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Lecture 28

# FINA 410 Lecture Notes - Lecture 28: Option Style, Profit Margin, Rainbow OptionPremium

12 pages53 viewsSummer 2017

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**preview**shows pages 1-3. to view the full**12 pages of the document.**CHAPTER 28 – THE OPTION TO DELAY AND VALUATION IMPLICATIONS

In traditional investment analysis, the decision to accept a project only when return on

project > hurdle rate + NPV projets ased o CF’s ad disout rates

Limitation of this view is that it does not consider the options associated with many

investments.

One of the limitations of traditional investment analysis is that it is static and does not

do a good job of capturing the options embedded in an investment:

o the option to delay it

o The other opportunities in the future that may be available just because we took

the investment

o the option to abandon it, if the cash flows do not measure up.

These optios all add alue to projets ad a ake a ad iestet

(from traditional analysis) into a good one.

This chapter considers the option to wait and take the project in a later period

Why would a firm want to do this?

o If the PV of CF’s are olatile ad a hage oer tie, a projet that does ot

pass now (-NPV), may become valuable in the future

o Maybe the project has a +NPV, but the firm may gain from waiting because the

project has a higher value if taken at a later date

Most valuable when a company has exclusive right to invest in a project

and becomes less valuable as the barriers to entry decline.

Three cases where the option to delay can make a difference when valuing a firm:

o 1) undeveloped land in the hands of real estate investor or company

The choice of when to develop depends on owner, and will usually begin

to develop when real estate value increases enough to justify it

o 2) a firm that owns a patent

since patent represents a firm with exclusive right to produce a product

or service it should be valued as an option so we produce the

patented product?

o 3) a natural resource company that has undeveloped reserves that it can choose

to develop at a time of its choosing—presumably when the price of the resource

is high

THE OPTION TO DELAY A PROJECT

Usuall e look at CF’s ad disout rates ad opute the NPV to see if acceptable

Hoeer, CF’s ad rates hage oer tie changing NPV so a project that has –

NPV today (rejected) may have a +NPV (accepted) in the future

o For regular firs, the fat that it a eoe positie i the future does’t

matter as they do not have a special advantage over their competitors (their

competitors will have a +NPV too)

In an environment where project can solely be taken by one firm, due to legal

restrictions or other barriers to entry the changes in the projects value over time are

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relevant and gives it the characteristics of a call option (right to buy) value = (V-X)

where X is initial upfront investment, and V is the PV of cash flows to the project

Payoff on the Option to Delay

NPVproject = V – X

o X: initial up-front investment

o V= PV of expected cash inflows from investing in project

Now assuming the firm has exclusive rights if discount rate or cash flows changes

the PV of CF’s V) may change over time while the initial up-front investment (X) stays

the same

o So even if currently it has a –NPV, it may still be a good project if the firm waits.

Decision rule:

o If V>X Invest in project as it has +NPV

o If V<X do not invest

if firm does not invest, it will still loose what it invested to get

exclusive rights to the project

Payoff diagram assuming firm has exclusive rights & firm holds out until end of period:

The profit diagram is that of a call:

o the underlying asset is the project

o the strike price of the option is the investment needed to take the project

We assume it to be constant

o the life of the option is the period for which the firm has rights to the project

o the value and variance of the underlying asset is represented by the PV of the

cash flows on this project and the expected variance in this PV

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Inputs for Valuing the Option to Delay

We need the same inputs as any option pricing model: value of underlying asset & the

variance in that value, time to expiration of the option, strike price, riskless rate, and the

equivalent of dividend yield.

Value of Underlying Asset:

o underlying asset is the project that firm has exclusive rights

o Value underlying asset = PVexpected CF’s not including intial investement

Solve PV with DCF using a risk adjusted discount rate

o May have a lot of error in CF estimates & PV especially for new business or if

it involves untested technology

This uncertainty is normal, and is what makes the option to delay

valuable

Variance in the Value of the Asset:

o The uertait o CF’s ad alue of the projet toda a oe fro either:

Potential market for product unknown

Technological shifts can change the cost structure and profitability of

product

o Value of option is largel deried fro ariae i CF’s higher variance =

higher value of the project delay option

So value of option to invest in a project in stable business < one in an

environment where technology, competition, and markets are changing

o Variance in PV can be estimated in one of three ways:

1. If we have invested in similar projects in the past, the variance in the

cash flows from those projects can be used as an estimate

Example. Gillet uses variance of introducing new blades

2. We can assign probabilities to various market scenarios, estimate cash

flows and a present value under each scenario, and then calculate the

variance across PVs

Could also use probabilities for each individual input, like market

share and profit margin, and use a simulation to solve variance in

the PV’s that eerge.

This approach tends to work best when there are only one or two

sources of significant uncertainty about future cash flows

3. We can use the variance in the value of firms involved in the same

business (as the project we are considering) as an estimate

Ex. Average variance of firms involved in software business can be

used as the variance in PV for software project.

Exercise Price on Option:

o Option to delay is exercised when firm owning rights decides to invest in it so

cost of making this investment is the exercise price

o Assumption: this cost remains constant (in PV $) and any uncertainty in this

iestet ith e refletig i PV of the CF’s o the produt

Expiration of Option & Riskless Rate:

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