corporate valuation, 2002-5, p. 1 institut for regnskab, tom hansen last session: the 5 steps...

Corporate Valuation, 2002-5, p. 1

Institut for Regnskab, Tom Hansen

•Last session: The 5 steps•Workshop

•Dialogue and coaching •Exercise 12.4

•This lecture: Options•Remember the mid stage report•Next

Options



CMK 20 Options

DCF determine whether to invest or not (in a project), using:

• we decide whether to invest or not now• the expected free cash flows, evaluated now• WACC (risk adjusted rate)

DCF assume “passive management in a static world”

What if management is not passive?• deferring investment in the project• expanding the scale of the project, if the project develop well?• contracting the scale of the project, if the project develop

badly?• reacting on new information

Option pricing - is the answer.



CMK 20 Options - example (I)

•Expected inflow = $200 in each period ($100 (p=0.5), $300 (p=0.5)).•Investment = $1,600; CC = 10%•Inflow = 200 in period 0; You will know whether future inflows are $100 or $300 at the end of period 0.

NPV = -1600 + 200/0,1 + 200 = 600

0

1600

200

21

200 200 Etc.



CMK 20 Options - example (II)

0

1600 21

100 100 Etc.Inflow = 100:

Inflow = 300: 0

1600 21

300 300 Etc.

Deferring investment decision

•Inflows = 100: max(0; -1,600/1.1 + 100/0.1) = max(0; -454.5) = 0•Inflows = 300: max(0; -1,600/1.1 + 300/0.1) = max(0; 1,545) = 1,545

Value of deferring investment = 0.5 * 1,545 + 0,5 * 0 = 772.5



CMK 20 Options - example (III)

Conclusion:

Traditional DCF-method: NPV = 600

Value of investment by deferring investment decision = 772.5

Value of deferring-option = 772.5 - 600 = 172.5



CMK.20 OptionsOptions to:

• abandon (put)resale /liquidation value• defer (call) development costs• expand (call) expansion costs• contract (put) contraction costs• switch (puts and calls) restructure +

shutdown costs

Of value when• uncertainty is high• adaptiveness is high• see exh.20.1 & 20.2



CMK.20: NPV, DTA & Option pricing (I)

assume:

•rf = 8%

•cost of capital = 17,5%•you have to decide now (at t = 0)

NPV = 117,5 / (1+17,5%) - 115/(1+8%) = -6,48

Conclusion: Do not invest

115

0 1

117,5

170 (p=0.5)

65 (p =0.5))



CMK.20: NPV, DTA & Option pricing (II)

DTA, assume:

•rf = 8%

•cost of capital = 17,5%•deferring investment decision until better informed

Value (DTA) = (0.5 * 55 + 0.5 * 0) / 1,175 = 23.4

Conclusion: Do not invest now, but option has high value; defer investment decision until better informed

P=0.5

P=0.5

t=0 t=1

Cash flow = 170, investment = 115

Cash flow = 65, investment = 115; do not invest



CMK.20: NPV, DTA & Option pricing (III)

Option:Synthetic option: N of investment and B bond (risk free)

Value of option = value (synthetic option) = N * value investment + B

N * value investment (up) + B*(1+rf) = value option (up)

N * value investment (down) + B*(1+rf) = value option (down)

· N * 170 + B*(1+8%) = 55· N * 65 + B*(1+8%) = 0

Solution: N = 0.524; B = -31.53

Value of option = 0.524*100 - 31.53 = 20.86The implied risk-adjusted rate = 31.9% (and not 17.5%)

Conclusion: Do not invest now, but option has high value; defer investment decision until better informed.



