Choosing a Fertilizer When the Cheapest Nitrogen Is Not the Best Buy
Musa farms one hectare of maize on a sandy loam in Kaduna State. His soil test shows adequate potassium but low phosphorus and low nitrogen. He has ₦200,000 set aside for fertilizer. The agro-dealer offers three products in 50 kg bags: urea (46% N) at ₦30,000; NPK 15-15-15 at ₦32,000; and ammonium sulphate (21% N) at ₦16,000. The extension officer recommends 120 kg N per hectare, applied in two splits. The rains have started and are expected to continue for about three weeks. Musa's only labourer broadcasts fertilizer by hand, and the field slopes gently. Musa wants to know which bag gives him the most nitrogen for his money, and whether he should simply buy the cheapest nitrogen and be done. He also remembers that last year's crop stayed pale and stunted until about six weeks after planting.
1. Calculate the cost per kilogram of nitrogen for each of the three fertilizers and rank them. Show your working for each.
Read the worked answer
Work out the nitrogen in one 50 kg bag first, then divide the price by it.
| Fertilizer | N in 50 kg bag | Price | Cost per kg N |
|---|---|---|---|
| Urea (46% N) | 0.46 × 50 = 23.0 kg | ₦30,000 | 30,000 ÷ 23.0 = ₦1,304 |
| Ammonium sulphate (21% N) | 0.21 × 50 = 10.5 kg | ₦16,000 | 16,000 ÷ 10.5 = ₦1,524 |
| NPK 15-15-15 | 0.15 × 50 = 7.5 kg | ₦32,000 | 32,000 ÷ 7.5 = ₦4,267 |
Ranking on nitrogen price alone: urea < ammonium sulphate < NPK 15-15-15. Urea is about 3.3 times cheaper per kg N than the compound.
The trap is stopping here. The comparison is only valid for the nitrogen; the NPK bag is also delivering 7.5 kg P₂O₅ and 7.5 kg K₂O, which have value of their own. A pure nitrogen comparison flatters urea whenever phosphorus is also needed.
2. Musa needs 120 kg N per hectare. Using urea, how much product does he need, how many 50 kg bags is that, and what does it cost? Given his ₦200,000 and the low phosphorus result, advise him on how to spend the money.
Read the worked answer
Urea for 120 kg N: 120 ÷ 0.46 = 260.9 kg urea, i.e. 5.22 bags. Bags are sold whole, so 6 bags = 300 kg = 138 kg N, costing 6 × ₦30,000 = ₦180,000. Five bags (250 kg) give 115 kg N for ₦150,000 - 5 kg short of the target.
The phosphorus problem. Five bags of urea would leave only ₦50,000, enough for one bag of NPK (₦32,000), which supplies just 7.5 kg P₂O₅. That is far below what a low-P soil needs.
A defensible plan within budget: 4 bags urea (₦120,000 → 92 kg N) + 2 bags NPK (₦64,000 → 15 kg N, 15 kg P₂O₅, 15 kg K₂O) = ₦184,000, giving 107 kg N and 15 kg P₂O₅. This accepts a small nitrogen shortfall in exchange for getting some phosphorus into the seedbed. Musa should also ask the dealer for a straight phosphate such as single superphosphate: since his potassium is already adequate, buying K inside NPK 15-15-15 is paying for a nutrient he does not need, so a P-only source plus urea would feed the crop more cheaply per hectare.
3. Give two agronomic reasons why the cheapest nitrogen per kilogram may still be the wrong purchase on this particular field, referring to the slope, the sandy soil and the hand broadcasting.
Read the worked answer
1. Volatilisation and runoff of surface-broadcast urea. Urea applied to the surface is broken down by the enzyme urease to ammonium carbonate, which can lose nitrogen as ammonia gas. On a warm, sandy, low-organic-matter soil the loss can be a large share of what was applied within days. Adding a gentle slope and hand broadcasting makes it worse: some granules roll downhill and concentrate in the furrows, and the first heavy rain can wash nitrogen off the field before it ever reaches the roots. Urea must therefore be incorporated, banded or placed in a furrow and covered, and split so that the second dose goes on when the crop can use it.
2. The cheapest N ignores phosphorus and sulphur. Musa's soil test says phosphorus is low, and last season's pale, stunted crop is the classic early nitrogen deficiency signal. Buying only urea fixes one constraint and leaves another. Ammonium sulphate costs about ₦220 more per kg N, but it supplies 24% sulphur and acidifies the soil - an advantage on an alkaline soil, a liability on an already acidic sandy one. The right answer is a small, calculated blend rather than the single cheapest bag.