FOR 215

APPLIED SILVICULTURE

Analyzing Forestry Investments 

Time Value of Money:

Interest  = the cost or price of money, depending whether one is the borrower or lender. 

Simple Interest = interest is paid or received annually but not allowed to accumulate. 

Compound Interest = interest is not paid or received annually, but is allowed to accumulate, and the unpaid interest is also entitled to earn interest.

The basic compound interest formula:          Example: $100 is invested at 4% annual interest 

1st year    $100  +  $100(0.04)  =  $104 

Or  $100(1 + 0.04)  =  $104 

Which is  $100(1.04)¹ = $104 

2nd year    $100(1 + 0.04)  +  $100(1 + 0.04)(0.04)  =  $108.16 

Or $100(1 + 0.04)(1 + 0.04)  =  $108.16 

Which is  $100(1.04)² = $108.16 

3rd year          $100(1.04)³ = $112.48          (the principal for each period is underlined)

Formulas: 

V_o    = initial value                          i  = rate of interest per period as decimal

V_n    = future value                         n  = number of interest bearing periods 

Future value of a single sum (Compounding) :            V_n  = V_o(1 + i)ⁿ

Present value of a future sum (Discounting) :          V_o  = V_n/(1 + i)ⁿ

Present value of a perpetual annual series: 

V_o  = r/i                     r  = Amount of annuity

                               i  = rate of interest per period as decimal

Determining rate earned or length of investment: 

(1 + i)ⁿ  =   V_n/V_o          or  i  =  nth root of (V_n /V_o ) - 1                       

Or     n  = Log [ (V_n)/(V_o)] / Log(1 + i)

             Perpetual periodic annuities: 

V_o  = R/ [(1 + i)^t  -  1]             R  = Amount of perpetual periodic annuity 

                                              t  =  time period between annuity payments 

Installment Payments: 

IP  = L_o  [ i(1 + i)ⁿ ] / [(1 + i)ⁿ  -  1]             IP  =  amount of installment payment

                                                    L_o  =  amount of original loan 

Sinking Fund Annuities: 

SFA  = V_n (i) / [(1 + i)ⁿ  - 1]  

Present Net Worth (PNW):  = V_n / (1 + i)ⁿ   -   C_n / (1 + i)ⁿ         V_n   =   known income in year n

                                                                                C_n   =   known cost in year n 

CONSIDERATIONS: 

‑ Investment period:         

Pine: 15-30 years for pulpwood; 30-50 years for sawtimber

Hardwood: 25-40 years for pulpwood; 35-80 years for sawtimber 

‑ Costs:          Establishment, site preparation, planting/seeding, TSI:  $50-$200/acre

Management:  $1/acre

Property taxes (land only): variable 

‑ Selling Price:  Stumpage 

‑ Tree Growth:  based on site index 

‑ Assumptions: Land cost variations, future stumpage