FortisBC Inc. (FortisBC) Application for a Certificate of Public ...

Appendix B: Risk and the Alternatives
Suppose that an investor has a bond that pays $1
per year in perpetuity. The formula relating the
price of the $1 per year and the rate at which the
future is discounted to the present at the interest
rate, r, is:
4. P b=(1/r).
If we have an investment that is likely to be destroyed
in any period at a rate of (1-π), then the
price of the $1 per year is now: 56
5. P b= (1-π)/(r+π).
Since P b and the rate of discount are inverses, the
discount of the future is:
6. (1/P b) = (r+π)/(1-π)
The text assumes for analytic simplicity that this
is approximated57 by (r+π) and that in turn, this is
represented by, R*+π: the alternative return available
to our grow-op operator. It is an alternative
at the same risk as would be found in the grow-op
business, which is what puts all legal investments
at risk.
Appendix C: A Richer Model Police Enforcement Enthusiasm
The primary problem with the model thus far is
that it does not take into account different conditions
that affect the number of busts carried out
by the police (or for that matter by others who
want to rip off grow-ops.)
To see how this affects the framework developed
above, assume that the number of busts, B, is a
product of the number of grow-ops, T; the number
of police assigned to the “grow-busters,” N;
the amount of security installed by the grow-ops
themselves, S; and other stuff, x. This leads to an
expression:
7. B= exp( b0). T N S x
that can be rewritten in log-linear form as:
56 That is, P ∑ 1
1
1
57 Clearly this is a better approximation, the smaller is π.
PUBLIC POLICY SOURCES, NUMBER 74
8. ln(B)=b 0+b 1ln(T)+b 2ln(N)+b 3ln(S)+b 4ln(x).
Since we know that the number of busts is related
to the total number of grow-ops as:
9.
⎛
⎜
⎜
T = B.
⎜
⎜ ⎛ C. 1 − ⎜
⎜ ⎜
⎝ ⎝
1
1 + R *
P.
or, for simplicity write as:
10. T=B.v
Appendix BCUC IR1 74.1
⎞
⎟
⎟
⎟
⎞
⎟ ⎟
⎟ ⎟
⎠ ⎠
where the expression in equation 9 in large brackets
is v. 58
Now take the natural log of both sides of 10 and
substitute from 8 so that we have:
Marijuana Growth in British Columbia 36 The Fraser Institute