Question

1. Suppose land is currently selling for $2,500 an acre and that you expect land prices to go up at an annual rate of 6 percent over the next 10 years.

a. Ignoring the annual net cash flow generated by this land for the moment, can you justify purchasing this land at this price if your required rate of return is 8 percent and capital gains are taxed at a 20 percent rate? Assume you plan to sell this land 10 years from now. Why or why not?

b. How would your decision change in part a if you received an annual rent payment of $200 an acre over this 10 year period?

Answer 1

a) Purchase of land not justified.

The required rate of return = 8%

Appreciation of land = 6%

Tax on capital gains = 20%

Therefore, realizable increase in land value = 6% * (1-20%) = 4.8%

The gains from purchase of land is lesser than required rate of return. Therefore, purchase is not justified.

b) Purchase is justified.

Annual rent payment = $200 = 8% of cost of land.

So, the effective return on land = 8% + 4.8% = 12.8%

This is higher than the required rate of return