Another Real Options question

[Allacalander]

I never should have started looking through the Copeland text. I just keep seeing more and more things that don't make sense.

Ok, so let's look at the sequential compound option problem late in the chapter (page 228 of JAM manual). In this example, it lists the bottom node of time 2 as 0. To me this means you exercised your adandonment option and got out with zero losses. But that's not true. If you make it to that node, you've already invested 500 dollars (200 at time 0, 300 at time 1) so you're already down 500 plus some interest (535.50).

I recognize that this is a sunk cost at time 2, but it is still a cost and shouldn't you consider that at time 0? It won't affect your choice of whether to abandon or not (at time 2), but it will affect the choice of whether to take the project on in the first place (at time 0). In other words, sunk costs don't matter at time 2, but we're not at time 2, we're at time 0 trying to evaluate whether to take on the project in the first place.

Take a look at the middle node. At this point, the project is expected to be worth 1000 with discounting. Your options here are to abandon, taking a loss of -535.50 or invest 700 more for an expected net gain of -247.12, not 300. So indeed, you DON'T abandon the project, but you are still expected to lose money. Even though its negative, it's your optimal choice. If you find yourself, as a manager, suddenly thrust into this position at time 2, you have to take the lesser of two evils and keep going. (Maybe your preceding manager was fired for getting into this mess in the first place)

When I work the problem this way, at each decision node you look at the expected outcome of the project considering all future costs and benefits, compared to all costs incurred to date. So when you get to your initial node, your choices are to abandon and get 0 or commit and have an expected NPV of 31 (this is close to Carmody's answer, but not exactly the same and nowhere near Copeland's answer.) Because the NPV is positive, you do commit and take the project. You end up with the same Abandon/don't abandon decision at each node, but you end up with different dollar results.

I wonder if this isn't similar to a project with dividends, only this one has negative dividends.

[hamstrman]

I recognize that this is a sunk cost at time 2, but it is still a cost and shouldn't you consider that at time 0?

Correct. You are considering it at time 0. At each node where the cost occurs, you subtract it out... If the value would be negative, you wouldn't include it because you'd never willingly invest in a negative NPV project (in these examples I mean, I know project interdependence may be a reason...) It would make the option cheaper and then you could make a profit by buying the cheap option, abandoning in the low state and making 0 instead of negative profits.



It won't affect your choice of whether to abandon or not (at time 2), but it will affect the choice of whether to take the project on in the first place (at time 0). In other words, sunk costs don't matter at time 2, but we're not at time 2, we're at time 0 trying to evaluate whether to take on the project in the first place.

Correct on all counts. And you ARE considering it. You'd see that you'd abandon if the bottom nodes occurred and you factor that in at time 0. Incorporating negative values at certain nodes is not assuming flexibility at all because it's assuming you are forced to invest despite a negative value. You wouldn't make the future value and you wouldn't incur the cost at that time. All prior costs are factored in at prior nodes.


Take a look at the middle node. At this point, the project is expected to be worth 1000 with discounting. Your options here are to abandon, taking a loss of -535.50 or invest 700 more for an expected net gain of -247.12, not 300. So indeed, you DON'T abandon the project, but you are still expected to lose money. Even though its negative, it's your optimal choice. If you find yourself, as a manager, suddenly thrust into this position at time 2, you have to take the lesser of two evils and keep going. (Maybe your preceding manager was fired for getting into this mess in the first place)

When I work the problem this way, at each decision node you look at the expected outcome of the project considering all future costs and benefits, compared to all costs incurred to date. So when you get to your initial node, your choices are to abandon and get 0 or commit and have an expected NPV of 31 (this is close to Carmody's answer, but not exactly the same and nowhere near Copeland's answer.) Because the NPV is positive, you do commit and take the project. You end up with the same Abandon/don't abandon decision at each node, but you end up with different dollar results.

I think this all comes down to your acceptance of sunk costs (or perhaps I'm missing something someone else here will see). You don't incur the future value of the past costs at each node if you incurred them when they would otherwise be incurred.

I wonder if this isn't similar to a project with dividends, only this one has negative dividends.


It is, actually if I remember correctly.