which means that $1000 today is equivalent to $ 1210 payable in 2-years

“Discount Factor” d2 =

Copyright K. Cuthbertson and D. Nitzsche

Discounted Present Value (DPV)

What is value today of stream of payments - usually called ‘Cash Flows’, assuming a constant discount factor? :

DPV = = d1 V1 + d2 V2 + ..

r = ‘discount rate’

d = “discount factor” < 1

Discounting, puts all future cash flows on to a ‘common time’ at t=0 - so they can then be “added up”.

Copyright K. Cuthbertson and D. Nitzsche

Investment (Project) Appraisal:Decision Criteria

Operating Cash Flows, (ie. revenues less operating costs, less taxes) V1 = $1100, and V2 = $1210

Then DPV(of ‘cash flows’ at r =10%) = $2000

Suppose Capital Cost (Investment Expenditure), KC = $2000

Net Present Value (NPV):NPV = DPV - KC

RULE: If DPV > KC then invest in project

OR If NPV > 0 then invest in project

Our project is just ‘on the margin’ since NPV = 0 when r=10%

Copyright K. Cuthbertson and D. Nitzsche

NPV (for given CFs) and the cost of borrowing, r

NPV

If r <10% then you would invest in the project

If r > 10% you would NOT invest in the project

NPV=145

NPV=0

r= loan rate or discount rate

r=5

r=10

Copyright K. Cuthbertson and D. Nitzsche

Businessmen think in terms the rate of return on the project

What is the rate of return (on capital investment of $2000) ?

It is the rate of return which gives NPV = 0

Hence the IRR is the ‘break-even’ discount rate and IRR = 0.10 (10%)

IRR INVESTMENT DECISION RULE

Invest in project if : IRR > cost of borrowing, r

Copyright K. Cuthbertson and D. Nitzsche

Intuitively what do NPV and IRR rules mean ?

If NPV = 0

OR, IRR = cost of borrowing then this implies

-the CF from the project will just pay offall the annual interest payments on the loan + the principal amount borrowed from the bank

Note: Internal funds are not ‘free’

Copyright K. Cuthbertson and D. Nitzsche

Intuitively what do NPV and IRR rules mean ?

Payoff all interest and principal if NPV=0 or IRR = 10% ?

- KC=2000 (borrowed at r=10%), CF are V1=1100 , V2=1210

Copyright K. Cuthbertson and D. Nitzsche

Valuation of the Firm:Enterprise Value and Equity Value

Copyright K. Cuthbertson and D. Nitzsche

General Case

V0 = FCF1 / (1+r) + FCF2 / ((1+r)2 + ……

FCF= Free Cash Flows

1) Sum to infinity and FCF is constant:

V0 = FCF / r

2) Sum to infinity and FCF grows at rate of g % p.a. (g=0.05 )

V0 = FCF1 / ( r - g)

Copyright K. Cuthbertson and D. Nitzsche

‘Enterprise Value’ and ‘Equity Value’

Enterprise DCF

In practice investment costs occur every year so:

V(whole firm) = DPV ( Free Cash Flows, FCF)

FCF = (Operating ‘cash flows’ - Gross investment) each year

Value of Equity

V(Equity) = V(whole firm) - V(Debt outstanding)

‘Fair value for one share’ = V(Equity) / N

N = no. of shares outstanding (+ ‘minority interests’)

Copyright K. Cuthbertson and D. Nitzsche

‘Enterprise Value’ and Equity Value

In an efficient market the price of the share(s) should equal ‘fair value’

We will learn how to value corporate debt, in later lectures

Copyright K. Cuthbertson and D. Nitzsche

‘Valuing the ‘Firm’ :Continuing Value

The DPV of ALL the firm’s future cash flows is often ‘split’ into two (or more) planning horizons:

‘ENTERPRISE DCF’

= DPV of FCF in years 1-5

+ DPV of ‘Continuing Value’ after year-5

Copyright K. Cuthbertson and D. Nitzsche

‘Valuing the ‘Firm’ :Continuing Value

Special Case A:

i) the discount rate is constant in each year

ii) Cash flows, FCF are constant in each year and persist ‘for ever’ (ie. perpetuity) then

CV = FCF/ r

This is often used to calculate ‘continuing value’, CV.

