Wednesday, February 01, 2012

Great Little Economics Story for Class

From Tommy the Tenured Brit, an example.  I have adapted it for teachers of Econ 101: This is a fine little problem to give in class, complete with video. The essentials:

  • Bridge revenue is tax-free, by law
  • Bridge toll is 80 pence, for multiple passages per day
  • Bridge revenue is 2,000 pounds per week in the busy summer, less in winter. About 80,000 pounds per year
  • Owner is responsible for upkeep and repairs on bridge and toll machinery, cost 15,000 pounds per year
  • Bridge "comes with" cottage, land, and fishing rights
  • The bridge just traded hands at a price of 400,000 pounds.  

1.  What is the implied discount rate (assuming that the bridge (with repairs), the tolls, and the tax break are all perpetual)
2.  Now assume that tax break is eliminated, the discount rate is the same as for #1, and that the effective average tax rate on the owners is 40%.  What would be the predicted change in price, or the capital loss the owners would be stuck with?
3.  Are the owners making a supernormal return because of the tax break?

Unless I have got me sums wrong, the answers are:

1.  16.25%
2.  New price would be 243,750 pounds.  So the tax break is worth 156,250 pounds
3.  Of course not!  The tax break is the reason that the bridge was worth 400k instead of 243k pounds.  But the implied rate of return is the same, because the tax rate is capitalized into the value.

Now, then, let's talk about capital gains taxes on investments in new plant and equipment, SHALL we?


doclawson said...

Nice Mike, but...

Basically, you're working the equation for a perpetuity. PV = CF/i

1. 400 = 65/i implies i=16.25% Agreed.

2. Holding i constant, the PV has to fall if the CF is taxed at 40%, so PV = 240 = 39/.1625. (I get 240 not 243.750. What am I missing?)

3. So you conclude that the rate of return is the same regardless and the tax simply capitalizes into the price of the asset.

But you ASSUMED this when you held i constant!

You and I would say that i has to stay the same because that's the required rate of return in the competitive market place.

BUT, the bedwetting lefties don't believe in economics. So their math is this:

400 = 39/0.0975.

They think taxing the bridge will only force the rich owner to earn a lower rate of return (9.75% instead of 16.25%) but no capital loss.

The bedwetters don't believe in reality, so the simple math problem won't convince them. It doesn't really get to the heart of the matter, which is how competitive markets work.

J Scheppers said...


I thing the difference is caused by Dr. Munger rounding the 16.25% to 16% prior to multiplying times the new net income.

I would add that the current discussion ignores the value of the cottage and fishing rights.

I concur that increasing capital gains taxes will significantly decrease the capital value of assets. I do think that care should be taken in designating specified products as tax exempt while others are taxed. The variation does cause distortions.

I would also argue that with the change in Tax rate the risk/reward position of the bridge owner changes sinces the gains are 40% less and the potential loss from the expected income is also reduced.

Operating costs of collecting all the tolls would likely also be a pain in the rear. So if taxed the owner would not shy away controversy. She could open the toll gate faster for the higher payers and slower for the lower paying clients and increase her revenue.

Mungowitz said...

Wow....those are really good comments.