Article Text

Marginal cost of the calving interval in beef cows is not uniform
  1. Didier Raboisson, DVM, PhD, dipECBHM and
  2. Philippe Citerne, DVM
  1. IHAP, INRA, ENVT, Université de Toulouse, Toulouse, France
  1. E-mail for correspondence; d.raboisson{at}


To understand the profitability of reproduction management measures, an economic assessment based on a beef cow life simulation was proposed. It accounted for the discounted feeding costs of the dam and its calves for the different periods of their lives up to their sale and for the overall production from calves adjusted by mortality and culling. The calibration was proposed for various combinations of typical French and European situations. The maximal cash flow was observed for the lowest calving interval, corresponding to the maximal number of calves produced. The marginal cost of the calving interval was not uniform: on average, it was twice as high at a calving interval of 360 days (€1/day) as at 500 days (€0.5/day). It was also higher when age at first calving was lower and when culling was late or the replacement rate was low. The results were sensitive to the costs of the calves’ diets and to the market prices for calves. These assessments may assist the evaluation of the profitability of various measures taken in the field when faced with deteriorating calving intervals in beef production.

  • beef
  • cow
  • calving interval
  • cost
  • economics

Statistics from


Reproduction management has been intensively studied for dairy cows, but research on beef cow reproduction is less developed. Beef cow reproduction, which is still primarily carried out via bulls, is not an issue in many herds. The reproduction performance of beef cows has not yet been thoroughly described and likely remains heterogeneous, depending on breeds, livestock systems, countries and management systems. For instance, the average calving interval of the four million French beef cows is reported to be approximately 410 days. The mean age at first calving is approximately 38 months, and the age at culling is almost nine years.1 2 Huge variations in the calving interval between livestock systems are observed, but these variations clearly demonstrate the potential for easy improvement of reproduction performance in beef cows. The usual recommendation of one calf per cow per year is not achieved in many herds. Whether this recommendation is still valid and sustainable is unclear. One key question is whether this objective should be achieved in herds for which the effort required to do so is high. Few simulation and economic approaches are available,3–5 and those that exist are dated. The present work aims to assess the costs of increases in the calving interval in beef production under French conditions to help define the profitability of reproduction management.

Materials and methods

The proposed economic model is adapted from a dairy model.6 It is based on the method of calculating the equivalent of the gain for a given period, which aims to assess the annual profitability of a firm using net present value (NPV). Applied to cows on a daily basis, the model gives the following:

Embedded Image(1)


Embedded Image(2)


CFd: cash flow of day d (income – expenses)

r: daily discount rate

R: annual discount rate

AgeCull: age at culling.

The NPV was then converted into equivalent annual cash flow (EACF):

Embedded Image(3)

To facilitate the calibration of the model, the cows’ days of life were divided into different periods pi (detailed in equation 5) so that:

Embedded Image(4)


CFpi: cash flow for the period pi

Dpi: duration of the period pi.

The NPV for the whole life of a cow can then be calculated as the sum of the NPVs for the cow’s three periods of life (first three items)—from birth to first calving, from first calving to last calving, and from last calving to culling—plus the NPV of calves produced (item 4), plus the NPV linked to the culling and heifers sold (last item):

Embedded Image(5)


AgeCalv1: age at first calving

CFd,p1: daily cash flow of cow during period 1 (birth–first calving)

CFd,p2: daily cash flow of cow during period 2 (first calving–last calving)

CFd,p3: daily cash flow of cow during period 3 (last calving–culling)

N: number of calvings

CalvInt: calving interval in d

CFCalfSold: cash flow of calves sold

NCalfSold: number of calves sold

AgeSold: calves’ age at sale

CFCull: cash flow of culled cows

CFHeiferSold: cash flow of heifer sold just before first calving

NHeiferSold: number of heifers sold.

N is calculated using CalvInt and the productive period as follows:

Embedded Image(6)

where Fatt is the duration from last calving to culling, including fattening period of the cow.

The model assumes a stability in herd size, and one female calf is considered to be kept for replacement, whereas all males are considered to be sold:

Embedded Image(7)

Embedded Image(8)

Embedded Image(9)


NMaleSold: number of male calves sold per cow

NFemaleSold: number of female calves sold per cow

NHeiferSold: number of females sold as in-calf heifer per cow

SuruRateMale: survival rate of male calves from birth to sale

SuruRateFemale: survival rate of female calves from birth to sale

SuruRateHeifer: survival rate of female heifers from age at sale of other female calves to their sale at their first calving

PcHeiferSold: percentage of females sold as in calf-heifer.


