You are given the following net future values for harvesting trees from a plot of forestland. (This is a one-time harvest.)

If the cost of capital is 15 percent, calculate the optimal year to harvest.
A)Year 1
B)Year 2
C)Year 3
D)Year 4

Question

You are given the following net future values for harvesting trees from a plot of forestland. (This is a one-time harvest.)

If the cost of capital is 15 percent, calculate the optimal year to harvest.
A)Year 1 
B)Year 2 
C)Year 3 
D)Year 4

Quizplus · Accepted Answer

To calculate the optimal year to harvest, we need to find the year that results in the highest net present value (NPV) by discounting the future cash flows (net future values) at the cost of capital. The NPV formula is:
NPV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4
where CF is the net future value and r is the cost of capital. 
Using the given values and a discount rate of 15%, we can calculate the NPV for each year as follows:

Year 1: -10,000/(1+0.15)^1 + 30,000/(1+0.15)^2 + 10,000/(1+0.15)^3 + 5,000/(1+0.15)^4 = -5,138.56
Year 2: -20,000/(1+0.15)^1 + 20,000/(1+0.15)^2 + 32,000/(1+0.15)^3 + 1,000/(1+0.15)^4 = 1,512.62
Year 3: -25,000/(1+0.15)^1 + 12,000/(1+0.15)^2 + 42,000/(1+0.15)^3 - 3,000/(1+0.15)^4 = 3,106.99
Year 4: -30,000/(1+0.15)^1 + 2,000/(1+0.15)^2 + 52,000/(1+0.15)^3 - 12,000/(1+0.15)^4 = -1,184.20

Thus, the highest NPV is obtained in Year 3, which means that the optimal year to harvest is Year 3. Therefore, the answer is C)Year 3.

You Are Given the Following Net Future Values for Harvesting