Final answer:
The competitive price of a utility meter is $15, calculated based on the annualized cost of the plant investment, the annual operating costs, and the cost of capital.
Step-by-step explanation:
To determine the competitive price of a utility meter, we need to take into account the initial investment, operating costs, and cost of capital. The question states that a utility meter plant costs $50 million to set up and can produce 500,000 meters annually, with production costs of $5 per meter. The plant has an indefinite physical life, and the cost of capital is 10%.
We use these figures to calculate the annualized cost of the plant investment. To find the annualized cost, we divide the initial investment by the lifespan of the plant. However, since the plant has an indefinite life, we instead use the cost of capital to annualize it: $50 million * 10% = $5 million per year. This annual cost is the amount needed to cover the capital investment.
Next, we add the annualized cost of the capital investment to the annual operating costs. With production costs of $5 per meter and a capacity of 500,000 meters, the operating cost is $5 * 500,000 = $2.5 million.
The total annual cost is the sum of the annualized investment and operating costs: $5 million + $2.5 million = $7.5 million per year. To break even, the revenue from selling 500,000 meters should at least match this amount.
Therefore, the break-even price per meter is calculated by dividing the total annual cost by the annual production capacity: $7.5 million / 500,000 meters = $15 per meter. So, the competitive price in a highly competitive market would need to be $15 to cover both the production costs and the capital costs.