Well, Collision, you did ask for it.

I'll look at a TTL12 J-2 ship, since that seems to be fairly common in
Golden Age settings, and do my best to belt the MGT2 trade bits into
some sort of sense.

A dton of biosphere has a sticker price of 200,000 Cr and requires 1 Power.

At TTL12, this gives an incremental powerplant cost of 66,667 Cr and
0.067 dton. (TTL12 fusion plant generating 15 power per dton and costing
MCr1/dton).

Assuming I've read the life support rules properly, that saves 2,000
Cr/mo in life support costs.

(Those with some finance background, please bear with me as I fill in
those without such background).

You're already familiar with a method for converting a large up-front
cost into a recurring payment - ie, a mortgage.  That's what I'll do here.

The annual interest rate implied by the ship mortgage rules works out
(iirc) to 5.56% pa.

GT: Starports p66:

"Starports are normally financed by the issue of low-risk Imperial
bonds. These bonds pay a 3% dividend per year, which the SPA must pay..."

Short-dated central-government-issued securities in its domestic market
are (usually) regarded as having very low default risk (for instance,
the last time the AU federal government defaulted on its domestic
obligations was in late 1929), so their interest rate is normally taken
as a risk-free rate.

GT: Far Trader p7:

"The return on Imperial bonds (considered risk-free) is so low that
people only invest in them to avoid keeping cash around."

This, combined with (GT:FT, p6) "an average annual growth rate of less
than 1%" leads me to put an upper bound on the 3I risk free rate of 1% pa.

Given that someone who might back a ship to the tune of X MCr can earn
3% pa on their money while sitting at home, they would logically require
a greater return on their capital to put it at risk as equity (ie,
ownership stake) in some sort of business.  Likewise, if they can invest
in ship mortgages and get around 5-5.5% pa while sitting at home, that
further raises the lower bound for the required rate of return on equity.

For simplicity, I'll add the mortgage risk premium (4.56% pa over the
risk free rate) onto the mortgage rate, so our punter would require
10.12% pa on their money to back a ship with equity.

As ships are conventionally financed with a 20% deposit (equity) and an
80% mortgage (debt), that works out to a weighted average cost of
capital of 6.5% pa.

A Cr266,667 mortgage over 40 years at 6.5% pa works out to Cr1,562 per
month.

Thus, at first cut, a dton of biosphere would seem to be a net
Cr438/month saving (up until at least covering the crew's life support
needs).

Not so fast, livewire.

As Trav ships generally tend towards "stuffed to the gills", they run
short of free space.  Where are you finding that 1.067 dton?  What are
you giving up?

The default answer is "cargo space", -and the resulting revenue.

How much revenue is lost is a nontrivial question to answer, especially
with MGT2's order-of-magnitude increase in freight rates going from 5 pc
travelled to 6 (Cr7,700/dton to Cr86,000/dton).  Whether the ship is in
tramp (25 jumps/yr) or liner (35 jumps/yr) service also has an influence.

To lower-bound things _on a full hold_, looking at cargo travelling 2 pc
(Cr1,600/dton) on a tramp trader:

Jumps/mo: 2.08

Revenue lost/mo: Cr3,328

Net cost per ton of biosphere: Cr2,890/mo

To break even under that assumption, on average a dton of biosphere has
to displace _less than_ 0.13 dton of cargo per month.  For a single dton
of biosphere, that works out to the cargo hold not being full at least
88% of the time (assuming no spec cargo).

And I come to pass - out.

Alex

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