Question 1 A forest stand yields a recurring timber harvest

Question 1.

A forest stand yields a recurring timber harvest income of $50,000 that occurs every 45 years.

A) Using a 7% interest rate, find the present value of the perpetual harvest income stream assuming that the first income occurs 45 years from now?

B) Suppose that there is also an annual property tax of $100. Compute the net present value of the same forest stand with the perpetual annual tax payment included

C) The asking price for the land is $1,000. Given theNPV in part B), Should you buy it? Why? or Why not?

Decision Tree Table for choosing present and future value equations. ltem to Number of Present or Annual or Perpetual or evaluate occurrences Future Equation to use Periodi Terminal Series na na 0 value payment:s Future Present na na Periodic Annual Periodic Vn Vo(1+i)\" Vo=Vn/(1+i)\" Vn=pl(1+i)n-1)/[(1+1)t-1)] Single Revenue Future Terminal Perpetual Vo= p/[(1+i)\'-1] Series of Equal payments Present Terminal Vo (1-1(1+)-1](1+i)) Cost PerpetualVo Annual Terminal Vo=p[(1+i)n-1)/[i(1+i)\") interest rate per year (in decimals) Vo = initial value (in time 0) V- value in time n n total number of years of compounding or discounting considered p = amount of payment occurring every t years t number of years in one multiyear group or interval of years (length of the interval) Payments occur at the end of the period or multiyear interval Please note: these equations can be used for months or weeks or any other length of time as long as the interest rate is defined at that period, n is defined as total number of periods, and t is the number of periods in one multiperiod group or interval. In this class, we will stick primarily to using the annual rates. Source: Figure 7.3 from Davis, et al. 2001 Forest Management, p. 341

Solution

Don\'t worry about large image size. Here are your answers showing how you have to use these formulas:

(A)

This question asks to compute the present value of a perpetual income stream, where $50,000 income is generated once every 45 years.

So,

Interest rate, i = 7% = 0.07

t = 45

p = $50,000

Equation to use:

V0 = p / [(1 + i)^t - 1]

= $50,000 x [(1.07)⁴⁵ - 1]

= $50,000 x (21.0025 - 1) = $50,000 x 20.0025

= $1,050,122.59

(B)

Present value of annual property tax (an annual perpetuity) = p / i = $100 / 0.07 = $1,428.57

Net Present value (NPV) of the perpetuity in part (A) net of annual tax = $(1,050,122.59 - 1,428.57)

= $1,048,694.02

(C)

Since asking price is extremely low compared to NPV of the land\'s benefits, you should buy it.