# Cornhusker Economics August 15, 2015Determining a Cooperative's Least-Cost Equity Position

A simple measure of interest coverage can serve as the basis for a valuable equity management and planning tool for both agricultural cooperatives and rural electric cooperatives (RECs). The times-interest-earned ratio (TIER) can be used by a cooperative to determine the least-cost mix of debt and equity capital that satisfies a particular interest coverage requirement given the cooperative's rate of return on equity and average interest rate. Identifying the least-cost mix of debt and equity is important because if the cooperative uses too much debt in its capitalization, it may be unable to cover its interest expenses; if it uses too much equity, its capital costs may be greater than necessary.

The interest coverage ratio, or TIER, is generally calculated by dividing earnings before interest and taxes (EBIT) by annual interest expense. For agricultural cooperatives that distribute net earnings to members as patronage refunds or RECs, which are exempt from income taxation, the interest coverage ratio (R) can be expressed in this form:

￼

where r_{e} represents the rate of return on equity,* i* represents the average interest rate, and *p* represents the equity position, which is defined as the proportion of total capital composed of equity. Total capital is usually considered to consist of equity and long-term debt, and annual interest expense consists of the interest on long-term debt.

Taking this expression for R and solving it for r_{e}, we can determine the rate of return on equity necessary for the cooperative to meet a particular value for the interest coverage ratio R̄ given its equity position and average interest rate:

The value of R̄ may be dictated by loan agreements, or the cooperative may set R̄ in an effort to ensure its net earnings and cash flow are sufficient for meeting its interest obligations and achieving its financial goals.

Alternatively, we can use this relationship to determine the equity position at which the interest coverage requirement R̄ is met given the cooperative's rate of return on equity and the interest rate. Let p^{*} stand for this value, which represents the least-cost equity position, i.e., the value of p that satisfies the interest coverage requirement at the lowest total cost of capital. At an equity position less than p^{*}, the interest coverage ratio would be lower than the required value; at an equity position greater than p*, the total cost of capital would be unnecessarily high. To solve for p^{*}, we must take into account the relationship between the rate of return on equity and the equity position. Simply put, the rate of return on equity will decline as the equity position is increased and the return on capital decreases relative to the stock of equity.^{1}

Determination of the least-cost equity position is demonstrated graphically in Figure 1. Each of the curves R_{1}, R_{2}, and R_{3} represents the combinations of re and p corresponding to a particular value of R (1.5, 2.0, and 3.0) as calculated from the first equation. For any value of R, the least-cost equity position p^{*} is determined by the intersection of the respective R curve and the curve representing the rate of return r_{e}. The shape of the curve for r_{e} reflects that the rate of return on equity declines as the equity position is increased. As the figure shows, the least-cost equity position increases and the rate of return on equity decreases as the interest coverage requirement is raised.

Total capital costs can be calculated from the weighted average cost of capital *k*, which is

where r_{e}, the rate of return on equity, is used to represent the cost of equity capital. Because the rate of return on equity determines which choices of cash patronage refunds, equity growth, and equity retirement are feasible, it represents the opportunity cost of equity for the cooperative's members. Thus use of the rate of return on equity as the cost of equity capital ensures that alternative uses for equity are appropriately considered in financing decisions. A cooperative's failure to take the opportunity cost of equity into account can result in an undervaluation of the cost of equity, thereby contributing to an overreliance on equity capital and an overinvestment in assets.

Jeffrey S. Royer, 402-472-3108

Professor, Dept. of Agricultural Economics

University of Nebraska–Lincoln

jroyer@unl.edu

^{1} For more on this point and this topic in general, see Jeffrey Royer, "An Equity Management and Planning Tool for Cooperatives," *Agricultural Finance Review* 75, 2 (2015): 267–81.