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# Math 101 for beef producers

## Nutrition with John McKinnon When I discuss various aspects of nutrition with producers, I often sense confusion when it comes to “as fed” versus “dry matter” (DM) conversions. Such conversions have a profound effect on our ability to predict feed intake and on our understanding of ration nutrient concentration, feed costs and on cost of gain calculations. If one is to understand nutrition, it is necessary to have a firm grasp on basic math concepts as they relate to cattle feeding. Below I will try to walk you through some of these concepts.

First, let’s consider feed intake. There are numerous factors influencing how much feed an animal consumes. These include age and weight of the animal, production expectations, environmental factors, as well as characteristics of the feed. The National Research Council in its 2016 beef cattle nutrient requirement publication developed equations that incorporate these factors and allows one to predict how much feed a given animal will consume. While valuable, one does not always have access to these equations or to a computer to run them on.

An alternative way to quickly estimate DM intake, and consequently, as fed intake is to calculate feed intake as a percentage (per cent) of body weight. For example, a pen of 600-lb. calves should consume approximately 2.5 per cent of their body weight on a DM basis. This equates to an expected DM intake of 15 lbs. (600 lbs. x 0.025).

The expected as-fed intake is calculated from knowledge of the DM content of the ration. For example, if the above ration was based on dry feed ingredients, the DM content of the ration would be approximately 87 per cent. In this case, the as-fed intake would be 17.2 lbs. and is calculated by dividing expected DM intake by the DM content of the ration (15 lbs./0.87). If the ration was silage-based with a DM content of 60 per cent, the as-fed intake would be 25 lbs. (15 lbs./0.60).

When using this method to estimate DM intake of feeder cattle, it is important to remember that we are dealing with a ratio between DM intake and body weight expressed as a percentage. Newly weaned calves under stress will typically eat between 1.5 and two per cent of their body weight (DM basis). As they adjust to their environment, intake typically increases to 2.5 to 2.7 per cent of body weight and then slowly drops with time on feed. Cattle close to market weight will typically consume 1.5 to 1.8 per cent of their body weight on a DM basis. This drop over time is a result of body weight increasing at a greater rate than the animal’s feed intake.

Despite the fact that the ratio decreases with time on feed, actual DM intake increases over most of the feeding period. For example, the 600-lb. steer eating at 2.5 per cent of body weight consumes 15 lbs. of DM while a 1,500-lb. steer consuming 1.8 per cent of body weight consumes 27 lbs. (1,500 lbs. x 0.018) of DM.

Similar calculations are required to understand nutrient levels in various feeds, particularly high-moisture feedstuffs. For example, barley silage at 35 per cent DM will typically have an as-fed crude protein concentration of 4.0 per cent. On a DM basis, the crude protein concentration of this silage will be 11.4 per cent (4.0 per cent/0.35).

Failure to make this conversion can lead to costly mistakes. For example, I find that many producers undervalue their silage, simply because they fail to consider its value on a DM basis. The argument they give is that their silage is worth \$70 per tonne as fed, while good hay costs \$100 per tonne. While there might be good reasons to feed more silage, cost is not necessarily one of them. In this case, the silage (35 per cent DM) at \$70 per tonne as fed, is worth \$200 per tonne (\$70/0.35) on a DM basis while the hay (86 per cent DM) is worth \$116 per tonne (\$100/0.86).

When calculating ration costs and the feed cost per lb. of gain, similar calculations are necessary. For example, a silage-based backgrounding ration at 50 per cent DM might be valued at \$85 per tonne. The value of this ration on a DM basis (\$85/0.50) is \$170 per tonne or \$0.077 per lb. DM (\$170/2,205). If our 600-lb. calf is gaining 2.0 lbs. per day and consumes 15 lbs. of DM, the feed cost is (i.e. 15 lbs. x \$0.077) \$1.16 per day or \$0.58 per lb. of gain (\$1.16/2.0 lbs.). To calculate the total cost of gain, you would need to include yardage, interest, morbidity, mortality and depreciation costs.

Knowledge of the cost of gain can in turn be used for break-even projections. For example, consider the situation where a producer wants to background 600-lb. calves valued at \$2 per lb. to a target weight of 900 lbs. If the total cost of gain is \$0.85 per lb. or \$255 (i.e. 300 lbs. x \$0.85) for the 300 lbs., the total investment is \$1,455 (\$1,200 + \$255) and the break-even selling price is \$1.62 per lb. (\$1,455/900 lbs).

While I can give other examples, those above highlight the importance of understanding the role that basic math plays in nutrition and cattle feeding.