# Return on Capital and Length of Leases

In return on capital calculations, the formula is generally operating income (annual) divided by total capital invested, to form a return on capital.  This figure can be used for various things, such as determining whether a company is making good investments by comparing the return on capital to a cost of capital.  The total capital can also be adjusted to include operating leases, by calculating a present payment of all future expenses on an operating lease, as described by Damodaran.  However, this number is also easily altered by adjusting the length of operating leases, disconnected from the true value or returns of a company.

Consider an example of a company which has an operating lease on a single widget as its only asset.  Suppose the lease is for \$20 for the first year, increasing 5% per year, and the lease is for two years.  The present value of this lease, at a 5% discount rate, is \$38.10.  Depreciation for this lease would amount to \$19.05/year (the value of the lease divided by the length of the lease).

Suppose that the company makes an operating profit of \$10 after all operating costs, including depreciation.  What is the return on capital for this company?  The company’s only asset is the lease, which is \$38.10, and their operating income is \$10.  Thus, the return on capital for our company is 26%.

What happens if the lease length in increased to five years instead of two years?  The lease payments here still rise 5% per year, but the lease is now five years long.  The present value of the lease using the same discount rate is now \$95.24.  Accordingly, the return on capital for the adjusted company is 11%.  But is the second company worse than the first?  Their costs are identical, and their operating income is identical.  The only difference is the length of the lease.  Why the huge difference in return on capital?

It appears to me that return on capital can vary widely based on the length of lease commitments, where short leases will lead to a much higher return than longer leases.  In the above example, there is little connection between the return on capital numbers and a realistic valuation of the company or its investments.  Perhaps this would make for a more meaningful number if we instead looked only at the annualized payments on the lease, rather than the total present value of the lease?  For example, the depreciation amount of the lease might be a much more reasonable denominator for the calculation.  This would dramatically alter the formula though, and disrupt the ability to compare this “adjusted” ROC to other accounting numbers.  This could be corrected by changing other accounting numbers as well to better parallel ROC, but I haven’t yet determined how to do that.