Question

You purchased bare land for $500 per acre as an investment to supplement your retirement income. After three years, you plan to reforest the property at a cost of $400 per acre. You estimate your income from selective timber harvesting will be $5,000 per acre beginning 25 years after the trees are planted and occurring every 10 years thereafter in perpetuity. You have annual property taxes of $2 per acre starting next year. What is the present value of the timber harvest income from this investment, assuming a 4 percent discount rate?

Answer 1

PV of cost of reforestation =400/(1+4%)^3=400/1.04^3=400/1.1249=$355.60

PV of property taxes=2/4%=$50

Total PV of cost =500+355.60+50=$905.60

First income will be after 25+3=28 years from today and will occur every ten years

Annuity of second income at end of 38 year will be given by:

FV= A*((1+r)^n-1)/r

Or, 5000=A*((1+4%)^10-1)/4%

Or, 5000=A*(1.04^10-1)/0.04

Or, 5000=A*(1.4802-1)/0.04

Or, A=5000*0.04/0.4802

Or, A=$416.45

Hemce PV of income at the 28th year=416.45/4%=10411.37

Total PV including income of 28th year=10411.37+5000=$15411.37

Hence PV of income today=15411.37/(1+4%)^28=15411.37/1.4^28=15411.37/2.9987=$5139.34

Hence Net PV=5139.34-905.60= $4233.60