Copyright K. Cuthbertson and D. Nitzsche

‘Valuing the ‘Firm’ :Continuing Value

eg. Project has

V5 =100 in year-5,6,7 etc., and r=0.10 then

Continuing value CV (at t=5) = 100 / 0.10 = 1,000

and

DPV (at t=0) of the CV = 1000/ (1+r)5 = 621

Copyright K. Cuthbertson and D. Nitzsche

‘Valuing the ‘Firm’ :Continuing Value

Special Case B:

If

i) the discount rate is constant in each year

and

ii)FCF’s grow at a constant rate each year, say after year-5 then

CV (at t=5) = FCF5 (1+g) / ( r - g) for r>g

Copyright K. Cuthbertson and D. Nitzsche

‘Valuing the ‘Firm’ :Continuing Value

Project has FCF=100 in year-5

FCF grows at rate g=0.03 (3%) and r = 0.10

Then:

Continuing value CV (at t=5)

= 100 (1.03) / (0.10 - 0.03)=1471

DPV( at t=0) of the CV = 1471/ (1+r)5 = 913

Notes:

CV is very sensitive to the choices made for FCF5, R and g.

CV can be a large & dominates DPV of the cash flows over years 1-5.

Copyright K. Cuthbertson and D. Nitzsche

Suppose

Value of firm using DPV of FCF’s is

Enterprise DCF = DPV (FCF 1-5yrs) + DPV (of CV)

= 679 + 621 = 1,300

Suppose: All equity financed firm N = 1000 shares and P= $1

Market Value (Capitalisation) = $1000

Hence the shares are undervalued by 30%

Possible purchase or takeover target (by ‘arbs’)

Copyright K. Cuthbertson and D. Nitzsche

Shareholder Value (All equity financed firm)

- If NPV of the project > 0 (discounted using RS)
- Implies the managers are ‘adding value’ for shareholders (which exceeds the return they could earn from investing their money in other hamburger firms).
- This is value based management or ‘creating shareholder value’.

Copyright K. Cuthbertson and D. Nitzsche

Copyright K. Cuthbertson and D. Nitzsche

Discount Rate: All equity financed firm

Note: ‘All equity’ financed = ‘unlevered firm’ - ie. no debt

Discount rate should reflect ‘business risk’ of the project.

Assume project is ‘scale enhancing’ (eg. more hamburger outlets for McDonalds)

Hence, has same ‘business risk’ as the firm as a whole.

Simple method

Use the average (historic) return on equity, RS (e.g. 15%) for this (hamburger) firm as the discount rate

This assumes the observed return on equity correctly reflects the payment for risk, that shareholders require from this hamburger company.

Copyright K. Cuthbertson and D. Nitzsche

Discount Rate: All equity financed firm

- If the project being considered by MacDonalds is to build hotels, then we would use the average stock market return in “hotel sector” (20%pa. say)
- - as this reflects the “required return on equity capital” for the shareholders in that sector.
- - see CAPM / SML / APT later, where we provide more sophisticated methods for choosing the appropriate equity discount rate.

Copyright K. Cuthbertson and D. Nitzsche

- Levered firm = financed by mix of debt and equity
- Assume debt-equity ratio will remain broadly unchanged after the new project is completed.
- Then discount FCF using:
- (‘After tax’)Weighted Average Cost of Capital WACC,
- WACC = (1-z) RS + z RB (1-t)
- z = B / V = propn of debt(bonds) , (1-z) = S / V
- V=market value of firm = S+B
- ‘weights’, z, sum to 1.

Copyright K. Cuthbertson and D. Nitzsche

- S = market value of outstanding equity ( = N x stock price)
- B = market value of outstanding debt (ie. bonds issued and bank loans)
- RS = average return on equity in hamburger industry
- RB = interest rate (yield to maturity) on say 10-year corp. AA-rated bonds(If hamburger company is rated AA by S&Poor’s)
- t = corporate tax rate
- Note: Market value (‘cap’) of the firm V = S +B

Copyright K. Cuthbertson and D. Nitzsche

Can Managers Increase the Value of the Firm?

- Assume firm is part-equity financed and part-debt financed
- Then the ‘intrinsic value’ of the firm is the DPV of its future cash flows from all of its current and future investment projects, discounted using WACC
- Managers can only increase the value of the firm by
- 1) investing in projects with ‘high’ FCFs
- 2) reducing the WACC
- ‘(2)’ is the so-called capital structure question - can managers change the mix of debt and equity financing to lower the overall WACC? - assuming FCF is unchanged - see Modigliani-Miller later

Copyright K. Cuthbertson and D. Nitzsche

What about (business) risk in DCF ?

