I was astounded to see someone ask the same question I asked myself the last time I saw King Kong. The article has some excellent links to historical value estimators, which people might find handy or just plain fascinating.
I cogitated on the question.
So here goes:
In the movie, Carl Denham announces to Jack Driscoll and Ann Darrow that the show has, in its first night, already made $10,000 in ticket sales.
I figure that the theater is a normal stage theater, which couldn’t have more than 1,000 or so seats. That means an average of $10/ticket. I think that’s a lot of money for 1933. In those days, you could get into a movie theater for 25 cents.
I’d venture to guess (and do no more than guess) that the best ticket for a hit Broadway show didn’t cost more than $20.
So we know that even with an outrageous price and no real knowledge of what they’re going to see, people were willing to fork over $10 to see a Carl Denham show. That’s half the cost of a hit Broadway show of the time.
Move to the present. Theaters are smaller, and ticket prices are higher. So say $100 is the top ticket price; then you’d pay $50 to see the modern Carl Denham extravanganza. Put it in Madison Square Garden, which I’m guessing holds in the neighborhood of 10,000 people. You then have ticket sales of $500,000. That’s not bad for a night’s work.
Now it’s your turn to answer the questions I’ve posed:
How big was Denham’s theater? How big were stage theaters of the time?
How much did a top ticket for a Broadway hit cost in 1933?
How much does a top Broadway ticket cost now?
How many people does Madison Square Garden hold?
and finally
Would you pay $10 for the experience of having a 20-foot (or was it 60-foot) high ape try to eat you?
Bonus question:
How are King of Kings (1927), King Kong (1933), and Gone with the Wind (1939) related?
If Carl Denham wanted to recoup part of his losses by selling Giant Monkey Meat to the Army for stew, how much–
[list=a]
[li]meat would he have gotten?[/li][li]money per pound, in period funds, would he be offered?[/li][li]would Denham make?[/li][li]ketchup would be needed?[/li][li]Lastly–how mant troops could be fed?[/li][/list]
All three were David O. Selznick or Selznick Studios productions and all three were filmed in whole or in part on the RKO/Culver City backlot. (Also, the giant wall in **King Kong ** was left over from King of Kings.)
Hawthorne’s answer is close but not quite correct.
Economists (I admit I am one) and accountants have a technique for converting values over time. Just as one must use an exchange rate to convert the value of a currency across places, one must use a slightly different, intertemporal, exchange rate to convert the value of currency over time.
We have banks and other savings opportunities which pay a rate of return. If the interest rate paid by these opportunities is 5% per year, then $1 will turn into $1.05 next year. This is what we call a “future value” calculation and it uses interest rates as an intertemporal exchange rate. This is the generally accepted technique for converting values over time.
Interest rates will reflect the level of inflation. This is, in part, the reason why my 1999 car loan has a 7.5% interest rate but my 2004 mortgage has a 5.25% interest rate. Inflation has fallen. So when one uses an interest rate in a future value calculation, one is simultaneously adjusting for inflation.
The average interest rate on a typical savings opportunity over the 1933-2003 period was 4% (source: data on 3 month T-bill from FREDII). So, using the calculator here (and choosing a monthly compound frequency, I’ll spare you a discussion of compounding), I conclude that 10,000 1933 dollars have a future value of 163,682 2003 dollars.
There is a technique for running this in reverse so that one can figure out how to convert 2073 dollars into 2003 dollars. We call this a net present value calculation. I would describe this in detail, but this discussion is probably sufficiently dismal already …
As an actuary, I’ll disagree with you somewhat, Profcon since Hawthorne did say that it depends on the reason for your comparison and there are lots of ways of comparing.
If you’re trying to compare ticket prices in 1933 with those in 2004, for instance, then the rate of return given by banks in the time interval is largely irrelevant. If you’re trying to ask what the cost of housing was in 1933 compared to today, or what a plumber earns, or how stock prices fared, or the cost of a doctor’s visit, then the rates of return offered by banks is irrelevant.
Agreed, that economists tend to assume that all such factors are “related” over the long run. However, reality is somewhat different than economic theory.
Actuaries know that there are several different factors involved in future projections as well as in historic comparisons. One of these, as you mentioned, is the average “rate of investment return” – if you’re trying to ask how much growth there was. But rates of wage inflation are yet another measure, and purchasing power (how much did a ticket cost?) is yet another. All are valid or not valid, depending on what you want to compare.
