Question

You have a 10-year- old, 1-acre, even-aged forest. You estimate that if you spend $35 per acre fertilizing this f rest every 5 years, you can receive $1,000/acre net stumpage returns 20 years from now. In 20 years, you predict a potential land sale price f $300/acre. Four fertilizer applications will be made, the first one now. Based only on the above value and cost projections, what is your net present value per acre now for this forest, if your minimum acceptable rate of return is 8 percent?

Answer 1

Let us analyze the cash flows in this case

Cash flow in Year 0=Co=Fertilizer application cost=-$35

Cash flow in Year 5=C₅=Fertilizer application cost=-$35 per acre

Cash flow in Year 10=C₁₀=Fertilizer application cost=-$35 per acre

Cash flow in Year 15=CF₁₅=Fertilizer application cost=-$35 per acre

Cash flow in Year 20=CF₂₀=Sale price+ Stumpage returns=300+1000=$1300 per acre

Present value of per acre forest, PV is given by

PV=-Co+C₅(P/F,8%,5)+C₁₀(P/F,8%,10)+C₁₅(P/F,8%,15)+C₂₀(P/F,8%,5)

PV=-35-35(P/F,8%,5)-35(P/F,8%,10)-35(P/F,8%,15)+1300(P/F,8%,5)

(P/F,8%,5)=1/(1+8%)^5=0.680583

(P/F,8%,10)=1/(1+8%)^10=0.463193

(P/F,8%,15)=1/(1+8%)^15=0.315242

(P/F,8%,20)=1/(1+8%)^20=0.214548

PV=-35-35*0.680583-35*0.463193-35*0.315242+1300*0.214548=$192.85

Present value of per acre forest is $192.85