Neco Model Questions Vol1 2024 Agricultural Science Question 37

A forest stand yields timber volume (m³/ha) according to \(V(t)=0.1t^{2}+0.8t\), where \(t\) is the age in years (5\le t\le 30). Planting and maintenance cost is \(\₦30,000\) per hectare incurred at the start of each rotation. Timber price is \(\₦8,000\) per m³. The annual discount rate is 12%. The farmer may harvest the stand after 10, 15 or 20 years and then re‑plant immediately, repeating the rotation indefinitely.\n\nFor each possible rotation age, calculate the present value (PV) of the net cash flow of one rotation and the equivalent annual cash flow (EAC) using \(EAC = PV\times i /[1-(1+i)^{-n}]\) where \(i=0.12\) and \(n\) is the rotation length. Which rotation age maximises the EAC and what is the corresponding EAC (rounded to the nearest thousand Naira)?