In short, you’ve mentioned another (amongst many) that Hawthorne didn’t choose to deal with other than the general comment that there are “lots” of ways. Since Staff Reports are not intended to be comprehensive text books, I think Hawthorne did a superb job.
I’m sorry, but I disagree with your response. How would you move funds over time? You could put them in your mattress, or a jar in the ground, and in that case the value of the funds would stay constant in nominal terms and decline in real terms.
However, most individuals do place funds in savings instruments in order to transfer those funds over time. This is not theory. This reflects the reality of how one stores value. Therefore, the interest rate is the appropriate way for individuals to compare value over time.
In addition, courts of law use the very technique I described to compute damages for future lost income due to death or injury. I reiterate, this is not theory. It is the commonly accepted means of comparing values over time. While it may be “one of many,” practically speaking it is the one that you will encounter more often than not in real life situations. Evolution is certainly one of many theories, but we give it a little more attention than the others …
We have a winner(s). The gate that appears in King Kong was left over from King of Kings, a Cecil B. DeMille production of 1927 (it was used as a temple). The gate was then burned to the ground and filmed as the burning of Atlanta for Gone with the Wind. The scene was the first one shot for GWTW; neither Gable nor Leigh appear in it, and Leigh had not even been cast! In fact, she arrived at the studio the night of the filming.
Well, no. You are factually wrong here. When an actuary is called on as an expert witness to calculate the value of lost future income, it’s not the expected future interest rate that is the determining factor, but difference between the expected future interest rate and the expected future rate of wage increases. That is, if your future wages are assumed to grow at 3% and the value of invested money is expected to grow at 5%, then the courts use the 2% difference to calculate the present value of the loss. (OK, technically, it’s not 5% - 3% but (1.05)/(1.03) hence 1.94%)
I don’t disagree that average interest rates are one way to compute the time-value of money, which is useful for some comparisons. I didn’t mean to imply that was theoretic. What I meant is that the connection between average interest rates and other economic factors is theoretical, and not borne out in reality.
If you want to calculate your social security benefits, for instance, they’re based on wage inflation, not on interest rates. If you want to compare the cost of a loaf of bread (or a ticket to a Broadway show), you’d use a CPI index, not interest rates. While you are correct, if you’re dealing with money-costs you wouldn’t hide them under a mattress, you WOULD hide a certificate of IBM stock from 1925 under the mattress and it would have increased in value far more than the bank’s interest rate. Or a painting by Picasso.
The SEC’s regulations on projecting future pension costs, for instance, depends on expected future interest rate, future wage increase rate, and the future CPI (since pensions post-retirement are often indexed by the CPI.) That’s three different measures, all used and all valid.
And even under SEC regulations relating to the past, there’s no clear-cut answer on what rates to be used – T-bills, long-term corporate bonds, short-term corporate bonds, bank prime lending rates, etc. would all produce different values.
I believe we’re beginning to get a bit closer to an agreement on how this is done in practice. First, your statement here is correct, but I wasn’t wrong. IF one assumes wages are not growing then one simply uses the interest rate to calculate PDV of a constant stream. When wages are growing, one STILL uses the interest rate to calculate the PDV but the stream must be adjusted for wage growth. In both cases, the interest rate is used.
I’m sorry, the connection between nominal interest rates and inflation is not purely theoretical. There is a humongous empirical economics literature which shows that something called the Fisher effect is a reality in the determination of nominal interest rates, particularly in the long run. The Fisher effect essentially implies that nominal interest rates and inflation will move very closely together given enough time. This means that average interest rates over long horizons will reflect the average rate of inflation in an economy, so using nominal rates will accomodate the inflation rate. This isn’t perfect (nothing is) but it is a solid way to adjust value over time for changes in prices.
Moreover, the US Treasury has recently introduced a new security, called Treasury Inflation-Protected Securities (TIPS). This bond pays the holder an extra benefit whenever inflation rises. The interest rate on this bond is proof-positive that markets price inflation experiences into interest rates IN REALITY. In “theory” a non-TIPS bond doesn’t adjust for inflation, so its yield should be higher because its return will be eroded by inflation. Let’s go here to check the reality. Today, a 5 year non-TIPS note has an interest rate (yield) of 3.7 while the TIPS note of a similar maturity has a yield of 1.17. When inflation rises, this gap will increase. In fact the US Treasury created an entire new market for these TIPS securities in no small part in order to use market interest rates to get a sense of inflation expectations in the economy. Such information is VERY practically useful to policymakers. If the tie between inflation and interest rates were theory, Treasury would have been far less likely to introduce this new security.