Embedded Image(10)

which is linked to equations 8 and 9:

Embedded Image(11)


NFemaleTot: total number of females produced.

In cases of NFemaleTot ≥ 1, CFp1 of the cow is only linked to feeding costs during this period. In cases of NFemaleTot < 1, CFp1 of the cow is also linked to the cost of a replacement heifer:

If Embedded Image ≥ 1,

Embedded Image(12)

If Embedded Image< 1, then

Embedded Image(13)


DietCostHeifer: daily cost of the heifer’s diet

PriceHeifer: market price of heifer.

Combining equations 12 and 13 led to equation 14, and equation 4 applied to CFp1 led to equation 15:

Embedded Image(14)


Embedded Image(15)

The cash flows of periods 2 and 3 were limited to the cow’s feeding costs, since cow products are included in items 4 and 5 (the last two of the five elements summed) of equation 5:

Embedded Image(16)


DietCostCow: daily cost of the diet for one cow.

Cash flows from cow products are then defined according to equations 17 and 18.

Embedded Image(17)

Embedded Image(18)

Embedded Image(19)


PriceCalf: market price of calf at sale

DietCostCalf: daily cost of the diet for one calf

PriceCull: market price of culled cow.

Lastly, the relation between replacement rate (RR), AgeCull and AgeCalv1 was defined as follows:

Embedded Image(20)

The parameters of the model are reported in Table 1. All DietCost values for cows, calves and replacement heifers were calculated from four livestock systems that represent four levels of farm intensification in relation to the calving period, the cost of feeding and the nature of feed. In cases 1 and 2, the calvings take place at the end of January (the calves are outside all summer), and in cases 3 and 4 they take place in August (the calves are in barns during the winter; higher sale price for calves). Feeding costs for calves and cows are low in cases 2 and 4 (grass, hay) and higher in cases 3 and 4 (corn silage, high quantities of concentrates). Typical diets were calculated for the animals’ different periods of life and corresponding mean costs assessed using the market cost of the feed, adjusted by the duration of each period. An increase in CalvInt is associated with an increase in the middle to end gestation period length, the diets of other periods being fixed for a given livestock system. A mean value of the four cases was also considered. DietCostHeifer was calculated for the subperiods birth to one year old, one to two years old, and more than two years old, and DietCostHeifer for the last subperiod was applied up to the first calving (depending on age at first calving of the given scenario). DietCostCow was calculated for the three main subperiods between two calvings or from last calving to culling (just before and up to two months after calving; mid-lactation; around weaning). The durations and frequency of these different subperiods were adjusted depending on scenarios and CalvInt calculated in the models. The prices of products were defined in accordance with the market situation in 2012. The sensitivity analysis focused on the prices of food and products.


Input parameters of the economic model


The results showed that AgeCalv1 and CalvInt highly influenced EACF (Fig 1). For instance, when the culling occurs at nine years old, EACF increased up to 50 per cent when AgeCalv1 decreased from 40 to 24 months, assuming daily heifer feeding costs stayed the same at any AgeCalv1. However, the higher EACFs observed when AgeCalv1 decreased from 40 to 24 months or from 40 to 36 months were completely lost when DietCostHeifer increased 52 per cent and 12.5 per cent, respectively, from the current level. The degree of EACF increase from a decrease in AgeCalv1 was slightly higher at low CalvInt than at high CalvInt. The results also showed that the decrease in AgeCull highly influenced EACF if the first calving was late, but that influence was limited in case of early first calving.

FIG 1:

Cash flow for different calving intervals and various combinations of parameters (example of culling at nine years old). RR, replacement rate.

The marginal cost of CalvInt (ie, the cost of one extra day of CalvInt) was not uniform and was highly sensitive to the value of CalvInt (Fig 2), that is, the marginal cost of CalvInt at 360 days was approximately twice as high as that at 500 days. The marginal cost of CalvInt was also higher when AgeCalving was lower and was higher when culling was later or RR was lower.

FIG 2:

Marginal cost of calving intervals for various combinations of parameter. RR, replacement rate.

The marginal costs of CalvInt for cases 1–4 were almost unchanged from the mean situation. The sensitivity analysis showed changes in EACF of 20 per cent and 28 per cent, with 20 per cent changes in DietCostCalf and PriceCalf (Fig 3), respectively.

FIG 3:

Sensitivity analysis of cash flow for different calving intervals and various combinations of parameters. RR, replacement rate.


