La Bourse / Volume IV / Nº IV.04 / Ten concept briefs

A man in a dark suit writing in an open book at a library desk, lamps lit among the shelves. — Plate IV.04 · Ten concept briefsThe Scaler's Book.Every plant has a capacity plate riveted to its frame. Very few have the other one — the number the ground will hand over, year after year, without being asked twice.

TEN CONCEPT BRIEFS · Chapter IV.04 — Manufacture at Biological Rates

One page each. A reader who reads only these ten pages has the chapter.

The order is the order of the decision itself: first what the ground gives, then how to express a plant's demand on it as one ratio, then what happens when that ratio goes above one, then what the whole thing is worth and to whom, and finally the instrument that funds it. Each brief stands alone and each names the figure it turns on, so a reader can take any one of them into a meeting by itself.

BRIEF 1 — The Renewal Rate

The idea. A biological input does not have a supply curve in the short run. It has a rate: a quantity per unit of time that the ground hands over, whether or not anyone is buying.

  increment  =  i · V        i = the biological rate,  V = the standing stock

The rate is measurable and it is a property of the site, not of the intention.

Worked example. The Collins Almanor Forest held 1,500,000,000 board feet of standing timber in 1941 and held 1,500,000,000 in 2000, having removed 2,000,000,000 in between over 59 years. Because the stock at the end equals the stock at the start, the mean removal is the mean increment: 33,898,305 board feet a year, or 360.6 board feet per acre per year, which against 1.5 billion standing is 2.260 percent a year.

The comparison that settles it. The Menominee forest's increment is 102.1 board feet per acre per year. Almanor's is 3.53 times that. Same century, same discipline, different ground.

Why it matters. Every capacity number for a plant running on wood, water, fibre or fish is a claim about this rate, whether or not anyone has measured it.

You already know this because you have never asked how many apples are in an orchard. You have asked how many it gives in a year.

BRIEF 2 — The Harvest-to-Increment Ratio

The idea. One number governs this entire discipline: annual draw divided by annual renewal.

  ratio  =  planned annual draw / verified annual increment

At or below 1.00 the stock holds or builds. Above it, the stock falls — and so, next year, does the increment, because the increment is a rate on the stock.

Worked example. Menominee Tribal Enterprises mills about 14,000,000 board feet of sawtimber against an increment of 24,000,000: a ratio of 0.583. Collins ran at 1.000 for fifty-nine years. The market-sized mill in this chapter starts at 1.770.

Why it matters. It converts an argument about temperament into an argument about arithmetic, and it fits on the front page of a capital paper. It is also the natural covenant for a lender, because it is verifiable by a third party.

You already know this because you already read a debt service cover ratio the same way: one number, a threshold at one, and everything above it is a different conversation from everything below it.

BRIEF 3 — Overshoot Lowers the Coupon

The idea. Running above the increment does not end in a stop. It ends in a permanently smaller rate, because you have shrunk the principal that the rate is paid on.

  V(t) = K + (V0 - K) e^(i t),   K = H / i

Worked example. A mill at 60,000,000 board feet a year on a forest with V0 = 1,500,000,000 and i = 2.260 percent needs a standing stock of K = H/i = 2,655,000,000 board feet to be sustainable, and does not have it. It draws the inventory to the operable floor of 450,000,000 in 28.61 years, consuming 1,050,000,000 board feet of standing timber. After that it runs at i × V_min = 10,169,492 board feet a year — 30.0 percent of the rate it began with.

Why it matters. The usual mental model of overshoot is "we get thirty good years and then it's over." The real model is worse and quieter: thirty good years, then seventy percent of the business, forever, on the same site with the same overheads.

You already know this because you have watched somebody live off capital. The problem was never the year the capital ran low. It was the income afterwards.

BRIEF 4 — The Crossover Is a Discount Rate

The idea. When you compare a lower-but-indefinite throughput with a higher-but-finite one, the answer is not a year. It is a discount rate — the rate below which patience is worth more than volume.

Worked example. Over a sixty-year appraisal, on cash flows alone, the rate-matched mill overtakes the market-sized one only below a discount rate of 1.974 percent — 0.87 times the forest's own biological rate. At 4.0 percent the market-sized mill is ahead by 11,253,773 dollars; at 6.0 percent, by 10,981,873.

Why it matters. It tells you precisely what you are arguing about. If your weighted average cost of capital is 9 percent and your crossover is 5 percent, no amount of conviction closes that gap — but three specific, nameable moves do, and they are Briefs 5, 8 and 9.

You already know this because you have seen two projects with identical cash flows rank differently in two companies. Nothing about the projects differed. The hurdle did.

BRIEF 5 — The Standing Stock Is an Asset

The idea. The single largest lever in this chapter is an accounting treatment, not an engineering one.

Worked example. At year sixty the market-sized mill stands on 450,000,000 board feet of timber and the rate-matched mill stands on 1,500,000,000. At a stumpage value of 250.00 dollars per thousand board feet that is 112,500,000 dollars against 375,000,000 — a difference of 262,500,000 dollars that a cash-flow-only appraisal simply does not see. Counting it moves the crossover from 1.974 percent to 5.172 percent.