- 1) Key practical method is to use “sensitivity” or “scenario” analysis.
- Sensitivity - ‘one at a time’
- 1) What is NPV if revenues are much higher/lower ?
- 2) What is the NPV if the discount rate is 1% higher?
- Scenario:
- 3) What is the NPV if both (1) and (2) apply. - scenario analysis
- (Monte Carlo simulation is a sophisticated way of doing this)
- Can “include” probabilities in (1) and hence calculate EXPECTED NPV and its standard deviation.

Copyright K. Cuthbertson and D. Nitzsche

What about (business) risk in DCF ?

- 2) Can use decision trees - particularly useful where there are strategic options in the investment decision
- -eg. Suppose you can abandon the project and sell the ‘plant’ for $10m if demand turns out to be ‘low’ in year-2. On the other hand if demand is ‘high’ then you will continue production in year-2.
- This affects the NPV of the project compared with the ‘normal case’ where you assume you do not abandon
- In fact the ‘correct’ way to evaluate these strategic options is (not surprisingly) to use ‘real options theory’, but this cannot be done here !

Copyright K. Cuthbertson and D. Nitzsche

VALUATION IN PRACTICE: EBITD, DEPRECIAITON, FCF

Copyright K. Cuthbertson and D. Nitzsche

Valuing a Company: ‘Cash is King’

Calculating ‘Free Cash Flow’ in Practice

- ACCOUNTING NIGHTMARES
- Earnings before interest, tax and depreciation,EBITD
- EBITD
- = R - C = Sales Revenues - Operating Costs (Labour+Materials)
- Free Cash Flow FCF
- = (R - C - T) - Inv(gross) - Increase in WC + (Net Non-Op. Inc)

Copyright K. Cuthbertson and D. Nitzsche

Valuing a Company: ‘Cash is King’

- Now the Accountants ‘Mess it About’
- Published ‘Earnings’ or ‘profit’ are usually presented after a deduction for depreciation: These would be ‘earnings before interest and tax’ EBIT
- So, EBIT = EBITD - D = (R-C) - D
- Hence, to get FCF ‘add back’ depreciation and deduct taxes:
- FCF =(EBIT - T) + D - Inv(gross) - Increase in WC +(N.N.Op.Inc)
- Also, you often ‘see’ (in the UK):
- Net Op. Profit (Less Taxes) NOPLAT = EBIT - T = R-C-D-T

Copyright K. Cuthbertson and D. Nitzsche

Valuing a Company

Copyright K. Cuthbertson and D. Nitzsche

Valuing a Company

Copyright K. Cuthbertson and D. Nitzsche

Valuing a Company

Copyright K. Cuthbertson and D. Nitzsche

Complementary Valuation Techniques: Economic Profit, EPEconomic Value Added, EVAAdjusted Present Value, APV

Copyright K. Cuthbertson and D. Nitzsche

Economic Profit

- EP and EVA are equivalent to ‘Enterprise DCF’ if the calculations
- are done consistently -ie. before the accountants get at the figures
- ECONOMIC PROFIT (McKinsey and Co)
- EP = ( ROC - WACC) x Capital Stock, K
- where Return on Capital, ROC = ‘Profit’ / K
- If ROC > WACC then the managers chosen investment projects are earning a rate of return in excess of WACC and therefore, the investment projects are ‘Adding value’.

Copyright K. Cuthbertson and D. Nitzsche

Economic Profit

- ECONOMIC PROFIT (Example)
- Profit = 150, K = 1000 hence ROC = 15% p.a.
- Let WACC = 10% p.a.
- EP = (15% - 10%) 1000 = $50 p.a.
- Your current stock of capital is being used in such a way as to generate $50 p.a. even after allowing for an annual ‘dollar capital charge’ of $100 p.a.

Copyright K. Cuthbertson and D. Nitzsche

Economic Value Added, EVA

- EVA= ‘Profit’ - ‘Capital Charge’ = 150 - (10%)1000 = $50 p.a.
- where ‘Capital charge’ = WACC x ‘Adjusted Capital’, K
- EVA is equivalent to EP if we measure ‘profit’ and ‘capital’ in the same way, for both techniques.
- eg. do we ‘add back’ to ‘capital’ past R&D expenditures on the grounds that this outlay increased ‘knowledge’ which is an ‘asset’

Copyright K. Cuthbertson and D. Nitzsche

EP and EVA

- You can compare different firms’ performance on EP and EVA in any one year (or over several years).
- The ‘plus’, compared to using say just ‘profits’ or ROC is that EP and EVA assess ‘profit’ in relation to ‘the cost of capital’.
- Value of the firm (at t=0 ) using EP or EVA
- = (Net) Capital Stock at t=0, K0
- + DPV ( of EP or EVA p.a., ~ WACC as discount rate)