We are drilling down into some deep finance issues here. And I thank you for this exchange, it has been quite interesting and stimulating. Here is my key point.
Nowhere in Hawthorne’s post did he mention the role of interest rates in calculating values over time. The post is interesting and engaging. But there is an ommission and it is an important one. When you say this:
you are saying that techniques for calculating values over time use interest rates PLUS other considerations.
You go to examples like this:
as a rationale for excluding interest rates from a present value calculation. However, this is not correct. Suppose I want to compare the price of a loaf of bread today to the price of a loaf of bread 5 years from now, and we know that bread prices increase 10% over 5 years. One might conclude that one would need 10% less “money” to buy the loaf today. But practically speaking this “inflation only” approach is wrong, it ignores the time value of money. Deciding to buy the loaf 5 years from now implies that you are not spending that money now. This gives you a new opportunity: to put the money you didn’t spend into a savings instrument which gives you an interest rate return (we call this the opportunity cost of buying the bread today). So buying today has two costs, the price of the loaf AND the foregone interest on the saving which not buying necessarily implies. One MUST consider this foregone interest because, in reality, it is a cost of doing business today. Firms, accountants, and the like routinely use this approach.
I humbly suggest that a complete and accurate portrayal of how value is compared over time in reality and practically MUST include a discussion of interest rates. Hawthorne’s did not and neither did the link to EH.net.
One can debate WHICH interest rate should be used, but an interest rate must be used (perhaps with additional considerations).
Maybe the GQ thread’s why my report got in this week, Tapioca Dextrin.
Thanks for your responses folks.
ProfCun, I don’t think the calculation you make is one of the right ones for the question. It’s the right answer to the question “Had the gross proceeds from the ticket sales been invested at the average return until now, how much would you have (before tax)?” But the question is "how much was it then in today’s terms?, not “how much would it be now?”
To be concrete: In year one, I have $100, the real interest rate is 5% and inflation is 5%. In year two, having $105 is like having $100 in year one. Sure, spending $100 in year one is foregoing $110 worth of goods in year two, but it’s still only worth $100 in year one. And that $110 worth of year two’s goods is only $105 worth of year one’s goods in year one’s prices.
633squadron’s suggestion is good. With a good idea about either seat prices or patron numbers, all sorts of comparisons with theatrical events could be made. There are people who’ve done film takings comparisons on that sort of basis.
hawthorne is joshin’ with ya. He had written the report a couple of months ago, and its turn in the queue of Staff Reports just coincidentally came up this week.
Thank you for your reflections Hawthorne. I thought your post was very interesting and illuminating.
Regarding:
Here is the first sentence of Veronica’s question:
Go here , here , here, or here. They all indicate that in order to calculate present value, one must use an interest rate.
Go to Mishkin, the canonical undergraduate textbook for money and banking. His discussion of present value uses an interest rate.
The question is about present value. The correct “textbook” answer to this question (in the real world, in college classes, and in research) involves using an interest rate. You can add other bells and whistles, but the interest rate must be used. And your response doesn’t mention interest rates at all. This is not an issue on the margin. It ignores a mainstream technique for calculating present value.
Why must and is the interest rate always used for calculating present value? There are two reasons: first, nominal interest rates (imperfectly) incorporate the rate of inflation. So when one uses a nominal interest rate, one is adjusting for inflation (when one adjusts for inflation, only, one is leaving out the real interest rate). So, in your example:
you wouldn’t have $105 in year two, in reality, except in extreme circumstances. The nominal rate would be approximately 10% (by the way, I’m assuming in your example that your interest rate is not quoted in annual terms but it applies to the entire two year horizon). A host of empirical papers show that the nominal rate would incorporate the rate of inflation. You would have approximately $110 in year two. This is almost certainly true of a 70 year horizon, per Veronica’s question.
Suppose we’re talking about a Tivo in your example. What is the Tivo worth to you if you buy it in year one? It is worth more than the $100 you paid for it. Why? If you buy it now, rather than two years from now, you sacrifice the $100 PLUS the additional purchasing power you would have if you didn’t buy it now and earned the payoff from savings. So it was worth more than the $100. So your analysis is off. You will only buy the object today if it is worth more to you than its price plus the foregone interest payment. Implicitly, when we decide to transact today, we are making a choice regarding the value of an object and what is foregone in savings returns when it is bought now. This brings me to my second reason you must use an interest rate:
Money has time value. So a transaction conducted today, versus some time in the future, always bears the additional cost of foregone interest payments. We call this opportunity cost. It isn’t theory, it is the principal which is used in practice.
