Question

Question 6 A landowner is considering a soil improvement project which (if completed) will increase the profitability of the land by $50/acre, beginning next year (for simplicity, assume it will last forever) a) If the project costs $750/acre (paid immediately) and the interest rate is 10% (0.1), should the project be completed? (Explain) b) Would the project be completed at a different interest rate? Explain why or why not.

Answer 1

Profitability rise by $50 per acre for lifetime.

Interest rate = 10%

a) Project cost $750 per acre.

Present value of first year increment in profit = 50 / 1.1

Present value of second year increment in profit = 50 / 1.12

Present value of third year increment in profit = 50 / 1.13

and so on.....

Sum of present value of all profit = (50 / 1.1) + (50 / 1.12) + (50 / 1.13) + ...............

It makes a geometric progression of r = 1 / 1.1

Sum of geometric prgression = a / (1 - r)

where,

a = (50 / 1.1)

r = (1 / 1.1)

Sum is = {(50 / 1.1) / [1 - (1 / 1.1)]}

= 500

As present value of all present value is 500 while cost is 750. Thus, this project would not be completed.

b) Yes, this project would be completed at a lower rate of interest which makes present value to be higher.

750 = (50 / r) + (50 / r2) + (50 / r3) + ................

750 = {(50 / r) / [1 - (1 / r)]}

r - 1 = 50 / 750

r = 6.67%