Question

As a chief engineer, you need to come up with the cash flow estimate for a newly proposed production line. Initially, the system is designed to have a maximum capacity (Cmax)of six million parts to produce per year, but the demand is expected to grow at an annual compound rate of 10%. Whenever the annual demand reaches 80% of the maximum designed capacity, the maximum designed capacity must be doubled in the subsequent year. The cost of meeting these future demands, as well as other projected financial data, are as follows:

Cost of building the production system as a function of maximum designed capacity:
1.5 M + 0.5(Cmax)0.7.
Initial demand = 3 million parts per year.
Demand growth rate = 10% per year.
Project life = 15 years.
Revenues per year = demand during year n × (5)1.05.
Expenses per year = $120,000 + demand during year n × (2)1.08.
Estimate the project cash flows over the project life.

Answer 1

The task is to forecast cash flows for a production line over 15 years, accounting for demand growth, capacity increases, and associated costs and revenues. Economies of scale are relevant, but the six-tenths rule is not directly applied in the cash flow estimation.

Step-by-step explanation:

The question involves the estimation of project cash flows for a new production line. The chief engineer is tasked to project the financial outcomes over a 15-year period, considering factors such as the initial demand, the rate of demand growth, when to double capacity, and the costs and revenues associated with various levels of production. The unique aspect of the system design is the requirement to double the maximum capacity once the annual demand reaches 80% of the current maximum capacity. Each capacity expansion follows a formula for cost as a function of increased capacity. Plus, revenue and expense calculations tie into the quantity of production, adjusting annually for inflation.

To calculate the cash flow, we need to forecast the annual demand and identify the years when capacity doubling will occur, tallying the cost of the capacity increase based on the given formula. Then, for each year, we calculate the revenue using the formula provided and the expenses. Finally, the yearly cash flow is the difference between the revenue and the total costs.

Understanding economies of scale is critical in this context. It is highlighted that doubling costs in chemical production only increases total costs by a smaller percentage (the six-tenth rule), which is beneficial for a discussion on economies of scale, although it is not directly used in the cash flow calculation for the production line in question.