<p>Reliable predictions of the cost of electricity from fusion power plants are fundamental to making sound investment decisions and efficiently allocating resources. Yet, without any detailed designs for fusion power plants, let alone any operational experience, how can we be sure that the projected costs of electricity that inform these decisions are achievable? Rather than trying to project the levelized cost of electricity (LCOE), here we recast the problem and instead work backwards from an assumed LCOE to calculate the implied cost of fusion hardware. In so doing it is possible to invalidate some claimed LCOE projections. Furthermore, this approach helps to elucidate a fundamental shortcoming of fusion power plant schemes that rely on a thermodynamic cycle for power generation: their low <i>net</i> thermal efficiency. The low net thermal efficiency, caused by the power plant itself being a major consumer of electricity, results in a relatively high cost of electricity. The low net thermal efficiency also implies that, on a per megawatt hour basis, cooling water demand from fusion thermal power plants will be significantly higher than for conventional thermal power plants. For fusion power to be widely adopted it will need to be economical. The economic implications of design decisions need to be widely understood early, lest ultimately uneconomical paths are followed. The easy-to-use methodology described herein can help researchers, even those unfamiliar with financial jargon or concepts, to understand how their design decisions may affect the financial viability of fusion power plant concepts.</p>