9.12 Opportunity and Transaction Costs: (Solution)
Here is the solution (and the “givens”) to the problem above.
We were given:
- T = Total required yearly outlay = $25 million (yearly)
- F = $100
- i = .05
Total Cost = Transaction + Opportunity Costs = (T/C × F) + (C/2 × i)
| Order Quantity | Transaction Costs | Opportunity Costs | (T/C x F) + | (C/2 x i) = | Total Cost |
| (T/C x F) + | (C/2 x i) = |
| $600,000 | ($25,000,000/ 600,000) (100) + | (600,000/2) (.05) = | 4,167 + | 15,000 = | $19,167 |
| $500,000 | ($25,000,000/ 500,000) (100) + | (500,000/2) (.05) = | 5,000 + | 12,500 = | $17,500 |
| $400,000 | ($25,000,000 / 400,000) (100) + | (400,000/2) (.05) = | 6,250 + | 10,000 = | $16,250 |
| $300,000 | ($25,000,000/ 300,000) (100) + | (300,000/2) (.05) = | 8,333 + | 7,500 = | $15,833 |
| $200,000 | ($25,000,000 / 200,000)(100) + | (200,000/2) (.05) = | 12,500 + | 5,000 = | $17,500 |
| $100,000 | ($25,000,000 / 100,000) (100) + | (100,000/2) (.05) = | 12,5000 + | 2,500 = | $27,500 |
You will note that as order quantities decrease, transaction costs (T/C × F) increase, but opportunity costs (C/2 × i) decrease. A low point in total cost – at around an order quantity of $300,000 – is also observed.
However, judging from this table alone in which order quantities were chosen arbitrarily, we cannot say that $300,000 is the unique solution to the problem; we can only say that it appears that the solution is in the vicinity of this amount (i.e., somewhere around $300,000).
We still must discover the unique solution to the optimal order quantity problem. For the moment, let’s put this off and instead, on the next page, graph the data from the table. A graph is worth a thousand words.
It is important to note that, at around 300,000 cash ordered, the transaction and opportunity costs are approximately the same. The costs will be exactly the same at the precise optimal cash order quantity.