Question

A local tree farm is trying to decide which fertilizer to use to grow its trees. It can either buy the famous Greenwood Fertilizer, which costs $5 and can grow a tree which can be sold for $8 in 2 years, or it can buy Brian and Peter’s Fertilizer which costs $4 and can grow a tree which can be sold for $10 in 5 years.

1. What is the NPV of each option given an annual effective interest rate of 5%? (5 points)
2. What is the rate of return of each option?Which option should the tree farm pick assuming an infinite time horizon? Why?

Answer 1

1. NPV calculation

Option 1 ( with Greewood fertilizer) : $2.256

Option 2 ( with Peter's Fertilizer) : $3.835

2. Rate of return calculation:

Option 1: 45.12%

Option 2: 95.875%

Option 2 should be chosen as it provides higher NPV.

Step-by-step explanation:

1. The detailed calculation for each option is:

Option 1: Present value of sales proceed - initial cost = (8/1.05^2) - 5 = $2.256

Option 2: Present value of sales proceed - initial cost = (10/1.05^5) - 4 = $3.835.

2. The detailed calculation for each option is:

Option 1: NPV/Initial cost = 2.256/5= 45.12%

Option 2: NPV/Initial cost =3.835/10 = 95.875%

To assess which option should be picked with the assumption of infinite time horizon, NPV should be key driver. As Option 2 has higher NPV, Option 2 is chosen.