Ross G. Drynan

The Value of Unrealized Farm Land Capital Gains: Comment

Plaxico and Kletke (PK) presented three alternative models for valuing farmland capital gains. Their first model assessed the present value of anticipated capital gains, assuming that they have value only when the asset is sold. Their second model viewed the value of unrealized capital gains as equivalent to a tax-deferred income stream with the tax being paid at capital gains rates either when the property is sold or at the end of the planning horizon. Their third model assessed the value of the capital gains as an equity base for further credit. Dunford has criticized PKs formulations, especially their second model. However, his alternative model perpetuates several errors made by PK. Other errors made by PK led them to an important conclusion about tax rate effects, which conflicts with conventional wisdom. In this comment we correct the models for these errors and offer some further thoughts on the assessment of the value of farmland capital gains. Dunford correctly comments that, because the capital gains on the farmland are not actually realized until year n, it is necessary to borrow for additional investments. The value of unrealized capital gains will depend on how the increased equity base is used in borrowing more funds and how the borrowed funds are invested. There are two possibilities. One is that each years capital gain is used as a basis for a one-year investment. Second, the gain can be the basis of an investment lasting for the whole planning horizon. The latter is equivalent to using the total accumulated value of capital gains each year as an equity base for an investment lasting one year. These two possibilities conform to Dunfords equations (2) and (3), respectively, equation (3) being identical to PKs third model. Since the first of these alternatives appears distinctly inferior, we concentrate on the latter. What these authors have failed to note is that it is only possible to use an unrealized capital gain as an equity base for an investment in periods after the gain occurs. All the models suggested by PK and Dunford for valuing unrealized capital gains imply that the farmland owner can borrow at the start of each year against the expected capital gain in that year. This is clearly not tenable and leads to an overestimation of the gains of about 5%. PK err further in the way in which they include tax and inflation in their models. The present value of any future cash sum can be calculated either by discounting the nominal sum with a nominal discount rate to year 0, or by discounting the real value, measured in year 0 dollars, of the cash sum by the real discount rate. Both methods necessarily lead to the same present value. For example, a future sum S,, when discounted at a nominal rate N, has a present value