The present assessment clearly showed that the marginal cost of CalvInt in beef is not uniform and depends on the value of CalvInt. This finding first implies that announcing the marginal cost of CalvInt without any reference to the value of CalvInt does not make sense. It also implies that the marginal cost of CalvInt varies greatly (almost by a factor of 2) depending on the herd (and its CalvInt value). The present results do not allow a per second definition of the profitability of measures taken to improve reproduction performance. Although improvement of CalvInt will lead to lower expected saved losses (ie, higher costs remaining) in a herd with high CalvInt than in a herd with low CalvInt, improvement may be easier to achieve in a herd with high CalvInt than in a herd with an already low CalvInt. The highest EACF is reached at low CalvInt, but the means needed to reach this point may be higher than the saved losses, suggesting that it is reasonable to accept higher CalvInt for some herds. The present results clearly show that improving CalvInt is economically interesting for both low and high CalvInt, but the saved losses are more or less high depending on CalvInt. In the field, practitioners have to define ex ante the needs and the price of means to be involved for an improvement in CalvInt, and to compare this with the expected saved losses reported in the present work, leading to define whether the intervention or change proposed is profitable or not. In many herds serviced by bulls, expenditures to reach low CalvInt may be reduced and low CalvInt likely remains an objective for such herds. Bulls may represent large fixed costs, in particular for herds with seasonal calvings. The marginal cost of CalvInt (or EACF) for a given CalvInt also varies with RR, AgeCalv1 or AgeCull. It bears remembering that low CalvInt may result in high RR, and thus focusing on CalvInt alone without adjusting for RR is an inappropriate basis for decision making. The present work also clearly shows that the highest cash flow is obtained at low CalvInt, even if the feeding costs of cows are reduced. Thus, low feeding cost does not seem a reasonable justification for the very high CalvInt that is sometimes observed, and improvement of profitability through reduced losses is therefore expected. For the whole life of a typical European beef cow, the marginal cost of CalvInt appears moderate (about €9 per extra day, ie, about €280 per extra month of CalvInt each year), but an annual reasoning at the herd level seems more appropriate in the field (as done along this paragraph).

Results in dairy already highlight that the marginal cost of CalvInt or days open is not uniform.6 7 However, for dairy cows, the highest marginal cost of extra days open or CalvInt is not observed for the lowest CalvInt but rather for higher one, which is the opposite of the present results. This difference accords with differences between main beef production from calves and main dairy production from milk. Increasing CalvInt tends to ‘dilute’ the production of beef cows when standardised by life-day, whereas this dilution is only seen after the milk peak in dairy. The adjustment for higher mortality and morbidity risk around calving must be made in dairy, leading to a trade-off between overall milk produced and production cost after diseases have been accounted for. The same issue exists in beef production because of the potential difficulties of calving, but there is not the same trade-off since CalvInt is negatively correlated to the number of calves per cow when standardised by life-day. EACF is not far from gross margin, allowing for easy comparison between the two, in spite of some systematic breeding or health items that have not been included. EACF is appropriate to compare investments with different durations, and the marginal cost of CalvInt is derived from EACF in the present work. The marginal cost of CalvInt retained here is an extrapolation of the usual definition of marginal costs, changes of EACF being seen as costs related to different CalvInt. Production bounded or unbounded subsidies for cows or calves were not included so that the results could be more applicable outside France, since these subsidies may change with time and are applied differently depending on country. The present model was static and determinist, but was able to consider (1) the whole life of the cow using discounted value, (2) the dynamism of the herd using culling, replacement and age at calving, (3) the natural mortality during the rearing period, (4) the precise feeding costs during the various periods of life, and (5) the limits of the assessment and the possibility of extrapolation out of the given conditions using multiple calibration and sensitivity analysis.

It is often said in France that the marginal cost of CavInt is €1 per extra day per cow, even if the origin of this statement is unclear. This statement is in accordance with the present results, on average, for low CalvInt (approximately €20 per cow per extra 20 days). Thus, the present work first improves upon the precision of this statement for various combinations of parameters, and second it shows that the marginal cost for high CalvInt and late first calving could be up to twice lower as in the opposite situation. Comparison of this study’s results with previous results3 5 remains difficult due to differences in the livestock systems studied and the dates of the previous models.


View Abstract


  • Competing interests None declared.

  • Provenance and peer review Not commissioned; externally peer reviewed.

Request permissions

If you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center’s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways.