Philly says Boy Scouts have to accept gays

[giblets]

That still doesn't make any sense. Could you provide more details?

Y= (((4x10^7)*(1.1))-4x10^7)^80) + 4x10^7 - (2x10^6)*(80)

This makes even less sense. For starters, (4x10^6)^80 is an unfathomably huge number.

Darn the city council, they could have had 1.4615x10^528 dollars by now.

[Ben Kenobi]

Should be ok now. My table is much simpler as I don't try to do it all in one step.

[BlackCat]

The city can take out a loan against the value of the building, invest the money, and repay the loan through other funds. Then their investment is earning money year after year, minus the mortgage.

Had they done so with a 10 year term, they'd have made about 12 million dollars over the last 80 years from the interest accumulated off the principle minus the mortgage and yearly write off of rent from the scouts.

This is serious BS. That is certainly not an option for a city. It might be a course for some private investor that are willing to take a risk, but certainly not for a responsible public oranisation as a city council.

Such actions could easily be illegal since public money can't be used in dangerous speculations as you suggest.

[giblets]

That still doesn't make any sense. Could you provide more details?

Y= (((4x10^7)*(0.1))*((1.1)^80)) + (4x10^7) - (2x10^6)*(80)

There, that's right.

(((4x10^7)*(0.1))*((1.1)^80)) + (4x10^7) - (2x10^6)*(80) = 8073600858

liar

4x10^7 is 40 million and 2x10^6 is 2 million. If those were intended to represent the value of the building and the value of the rent respectively then you're off by a factor of ten.

I'm going to assume you mean a nominal interest rate of 10%.

An asset worth 4 million in today's dollars would only be worth $330k back in 1926. Even if the city earns 10% nominal interest on that each year for 80 years that only leaves them with $675 million. Inflation is kind of a big deal when we're talking about a period of eighty years.

Also you're ignoring the fact that if the city council had collected rent, then under your assumptions the rent could have collected 10% interest. So the initial rent payment (let's assume rent in real dollars has been constant, meaning in 1926 it would have been $16400 or so) would have gathered eighty years of interest and resulting in $33.6 million. The next rent payment would have collected seventy nine years of interest resulting in $30.9 million. And so on. The total is over half a billion in today's money.

So, even granting your silly assumptions the city could not have profited from the agreement by more than $200 million or so since then. However the city doesn't actually start with $330k that can collect interest. What you're really suggesting is they take out a mortgage, invest the money somewhere that earns an interest rate of 10%, and keep the difference. If they can get a mortgage rate of 5% APR and take out a mortgage for the full value of the property then they add $200k in 2009 dollars to the city treasury every year by doing this, which is the same as the money they lose every year by not charging rent. The difference between the rate of return that the city can earn by investing and the mortgage rate the city can get has to be a full 5% APR just for the city to break even on the deal (not including the value of the building's construction). I'm not convinced that such a huge gap exists.

[Ben Kenobi]

An asset worth 4 million in today's dollars would only be worth $330k back in 1926. Even if the city earns 10% nominal interest on that each year for 80 years that only leaves them with $675 million. Inflation is kind of a big deal when we're talking about a period of eighty years.

Thank you. I was curious about these numbers. The same is also true of rent, but they don't follow each other exactly. They wouldn't be paying 200k back in 1928, so it's improper to say 200k * 80 to say how much rent that the scouts didn't have to pay.

Also you're ignoring the fact that if the city council had collected rent, then under your assumptions the rent could have collected 10% interest.

This is a good point. However, you'd have to factor inflation into the rent collection. Basically, you'd have a compounding and increasing amount and have to take that away from the compounding 4 million bundle.

So the initial rent payment (let's assume rent in real dollars has been constant, meaning in 1926 it would have been $16400 or so) would have gathered eighty years of interest and resulting in $33.6 million. The next rent payment would have collected seventy nine years of interest resulting in $30.9 million. And so on. The total is over half a billion in today's money.

That sounds right. Thank you. The two forces counterbalance each other.

So, even granting your silly assumptions the city could not have profited from the agreement by more than $200 million or so since then. However the city doesn't actually start with $330k that can collect interest. What you're really suggesting is they take out a mortgage, invest the money somewhere that earns an interest rate of 10%, and keep the difference.

Yes, that's the entire assumption. This will lower the rate of compounding on the principle? Could you put in the compounding rate with the 5 percent APR taken into account?

If they can get a mortgage rate of 5% APR and take out a mortgage for the full value of the property then they add $200k in 2009 dollars to the city treasury every year by doing this, which is the same as the money they lose every year by not charging rent. The difference between the rate of return that the city can earn by investing and the mortgage rate the city can get has to be a full 5% APR just for the city to break even on the deal (not including the value of the building's construction). I'm not convinced that such a huge gap exists.

It doesn't have to be a huge gap. Just a small one year after year, after factoring the rent calculation into everything else. The biggest drag is actually the amount they could have collected into rent compounding every year, because this will eventually catch up to the principal over time. It's just that the principal has such a huge lead in compounding, that this will take a very long time.

The maintenance payments over the years have to be factored in to.

Thanks for taking the time to work out these numbers.