Cull decisions and cull indexes

Definition

A cull decision asks one question: is the herd better off keeping this cow, or selling her now and putting a replacement in her place? A cull index (or cow value) ranks cows on the answer, so the lowest-ranked cows are culled first when slots, feed or heifers are limited.

The standard economic answer is the retention payoff (RPO), also called cow value: the expected present value of keeping the cow, minus the expected present value of replacing her today. Keep her while it is positive. Two values go into it:

Value of keeping: her expected future net income (milk minus feed and other variable costs, plus calf value), adjusted for the risk that she dies or must be culled involuntarily, plus her salvage value when she eventually leaves.
Value of replacing now: her beef value today (estimated weight × cull price, net of selling costs), minus the cost of a replacement heifer, plus the replacement’s expected future net income.

The main inputs that move a cow’s value:

Pregnancy status and days carrying calf. A pregnant cow is worth much more than an open one at the same DIM, because the next lactation is close. The value of a pregnancy falls as DIM rises.
Production relative to herd mates, adjusted for lactation and DIM (e.g. 305ME or a relative-value item), and expected persistency.
Lactation and DIM: older and late-lactation open cows have less future income left.
Health and udder history: chronic high SCC, repeated mastitis, lameness and other events that raise involuntary-cull risk or cost.
Market prices: milk price, feed cost, cull cow price and replacement heifer price. A high heifer price relative to cull price makes marginal cows worth keeping longer.
Slot constraint: if the barn or a quota is full, a slot has an opportunity cost (the replacement’s value). If there are empty stalls and no heifer waiting, the comparison is the cow against an empty stall, and a cow with a positive daily margin is worth keeping.

Left out on purpose: book value, purchase price, what was already spent on breeding or treatment, and depreciation. These are sunk costs. They matter for tax, accounting and loan collateral, not for whether keeping the cow beats replacing her.

Most cows that leave a herd are not ranked out: they are involuntary removals (death, injury, severe disease). A cull index steers the voluntary part, and the timing of planned culls. See cull rate.

Formula

Plain text:

RPO = PV(expected future net income of the cow, incl. eventual salvage)
      − [ beef value now − replacement cost + PV(expected future net income of the replacement) ]

keep if RPO > 0; with limited slots, cull lowest RPO first

beef value now ($) = estimated live weight (lb) / 100 × cull price ($/cwt live) − selling costs
daily margin ($/day) = milk (cwt/day) × milk price ($/cwt) − feed cost ($/day) − other variable costs ($/day)

LaTeX:

\mathrm{RPO} = \mathrm{PV}_{\text{keep}} - \left( V_{\text{beef}} - C_{\text{repl}} + \mathrm{PV}_{\text{repl}} \right)
\qquad
V_{\text{beef}} = \frac{W_{\text{live}}}{100} \, P_{\text{cull}} - C_{\text{sell}}

Present values discount monthly cash flows and weight each month by the probability the cow is still in the herd. Full models (e.g. dynamic programming, Groenendaal et al. 2004; Cabrera 2012) also re-decide every month, so the cow keeps the option to be culled later.

A simpler short-run screen is daily margin against beef value: an open, late-lactation cow whose daily margin no longer covers the income lost by holding a slot (or the drop in her beef value) is a cull candidate.

How to pull it in DC305

DC305 holds most of the cow-level inputs; market prices and replacement cost come from outside it.

LIST ID PEN LACT DIM RC DCC TBRD MILK 305ME LGSCC FOR LACT>0 DOWNBY DIM
LIST ID PEN LACT DIM TBRD MILK FOR RC=1 LACT>0          do-not-breed cows
LIST ID PEN LACT DIM TBRD MILK FOR RC=3 DIM>200         late open cows

Health history comes from treatment and disease events (mastitis, lameness, metabolic events), whose names vary by herd.
DC305 has a cow value command, COWVAL: the cow’s value relative to an average fresh heifer, plus her pregnancy value. The item CWVAL carries cow value in common setups (LIST ID PEN LACT DIM CWVAL FOR LACT>0). Many herds also define their own relative-value or cull-flag items; their names and formulas vary by herd, so check the herd’s private dc305-vocab mapping and the item definition before trusting one.
Estimated weight usually isn’t in DC305; use a breed-and-lactation default or the herd’s own scale data, and price from cull cow value.

Typical range

Herd context: US Holsteins, freestall or dry-lot, stable herd size with heifers available.

Cow value is herd- and price-specific; there is no universal benchmark. Rules of thumb from published models:

Pregnant cows are almost always worth keeping over a replacement unless very low producing or chronically sick.
Value of a new pregnancy averaged $278 per cow and the cost of a pregnancy loss averaged $555 in De Vries 2006, a bioeconomic model of a general US Holstein herd at that paper’s 2006 prices and assumptions. The value of a new pregnancy rose with DIM early in lactation and usually fell later; high producers and first-lactation cows reached higher values that peaked later in lactation. The cost of a loss rose with gestation length.
Open cows lose value steadily as DIM rises; most models mark them for culling (DNB) somewhere around 150–300 DIM depending on production and parity.

Voluntary share of removals in US herds is usually small compared with involuntary removals; see cull rate.

Common mistakes

Counting sunk cost. “She cost us $2,000 and we just treated her” is not a reason to keep a cow. Only future cash flows count.
Using book value. Depreciated book value is an accounting number, not a market or future value.
Ignoring pregnancy status. Ranking on milk alone culls pregnant cows that are worth keeping and keeps open cows that aren’t.
Comparing raw milk across lactations and DIM. Use a lactation- and DIM-adjusted measure (e.g. 305ME or a relative value).
Ignoring the slot. With empty stalls and no heifers, culling a cow with a positive margin loses money. With a full barn and heifers waiting, keeping a marginal cow costs the heifer’s income.
Using a fixed cull price. Cull prices are seasonal and can move a lot. Re-run rankings with current prices.
Holding DNB cows too long. A cow marked DNB still eats and holds a slot. Plan her exit date (dry, sell at a target weight or at a margin cut-off).
Trusting a herd’s cull index item without reading its definition. User items differ in inputs and weights.