Question

Doctor Bob purchased 100 acres of land 10 years ago for $5000 per acre. If he could have alternately invested the money at 6 percent per year, what price per acre must he receive today to break even with his opportunity rate? If Doctor Bob sold the land at $12,500 per acre today, what was his actual rate of return?

Answer 1

If Doctor Bob could have invested money at 6% per year, the value of such investment after 10 years would be calculated using following formula

Future Value = Present Value *(1+ rate)^Number of years

Present value = 5000(per acre) *100(acres) = 500,000$

rate = 6%

Number of years = 10 years

Futue value (that is at the end of 10th year) = 500000*(1+0.06)^10 = 895,423.8483$

If he invested that amount 10 years ago he would have accumulated amount that is equal to 895,423.8483$

In order to find breakeven with the same rate, we have to divide the accumulated amount by number of acres

= 895423.8483/100

= 8954.2385$ per acre.

If doctor bob solds the land for 12,500 his actual return would be calculated as

=(Ending value - Beginning value )/Beginning Value

= (12500-5000)/5000

= 150%