Investment under uncertainty

Question 1

abstract difference between DP and CCA

Answer 1

They make different assumptions about the financial markets. Also about the discount rate.

Question 2

Core of CCA

Answer 2

Relate our project to existing assets that has market values or implicit market values. this can then be used with no arbitrage to value our own shit.

To quote the book: “All we need is some cobination or portfolio of traded assets that will exactly replicate the pattern of returns frm our investment project at every future date and in every future uncertain eventuality”.

Question 3

elaborate on the parameters we are working with in the DP case

Answer 3

I: sunk cost investment, factory or soemthing similar. Produce one widget yearly forever

r : interest rate

P: price. In period 0 it is P_0. Then, the next period it is P_0(1+u) with probability q, and P_0(1-d) with probability (1-q).
This is then locked in.

The scenario they are painting here is that we can either invest right now immedaitely and lock in a certain price P_0. OR we can wait a year and lock in a new price, that is uncertain. It is either an up or a down movement relative to the certain P_0 price. Therefore, we can reduce uncertainty by waiting.

Question 4

give the static immediate NPV view of the DP investment. When invest?

Answer 4

we sum and discount based on the first known price and of course the expected future price. We do not know the later price, but we use expectation.

The outcome is static NPV.

if V_0 > I, invest.

Question 5

give the net payoff “formula” for the static NPV case

Answer 5

= max[0, V_0 - I]

Question 6

now we have considered investment at time …`

Answer 6

time 0

Question 7

We have considered investment at time 0. WHat is the actual case?

Answer 7

Investment remains available in future periods.

Question 8

elaborate on the trdeoff in the actual case

Answer 8

We can wait and see what happens. this entails giving up some early revenue at the benefit of reducing uncertainty.

by period 1 and later, the conditions do not change. therefore we can wait to period 1 and have an informed decision.

Question 9

elaborateo n perpetual fuckery in this book

Answer 9

It tends to always include the first/immediate period, and this means that we cannot use “x/r”

Question 10

how can we mathemtically give the firm’s investment opportunity when there are two options: 1) invest now, 2) invest later?

Answer 10

We take the max of the following quantities:
1) time 0 investment
2) time 1 ivnestment

1) V_0 - I

2) 1/(1+r) E_0[F_1], where F_1 is the continuation value

F_0 = max{V_0 - I, 1/(1+r) E_0[F_1]}

The firm’s optimal decision is the one that maximizes this net persent value.

This is the essential idea/core of DP. Maximize net present value by comparing alternatives.

Question 11

elaborate on the core of DP

Answer 11

We split the whole sequence of decisions int otwo parts:
1) the immediate choice
2) the remaining decisions, all of whose effects are summarized in th econtinuation value.

to find the optimal sequence of decisions we work backwards. We find the continuation value at the last relevant decision point, which is F_1 in our example. Then, at the decision point before that, we know the expected continuation value and therefore can optimize the current choice.

if we have more periods, we’d do the same repeadelty.