CMK.20: NPV, DTA & Option pricing (IV)

Conclusion:• NPV (without flexibility) = -6.5• Value (DTA (with flexibility)) = 23.4

· hence value of flexibility (option to defer decision) = 29.9• Value (Option pricing (with flexibility)) = 20.9

· hence value of flexibility (option to defer decision) = 27.4

Do not use the DTA-valuation method shown at page 8, as:• the risk of an option on an underlying risky asset is always

greater than the risk on the asset (31.9% vs. 17.5%) • there is no single, constant discount rate because it changes with

time (info) and underlying conditions (risk)

Use the synthetic option valuation method instead (p. 9), as:• The valuation of the option is based on a synthetic option

consisting of (parts of) the original investment (which value we know) and risk free bonds (which value we also know)

• The implied risk-adjusted discount rate can be found



CMK.20 Options

• Options “takes care” of flexibility and of uncertainty that is gradually solved over time. They presume:

· decision taking in the future, contingent on the arrival of new information and learning,

· not (decision taking) now - based on expectations of future information (vs. NPV)

• managing real options is managing of flexibility - the value of real options stems from flexibility



CMK 20: Valuing options1. Compute base case present value without flexibility using DCF.2. Model the uncertainty using event trees.3. Identify and incorporate managerial flexibilities creating a decision tree.4. Calculate option price.

Note:• The event tree quickly becomes large (Exhibit 20.5) • If more flexibilities are modeled into a decision tree,

the decision tree becomes very large and complex (Exhibit 20.9)

• But the basic calculations and principles in a big decision tree are exactly the same as describe in p. 7 & 9



CMK.20 Ending remarks• Until now we have only been looking at options on

the asset side, but• also liability options exists (the company have given

(or sold) call options). Examples are:· Convertible debt· Preferred stock (that can be converted to

common stock).· Warrants· Executive stock options

• The value of these liability options should be

subtracted from the enterprise value (in order to find the value of equity).

• The value of liability options should be included in the calculation of WACC.



Luehrman: Investment opportunities

The correspondence between project characteristics and the option value drivers shows us, that deferral has two value elements to be included

• earning the time value of money on the postponed exercise price X, = (X-PV(X))

• the world may change / is uncertain

ad1.NPV= S-X, where S is the value of investmentmodified NPV = NPV + time value = S-X+(X-PV(X))=S-PV(X)converted to a ratio to handle it easier NPVq=S/PV(X)ad2. Measure uncertainty by assessing probabilities and let the option-pricing model quantify the value. The measure is cumulative variance in returns but we utilize the square root of this called cumulative volatility (*t1/2)



Luehrman: Investment opportunities

These two metrics combine the 5 option variables into two dimensions (see p.55) called Option spaceOption space is priced via a table (see p.56)

•Value of option = tablep.55(NPVq, *t1/2) * S

“How to do” in 7 steps (p.58)• sequential investment: 2 decisions to take: invest

now? & given we invest now, invest in 3 years?· The first decision should be taken now. The 2.

decision you do not have to take now.• NPV = NPV(phase 1 + phase 2) = NPV (phase 1) +

NPV (phase 2) = (16.3 - 16.2 = 0.1 or 16.3 - 69.6 = -53.4)

• Value = NPV (Phase 1) + option value (phase 2) (= 16.3 + 48.6 = 64.9)

DCF

BS



Luehrman: Strategy as options

• Use the two option value metrics (NPVq and cumulative volatility) to locate the project in the “option space” to obtain the effect of uncertainty and active decision making

• The tomato garden metaphor divides the garden in 6 regions, giving us 6 possible actions instead of just two (invest / not invest) - also taking the likelihood of the projects future attraction into consideration.

• Never (6) and Now (1) combined with sure, maybe, and probable. (se p.94).

• This is a dynamic approach where time moves the opportunity upward and to the left, and active management can move it downwards and to the right



Luehrman: Strategy as options

Cum

ulat

ive

vola

tili

ty (*

t1/2 )

0Value to cost S/PV(X)

0 1

Region 1: Invest now

Region 2 maybe now

S-X > 0

Region 3 probably later

S-X< 0

Region 4 maybe later

Region 5 Probably never

Region 6 Never Invest



Kasanen & Trigeorgis

• Strategic investment planning

• 3 strategic sources of value

· flexibility (operating real options)

· synergy between projects (interdependencies between projects)

· sequential project interdependencies (growth options)



NEXT - 28. OctoberWorkshop•Dialogue and coaching •Exercise 20.5

Lectures• Applying valuation (chap 14, 16-18):

· Multi business companies· Cyclical companies· Foreign companies

corporate valuation, 2002-5, p. 1 institut for regnskab, tom hansen last session: the 5 steps...

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