Copyright K. Cuthbertson and D. Nitzsche

SELF STUDYComplementary Valuation Techniques:

- Simple proof that ‘Enterprise DCF’ and EP or EVA are equivalent:
- Assume K0 = 1000 (no depreciation), ROC = 15%, ‘Profit’ = 150 (perpetuity)
- 1) ‘Enterprise DCF = ‘Profit’ / WACC = 150/0.10 = $1500
- 2) EP or EVA: EP = (15% - 10%) 1000 = $50 p.a.
- 3) V(firm) = K0 + EP / WACC = 1000 + 50 / 0.10 = $1500

Copyright K. Cuthbertson and D. Nitzsche

Complementary Valuation Techniques: ROC, EVA and EP

- EVA Capital,K ROC WACC
- General Electric 2515 51,017 17.7 12.7
- General Motors -3527 94,268 5.9 9.7
- Johnson & Johnson 1327 15,603 21.8 13.3
- A positive return on capital of 5.9% for GM is ‘not enough’ if you have a WACC of 9.7%
- - it results in a negative EVA (or EP)
- Source: Fortune Mag 10th Nov 97.

Copyright K. Cuthbertson and D. Nitzsche

Adjusted Present Value, APV(Not Examinable)

- When using ‘Enterprise DCF’ we discounted the FCF using ‘after tax’ WACC
- Our measure of FCF did not contain any ’tax offsets/shields’ on (debt) interest payments (the only tax offsets we considered were on depreciation).
- This was because these ‘tax offsets’ are taken care of in the denominator, the WACC, which is reduces the cost of debt to Rb(1-t).
- APV and Enterprise DCF give the same value for the firm if consistent measures of the cost of equity and debt are used. This is a difficult area which we cannot pursue here but note that
- APV = FCF discounted as if firm is all-equity + DPV of ‘tax offsets’
- See Copeland, T. Koller, T and Murrin, J. Valuation (J. Wiley) for the best practical account of this and other valuation issues.

Copyright K. Cuthbertson and D. Nitzsche

END OF LECTURESELF STUDY SLIDES FOLLOW

Copyright K. Cuthbertson and D. Nitzsche

SELF STUDY

- 1) SOME PATHOLOGICAL CASES
- ~ COMPLICATIONS WITH IRR !
- 2) OTHER METHODS USED IN INVESTMENT APPRAISAL
- (These are of minor importance but you should be aware of these issues)

Copyright K. Cuthbertson and D. Nitzsche

Complications: Mainly with IRR !

- Table 2: ‘DIFFERENT CASH FLOW PROFILES
- Project A (-100, 130)
- Project B (100, - 130)
- Project C (-100, 230, - 132)
- -------------------------------------------------------------
- Project A ~ ‘normal’
- Project B ~ ‘Rolling Stone’s Concert’
- Project C ~ ‘Open cast mining’
- -------------------------------------------------------------
- IRR gives wrong decision for B and C
- NPV gives correct decision for A,B,C
- ANSWER: Use NPV !

Copyright K. Cuthbertson and D. Nitzsche

Complications: Mainly with IRR !

- Mutually exclusive projects
- (eg. garage or hamburger joint on one site, BUT NOT BOTH)
- - use NPV not IRR criterion
- (afficionados could use the incremental-IRR criterion ! )
- Capital Constraint
- (ie. not enough funds for all projects with NPV>0)
- - rank projects by the ‘profitability index’, PI where:
- PI = ( NPV / Capital Cost) = “bang per buck”
- Choose those projects with largest PI values until you exhaust your funds.

Copyright K. Cuthbertson and D. Nitzsche

Investment Appraisal: Alternative Methods

- Year-0 Year-1 Year-2 Year-3 Year-4
- FV -1000 500 500 700 0
- d 1.0 0.8696 0.7561 0.4972 -
- PV -1000 435 378 348 -
- Note: NPV = 161
- 1) Payback Period = 2 years
- 2) Discounted Payback = 2-3 years

Copyright K. Cuthbertson and D. Nitzsche

Deficiencies: Alternative Methods

- Either
- Ignores cash flows after payback period
- (eg. never invest in ‘Dolly the sheep’)
- OR
- Ignores time value of money

Copyright K. Cuthbertson and D. Nitzsche

END OF SLIDES

Copyright K. Cuthbertson and D. Nitzsche

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