Comments

Hi Sheridan,

How are you? I hope that you had a good vacation. Vasant and I looked at
your memo and found it to be interesting. I shall first briefly summarize
our understanding of the methodology you propose. The comments follow.
Finally, I shall sketch a simple gas field project you can use as a test case
in further refining the model.

It appears that you are proposing a state-space approach where probabilities
of different states at various future dates are specified. The next step is
to assume a discount rate and to compute the present value by following the
branches from the origin to one of the terminal points. Traversing through
the tree in this manner over many iterations will permit us to compute the
average present value of the project. Also, you are using the simulation to
assign a value of the project to each node. Thus each node will have a cash
flow associated with it which will occur if the node is reached and a value
which is an expectation of the value to be realized going forward. If some
of these values turn out to be negative, zero-coupon, risk-free bonds are
purchased to neutralize the negative realization.

Next, we find a comparable and apply the expected rate of return back to our
project (based on the variance of the returns) . We iterate until
convergence.

Finally, we subtract the initial investment and the computed risk capital
from the PV of the gross cash flows (including debt) to determine if the
project merits further consideration.

Comments/Clarifications

1. The money is being set aside to avoid negative values. It is not clear
if you mean the values of the cash flow or the PV at the node. Anyhow, we
shall be setting aside money not just for that specific node but all nodes at
that cross-section of time as the risk-free asset pays in all states of
nature. This will have to be done every time there is a negative
realization. Thus, for the typical project we have, the value of risk
capital may be extremely high, as we are not following a tail-based norm
anymore.

2. Your memo appears to suggest that debt capacity is contingent on all
values being positive. If so, we are only issuing risk-free debt. Also, a
project with a single negative value at each cross-section of time will not
have a positive debt capacity.

3. It seems that our optimization argument is the discount rate, which is
obtained in each step from the comparison investment (by equating the
variances). It is not clear if changing the discount rate will have such an
effect on the project variance so as to lead to a global convergence. Also,
our project has a finite life and the market-based assets will have infinite
lives. In the light of this fact, how will we define the relevant variance?
Is it the spot variance of the returns of the comparison investment?

4. Finally, our criterion is to subtract from the average PV the investment
and also the risk capital. Setting risk capital to zero, this model closely
resembles the intuitive present value criterion and endogenously determines
the discount rate.

Gas Field Case

To facilitate your thinking, we are providing a gas field example below.

We invest x million dollars to buy and develop a gas field. A profile of
expected production and variance of the production per year is available from
the engineers at the beginning. Production will be autocorrelated, as the
profile will shift up or down based on the actual gas reserves being more or
less than the estimated reserves. We assume the life of the field to be 10
years with no salvage value. There are fixed and variable operating costs.
It might be useful for you to think about applying the framework to this
problem.

Do let me know if you have further questions.

Rakesh