To All,
I will repost the problem here and then space down and post the (my?) answer at the bottom.
An Economic Puzzle
Assume that you are the owner of a new, private, diamond marketing company located on a remote, tax-free island nation. Your entire company assets consist of an inventory of 65 large, identical, flawless, uniquely cut diamonds, which you have just acquired from the estate of a world famous diamond cutter for $24.375M in cash, or $375K each. Your company has a single employee, holding the title of President and Marketing Manager, and earning an annual salary of $250K, which represents and includes the entire annual expense budget for the company. The entire net cash flow of the company, revenues minus expenses, is paid out to you in an annual dividend and is placed in an interest-bearing demand account compounding at a 4.5% real (and nominal) rate per annum, a rate that results in a time to double of 16 years.
The annual market demand schedule for your diamonds is presumed to be time-invariant, to have a perfect unitary price elasticity of demand and no possibility of price discrimination, and to have a demand independent of previous sales. In particular, a price of $1M produces a demand for 1 diamond per year, a price of $500K produces a demand for 2 diamonds per year, and so forth.
Your President has just presented you with an offer to reduce his current year's salary from $250K to $125K in exchange for a single diamond which he intends to have crafted into a unique engagement ring to bestow on his prospective fiancee.
Is a decision to accept this offer, a form of partial non-cash compensation, of a one-time salary reduction of $125K in exchange for a diamond whose cash acquisition cost was $375K, and which has a possible market value of up to $1M, and a net cash flow of up to $750K, financially justified? Why, or why not?
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Answer to an Economic Puzzle -
The first thing to decide is the sales schedule. Since increasing the sales rate from 1 to 2 diamonds a year doesn't increase the total revenue, it is clear that 1 diamond will be sold a year for 65 years.
The key is that the opportunity cost to the company of saving the $125K in salary is foregoing the $1M sale price of a diamond, but that is delayed 64 years into the future as there is no current opportunity cost at all until the last diamond is removed from inventory. Investment of the $125K savings at 4.5% for 64 years would result in $2M at that time, a 16 fold (four doubles) increase, as compared with the $1M sale price of the diamond in year 65 less the $250K salary for a net of $750K. Alternately, working backwards, the discounted present value of the net proceeds of $750K in year 65 is only $750K/16 or $46.875K. In either case, it is clear that the one time salary reduction is a good investment.
Note that the initial acquisition cost of $375K per diamond does not figure in the answer to the salary reduction question. This is because it is a sunk cost as far as deciding whether or not to accept the salary reduction offer. However, even in the first year, the $375K cost diamond has only returned a double to $750K. In the ninth year, an investment of the $375K at 4.5% would have compounded to the $750K breakeven level. Thus only the first eight diamonds show a real profit, the ninth is breakeven and all the rest lose money. Not wanting to bother working out the total profit or loss for all 65 diamonds, it nevertheless seems likely that it is a loss.
While this problem has little or no unique Austrian economic content, as the fact of opportunity cost (as opposed to accounting cost), sunk costs and the time value of money should all be mainstream economics as well, it serves to show that what looked initially like a silly choice, was fully justified. In fact this problem has a similar appearance, although for different reasons, to that of employee stock options.
Regards, Don |
