Investments under uncertainty Flashcards
(14 cards)
the 3 characteristics of investment decisions
1) Many costs are irreversible
2) Uncertainty in regards to both costs and profits
3) There is some leeway in regards to the timing. We can adjust our timing to get more out of our decisiosn
shortcomings of the NPV method
1) It has a now or never approach. It assume that we either invest now, or never.
2) It assumes that decisions are reversible should things not go as expected.
As a result, the NPV method is bad.
The irreveribility is important. if we do not model it, we can be inclined to make big capital sacrifices and lose on them. If uncertainty is large, this is dangerous.
what is the option view
A firm that look at some project:
“The firm has the right/option to invest, but not the obligation to do so. What is this right worth?”.
define sunk costs in this case
business or industry specific costs.
we also have the lemons problem for basically everything.
cost of delay?
risk of new entrants, foregone cash flows
in the most ismple case, what is the value of having the ability to wait vs investing immedaitely with a “now or never” approach?
The difference between the expected value from the flexible option, and the static NPV
We can itnerpret this number “we would pay this number to go from a scenario where we cannot delay, to a scenario where we can delay”
elaborate on creating a risk free portfolio in the widget example
We have up and down scenarios.
We are just going to select a portfolio consisting of the investment project and some number of shorted widgets. The number of shorted widgets makes sure that in these two scenarios, the portfolio is worth the same. If the portfolio is worth the same in “all” scenarios, it must be risk free.
if we have static NPV of 600, but 773 from option price. What do we refer to the 773?
Opportunity cost
elaborate deeply on the widget 2 scenario examples with risk free etc
We have an investment project, and we have widgets.
We use the two types of assets to create a portfolio that is the value in both scenarios. This is done by adjusting the number of widgets we short.
if the portfolio earn the same, it is risk free.
NB: We must pay people for the short widgets if the widgets have expected value 0. If the expected return on holding the widgets is 0, no one would hold that shit with no compensation. Therefore, they must be payed the risk free rate.
Then we solve the equation where we have dollar return on one side and dollar risk free rate in terms of the original portfolio value on the ither side.
what is the meaning of the widget example?
We have a case, we create a risk free portfolio, and we use this fact to see what the value of the option is by using risk free return.
The example assumes that we final outcomes and probabilities.
This allows us to “know” what the value is with certainty in these states/scenarios. Sort of like knowing the payoff.
Then we basically solve “what must the original option value be if we are to gain the risk free rate of return”.
The trickery arise from the widgets used to short. However the point is that we create a risk free portfolio. This allows us to know the return. The combinatio nof knowing the return and the payoffs in each state givesu s the ability to compute the option value at tiem 0.
Note that the way we find the option value at time 0 is by using the total portfolio. Assuming the prices of the widgets are known, this allows us to isolate for the investment value.
go through the widget case, but change the investment from 1600 to be simple “I”
We still have known prices. 200 at time 0, 300 or 100 at time 1. 50-50.
We leverage the same principles. Create the risk free portfolio.
Ø1 = Ø1
F_1 - nP1 = …
In this case, F_1 is not known, because it consists of the investment as well as the revenue.
F_1 = 300+3000 - Investment= 3300 - investment (good case)
F_1 = 1100 - investment (bad case)
3300 - Investment - n300 = 1100 - Investment - n100
HOWEVER: The book apparently still consider only one state to be profitable, so the other is sat to 0 regardless.
We get:
3300 - Investment - n300 = 0 - n100
3300 - investment = 200 n
3300/200 - investment/200 = n
n = 16.5 - 0.005 investment
From this, we have that the number of widgets we short is equal to 16.5, less some small amounts of the investment.
now we go to the process of figuring out the values.
F_1 in bad state is 0.
F_1 in good state is: 3300-investment
We then consider the ultimate line:
ø_1 - ø_0 - short =
We have already determined a value for n that makes ø_1 equal in both cases. This value is “16.5 - 0.005 investment”.
Ø_1 is either = 3300 - investmetn - 300n
OR
Ø_1 = -100 n
Since they are equal regardless, we can set ø_1 = -100n.
then we solve:
-100n - (F_0 - 200(16.5 - 0.005 investment)) - 20 (16.5 - 0.005 investment)
-100n - (F_0 - 3300 + investment) - 330 + 0.1 investment
-100 (16.5 - 0.005 investment) - F_0 + 3300 - investment - 330 + 0.1 investment
-1650 + 0.5 investment - F_0 + 3300 - investmnt - 330 + 0.1 investment
1650 - 330 - 0.4 investment = 0.1 (F_0 - 200(16.5 - 0.005 investment))
1320 - 0.4 ivnestment = 0.1 (F_0 - 3300 + investment)
1650 - 0.5 investment - F_0 = 0.1 F_0
F_0 = 1500 - 0.455 Investment
KEY TAKEAWAY:
We make it so that the portfolio is worth the same in both scenarios (Ø_1)
F includes the investment. but it depends on when the investment is. In this example, we consider the investment to occur at time 1, and we ask ourselves what we are willing to pay for this.
From the result, we see that the value of the situation, F_0, decrease with higher investment cost. This makes a lot of sense.
important to remember if we let the probabilities be variable?
Now the required amount in regards to the short position will change. This is becasue the ones who we short to will require something that depends on the probabilities. In earleir examples, 50-50 up and down in addition to 300 vs 100 gave expected value equal to current value. Since no difference, they require risk free asset.
given the flexible investment cost, when should we invest today?
we should invest today if the investment cost + F_0 is less than the V_0 value.
V_0 > Investment + F_0
RECALL WHY:
When we add investment together with F_0, we are figuring out how much it cost to BOTH start the project AND not wait. Not waiting has a cost.
F_0 is the value of the wait option, while investment is the start up cost.
In our example, V_0 is 2200.
2200 > Investment + (1500 - 0.455 investment)
2200 -1500 > investment - 0.455 investment
700 > 0.545 investment
investment < 700 / 0.545
investment < 1284
Meaning, if the investment cost is less than 1284 dolla,r we should invest today rather than wait.
