Functional obsolescence in a ring-spinning mill: equivalent asset or modern equivalent?
A cotton spinning mill in Coimbatore operates 24 ring frames, each with 1,200 spindles, installed in 2013 at ₹1.65 crore per frame. The current replacement cost new of an equivalent ring frame is ₹2.10 crore; a compact spinning frame with the same spindle count costs ₹2.90 crore. The mill’s ring frames consume 9% more power and require 12% more labour than compact frames. Annual power cost for the spinning section is ₹6.20 crore and labour cost is ₹4.80 crore. The valuer estimates physical deterioration at 45% and remaining life at seven years. The discount rate is 13% and the corporate tax rate is 25%. The management argues that because compact frames are now the industry standard, the mill should be valued using the compact frame’s replacement cost. The bank wants a cost-approach value for the ring frames only.
1. Quantify functional obsolescence using the excess operating cost method, stating whether you use pre-tax or post-tax costs.
Read the worked answer
Excess operating cost.
Power disadvantage = 9% × ₹6.20 crore = ₹0.558 crore per year.
Labour disadvantage = 12% × ₹4.80 crore = ₹0.576 crore per year.
Total excess cost = ₹1.134 crore per year.
Tax consistency. If the discount rate is a post-tax WACC, the excess cost should be after tax:
₹1.134 crore × (1 − 0.25) = ₹0.8505 crore per year.
If a pre-tax discount rate is used, keep the excess cost pre-tax. Mixing a pre-tax cost with a post-tax discount rate would overstate obsolescence.
Capitalisation. Seven-year annuity factor at 13%:
[1 − (1.13)^−7] ÷ 0.13 = 4.422.
Functional obsolescence = ₹0.8505 crore × 4.422 = ₹3.76 crore.
Interpretation. This is the present value of the extra operating cost that a buyer would incur by using the ring frames instead of compact frames. It is a deduction from the depreciated replacement cost of the ring frames, not from the compact frame price.
2. Compute the RCNLD of the 24 ring frames before and after functional obsolescence.
Read the worked answer
Replacement cost new.
Use the equivalent ring frame, not the compact frame:
24 × ₹2.10 crore = ₹50.40 crore.
Physical deterioration.
45% depreciation:
RCNLD before functional obsolescence = ₹50.40 crore × (1 − 0.45) = ₹27.72 crore.
Functional obsolescence.
Deduct the post-tax capitalised excess cost of ₹3.76 crore:
₹27.72 crore − ₹3.76 crore = ₹23.96 crore.
Check. The deduction is about 13.6% of the pre-obsolescence RCNLD. That is plausible for a 9% power and 12% labour disadvantage over a seven-year remaining life. If the valuer used the pre-tax excess cost of ₹1.134 crore, the deduction would be ₹5.01 crore and the result ₹22.71 crore; that is acceptable only if the 13% discount rate is also pre-tax. The answer must state the convention.
3. Should the compact frame’s ₹2.90 crore replacement cost be used instead? Explain the risk of double counting.
Read the worked answer
No, not in the same calculation as the excess-cost adjustment.
The cost approach values the subject asset by reference to an asset of equivalent utility. The existing ring frames produce ring-spun yarn; the equivalent replacement is a ring frame at ₹2.10 crore. The compact frame at ₹2.90 crore provides superior utility: lower power and labour. That superiority is exactly what the ₹3.76 crore functional obsolescence deduction measures.
Double-counting risk. If the valuer uses the compact frame’s ₹2.90 crore as RCN and also deducts the excess operating cost of the ring frames, the same disadvantage is penalised twice: once through the higher benchmark cost and again through the obsolescence deduction. The result would be internally inconsistent.
When the compact frame may be the benchmark. If the market now requires compact yarn and ring-spun yarn cannot be sold at a normal price, the compact frame may be the modern equivalent asset. In that case, the valuer should use the compact RCN, adjust for any difference in capacity or quality, and not also deduct the full excess operating cost. The chosen model must be disclosed and consistently applied. For the bank’s cost-approach request for the ring frames only, the equivalent-ring-frame model with a functional obsolescence deduction is the defensible route.