Real Options and Other Topics in Capital

Budgeting

Chapter 13

Identifying Embedded Options Valuing Real Options in Projects

13-1

13-2

What is real option analysis?

Real options exist when managers can influence the size and riskiness of a project’s cash flows by taking different actions during the project’s life.

Real option analysis incorporates typical NPV budgeting analysis with an analysis for opportunities resulting from managers’ decisions.

13-3

What are some examples of real options?

Growth/expansion options

Abandonment/shutdown options

Investment timing options

Flexibility options

13-4

Investment Timing Option

Project X has an up-front cost of $100,000. The project is expected to produce after-tax cash flows of $33,500 at the end of each of the next four years (t = 1, 2, 3, and 4). The project has a WACC=10%.

The project’s NPV is $6,190. Therefore, it appears that the company should go ahead with the project.

However, if the company waits a year they will find out more about the project’s expected cash flows.

13-5

Investment Timing Option

If they wait a year: There is a 50% chance the market will be strong

and the expected cash flows will be $43,500 a year for four years.

There is a 50% chance the market will be weak and the expected cash flows will be $23,500 a year for four years.

The project’s initial cost will remain $100,000, but it will be incurred at t = 1 only if it makes sense at that time to proceed with the project.

Should the company go ahead with the project today or wait for more information?

13-6

Investment Timing Decision Tree

At WACC = 10%, the NPV at t = 1 is: $37,889, if CF’s are $43,500 per year, or

-$25,508, if CF’s are $23,500 per year, in which case the firm would not proceed with the project.

50% prob.

50% prob.0 1 2 3 4 5 Years

-$100,000 43,500 43,500 43,500 43,500

-$100,000 23,500 23,500 23,500 23,500

13-7

Should we wait or proceed?

If we proceed today, NPV = $6,190.

If we wait one year, Expected NPV at t = 1 is 0.5($37,889) + 0.5(0) = $18,944.57, which is worth $18,944.57 / 1.10 = $17,222.34 in today’s dollars (assuming a 10% WACC).

Therefore, it makes sense to wait.

13-8

Issues to Consider with Investment Timing Options

What is the appropriate discount rate?

Note that increased volatility makes the option to delay more attractive. If instead, there was a 50% chance the

subsequent CFs will be $53,500 a year, and a 50% chance the subsequent CFs will be $13,500 a year, expected NPV next year (if we delay) would be:

0.5($69,588) + 0.5(0) = $34,794 > $18,945

13-9

Factors to Consider When Deciding When to Invest

Delaying the project means that cash flows come later rather than sooner.

It might make sense to proceed today if there are important advantages to being the first competitor to enter a market.

Waiting may allow you to take advantage of changing conditions.

13-10

Abandonment/Shutdown Option

Project Y has an initial, up-front cost of $200,000, at t = 0. The project is expected to produce after-tax net cash flows of $80,000 for the next three years.

At a 10% WACC, what is Project Y’s NPV?

0 1 2 3

-$200,000 80,000 80,000 80,000

10%

NPV = -$1,051.84

13-11

Abandonment Option

Project Y’s A-T net cash flows depend critically upon customer acceptance of the product.

There is a 60% probability that the product will be wildly successful and produce A-T net CFs of $150,000, and a 40% chance it will produce annual A-T net CFs of -$25,000.

13-12

Abandonment Decision Tree

If the customer uses the product, NPV is $173,027.80.

If the customer does not use the product, NPV is -$262,171.30.

-$200,00060% prob.

40% prob.

1 2 3 Years0

150,000 150,000 150,000

-25,000 -25,000 -25,000

$1,051.84-

)3.171,262$-(4.0)8.027,173($6.0)NPV(E

13-13

Issues with Abandonment Options

The company does not have the option to delay the project.

The company may abandon the project after a year, if the customer has not adopted the product.

If the project is abandoned, there will be no operating costs incurred nor cash inflows received after the first year.

13-14

NPV with Abandonment Option

If the customer uses the product, NPV is $173,027.80.

If the customer does not use the product, NPV is -$222,727.27.

-$200,00060% prob.

40% prob.

1 2 3 Years0

150,000 150,000 150,000

-25,000

$14,725.77

)27.727,222$-(4.0)8.027,173($6.0)NPV(E

13-15

Should an abandonment option affect a project’s WACC?

Yes, an abandonment option should have an effect on the WACC.

The abandonment option reduces risk, and therefore reduces the WACC.

13-16

Growth Option

Project Z has an initial cost of $500,000.

The project is expected to produce A-T cash inflows of $100,000 at the end of each of the next five years, and has a WACC of 12%. It clearly has a negative NPV.

There is a 10% chance the project will lead to subsequent opportunities that have an NPV of $3,000,000 at t = 5, and a 90% chance of an NPV of -$1,000,000 at t = 5.

13-17

NPV with the Growth Option

100,000 100,000 100,000 100,000 100,000

-$500,000

10% prob.

90% prob.1 2 3 4 5 Years0

100,000 100,000 100,000 100,000 100,000-$1,000,000

$3,000,000

At WACC = 12%, NPV of top branch (10% prob) =

$1,562,758.19

NPV of lower branch (90% prob) = -$139,522.38

13-18

NPV with the Growth Option

If the project’s future opportunities have a negative NPV, the company would choose not to pursue them.

The bottom branch only has the -$500,000 initial outlay and the $100,000 annual cash flows, which lead to an NPV of -$139,522.

The expected value of this project should be:

NPV = 0.1($1,562,758) + 0.9(-$139,522)

= $30,706.

13-19

Flexibility Options

Flexibility options exist when it’s worth spending money today, which enables you to maintain flexibility down the road.