Finally, to a movie studio, the mainstream technique I am describing is exactly the right way to compare values over time. Here is the example from Veronica’s question:
Suppose the movie studio would like to know the value of making King Kong. Suppose further that this $10,000 was the only revenue the movie ever received. Finally, suppose the movie studio spent $9,000 in 1932 order to make the movie. How would you “compare” the cost of the movie production to its future revenue ($10,000)? You wouldn’t use an inflation rate if you were a movie studio. You would use an interest rate. In my example, if the movie studio could have earned more than a 11.11% ( = [10 - 9] / 9) interest rate on a one-year savings instrument of lower risk than movie production (say a certificate of deposit with the Bank of Hollywood), King Kong should have never been made because its future value wasn’t sufficiently high, relative to the time value (i. e. interest rate) associated with the funds put into the movie. One simply can’t ignore interest rates when one thinks about the reality of making and / or buying stuff.
Thank you for responding to my posts. I appreciate that I’m not being treated like some overly persistent wacko (although my behavior could be confused as such ). I’m only putting time into this so that the information conveyed to readers is as accurate as possible. I enjoy the Straight Dope a great deal and I’ve learned much from it.
I ain’t not economonomist, I’m a actuary. Let’s not use TiVo, let’s use, say, a VCR. When I bought a VCR in 1982, the cost of the machine was around $1000. You would say that the present value of that money is (I’m making this number up) $2500, because I could have invested the money over the last 20 years.
But I could buy a VCR today for around $60, and it would include way more features than my 1982 version.
My point is that the cost of a market basket of goods (and especially things like technology and housing) over time is not tied to bank interest rates.
Well, sure. But when I hear an ordinary mortal say that something is “a luxury”, I don’t assume that they mean that it has an expenditure elasticity of greater than one. I assume they use the term as a lay person.
I think my interpretation of the question is what was sought, notwithstanding the fact that the words “present” and “value” were used in close proximity to each other:
So when Marlowe greases some guy with a 10 spot, I wanna know how much that makes him talk. That depends on how many days a slimeball would have to work to make ten bucks, or how many jars of hooch we’re talking - not how much that ten bucks would be be had it been invested.
The key here, I think, is that you’re talking about behaviour over time and I’m not. I’m talking about comparing values between times. In my example, I say that having $105 in year two is like having $100 in year one. Having $110 in year two is like having had $100 in year one: you could use it to buy either $100 worth of stuff in year one or $110 worth of year two’s good in year two or equivalently $105 worth of year two’s good valued at year one’s prices. How a person would apportion their purchases over time depends on their discount rate. That’s all about preferences and behaviour over time - where interest rates certainly do come into it (as a proxy). I don’t talk about that stuff, and I don’t need to.
Nothing I’m saying should be taken as saying that NPV calculations are unimportant: just that they don’t apply to this question, properly interpreted.
Ok, maybe I misunderstood the point of your response. I guess your discussion is fine if it was designed to give a lay person a lay answer, regardless of the accuracy of that response in reflecting how other lay people typically think about and do compare values over time (in business situations, in college classes, etc).
However, perhaps Veronica had heard the term “present value” before and specifically wanted to know what that term meant? When someone asks you for a soda, do you give her / him soda water? Should we second guess Veronica in this way, especially given that soda / present value have specific connotations which should not be overlooked?
OK, the slime ball would be able to work AND put those funds into a bank earning interest in order to accrue funds. Ignoring the interest rate gives you the wrong answer about how much the bribe is worth to the individual in terms of labor effort. Once again, your “counter” example is evidence that interest rates are relevant in these comparisons.
The bottom line is that if you conducted valuation computations over time as an accountant, and you ignored the interest rate, you would have bad books and you would be fired. If you did the same on my exam, I would reduce your grade. Interest rates are paramount in these computations, and they can not be thoroughly ignored in an accurate response.
You do need to talk about interest rates because Veronica specifically asked about present value, and there is an acceptable technique for doing this which involves interest rates. If I asked about molecular bonds and you started talking about ropes then you are answering the wrong question and you are ignoring the way chemists think about molecules. The same holds true in accounting / finance / economics and you do a disservice by ignoring the mainstream way of calculating present value.
). I’m only putting time into this so that the information conveyed to readers is as accurate as possible. I enjoy the Straight Dope a great deal and I’ve learned much from it.