The figure. 3.198 points of discount rate, bought with one line of accounting treatment and no change to the physical plant.

Why it matters. The market-sized mill is not out-earning the rate-matched one. It is selling an asset and booking the proceeds as operating income, and an appraisal that ignores the asset cannot tell those two things apart.

You already know this because nobody thinks a company that sold its head office had a strong quarter. They think it sold its head office.

BRIEF 6 — Design to the Lower Bound

The idea. A renewal rate is an estimate with an interval. Sizing a plant to the point estimate is sizing it to a coin toss.

  design point  =  point estimate x (1 - z · CV)

Worked example. At a coefficient of variation of 20.0 percent and a 90 percent one-sided bound (z = 1.2816), the design point is 74.4 percent of the estimate: 25,209,492 board feet rather than 33,898,305. That gives up 8,688,814 board feet of capacity, 10,426,576 dollars of capital and 1,303,322 dollars a year of contribution, and costs 1.677 points of crossover.

Then buy the interval down. Halve the CV to 10 percent and the design point rises to 87.2 percent, returning 4,344,407 board feet and 651,661 dollars a year. An independent cruise costs about 45,000 dollars: a payback of 0.83 months.

Why it matters. This is the rare case where better measurement pays for itself in weeks, and where the conservative design and the profitable design are the same design.

You already know this because you do not load a crane to its mean rated capacity.

BRIEF 7 — Siting Is the Capacity Decision

The idea. For a plant running on a renewing input, where you put it sets what it can make, by orders of magnitude, and the decision is normally taken by people who never see the process design.

Worked example. Recharge to the High Plains aquifer runs from 0.024 inches a year in the Southern High Plains of Texas — 0.6096 millimetres — to 6.000 inches, 152.40 millimetres, in south-central Kansas. The same plant on the same 50.0 square kilometre capture zone sustains 30,480 cubic metres a year in Texas and 7,620,000 in Kansas. At 3.50 litres of water per litre of product, that is a 74,212 barrel brewery or an 18,552,876 barrel one.

The figure. 250 times the sustainable throughput, identical capital.

Why it matters. No process improvement anywhere in the discipline is worth two orders of magnitude. Site first, then measure the rate, then size the plant.

You already know this because you already accept that a hydroelectric scheme is a decision about a river, not about turbines.

BRIEF 8 — The Concession, Priced

The idea. A rate-matched plant cannot serve a demand spike. Not "struggles to" — cannot. Price it rather than wave at it.

Worked example. A spike every 12.0 years, lasting 2.0 years, bringing 40.0 percent more volume and 25.0 percent more margin. The rate-matched mill is asked for 13,559,322 board feet a year it cannot make, forgoing 5,084,746 dollars a spike — but it does capture the uplift on everything it sells, 2,542,373 dollars of scarcity rent, so the net is 2,542,373, or 211,864 dollars a year expected: 4.17 percent of contribution. Add permanent customer attrition of 0.600 percent of margin per spike — 5.02 basis points a year, leaving 97.04 percent after sixty years.

The figure. 4,837,339 dollars at a 5 percent discount rate, 6.48 percent of NPV, 0.620 points of crossover.

Why it matters. Priced, it is a line in the paper. Unpriced, it is the objection that ends the meeting.

You already know this because an insurer does not argue about whether storms happen. It prices them.

BRIEF 9 — Selling the Inflexibility

The idea. The thing the design costs you is also the only thing you have that your flexible competitor cannot sell: certainty of supply.

Worked example. Sell 60.0 percent of output on firm multi-year contracts at an 8.0 percent premium and that is 244,068 dollars a year against an expected spike cost of 211,864 — a cover ratio of 1.15 times, and the crossover returns from 4.552 percent to 5.145.

Why it matters. In the spike, the flexible supplier is selling his surge to whoever pays most, which means his long-standing customers are the ones he disappoints. The rate-matched plant is structurally incapable of doing that, and structural incapacity is what makes a promise credible.

You already know this because you have paid more for a fixed-rate mortgage than the floating rate on the day you signed it, and you were not being irrational.

BRIEF 10 — The Increment-Based Borrowing Base

The idea. Reserve-based lending sizes a facility against a depleting reserve, certified annually. Invert it: size the facility against the verified annual increment.

Worked example. Almanor's increment of 33,898,305 board feet at 250.00 dollars per thousand is 8,474,576 dollars of increment value a year. A four times base is 33,898,305 dollars of facility against a rate-matched mill costing 40,677,966. The covenant is the ratio — ≤ 1.00, on a three-year rolling mean — and a breach reduces the base rather than accelerating the loan, because the lender's security is the increment itself. Certification costs 45,000 dollars for the cruise, 12,000 for metering and 8,000 for assay: 65,000 dollars, or 0.160 percent of the plant's capital cost.

Why it matters. An undepleting security supports a longer tenor, and tenor is where the cost of capital actually lives. It also prices a borrower at 0.583 differently from one at 1.000, which no instrument in the market does today.

You already know this because a lender against a rental property looks at the rent roll, not the sale price. This is the same instrument, pointed at biology.