Safety analysis under uncertainties for investment alternatives over multiple periods using the total-cost unit-cost domain

This paper proposes a method for evaluating the profitability and safety of investment alternatives under uncertainties. The paper assumes that each alternative is composed of initial investment, annual fixed cost, machine life, and interest rate. For the product produced as a result of investment, assumptions are made on its unit sales price, sales volume, unit variable cost, and product life. As a result, each alternative is composed of such factors as sales price, annual sales and production volume, unit variable cost, and annual fixed cost. The paper examines the case in which the values of the above-mentioned four factors fluctuate from period to period, as can be frequently observed in reality. The paper first defines the profit equation as a function of the four factors. It then proposes a total-cost unit-cost domain, in which the horizontal axis represents total income and expenditures, while the vertical axis refers to unit price and cost, for each j-th period over the planning horizon. Both of the domain's axes are converted to the ratio as compared to net income for the first year, which is referred to as the normalized total-cost unit-cost domain. The paper then discusses a method to consolidate multiple normalized domains into a single total-cost unit-cost domain. For the proposed single domain, fluctuation from the expected value for each of the four factors can be visually displayed and analyzed. A systematic procedure for identifying a safer area against changes in each factor is presented. The validity of the proposed procedure is confirmed using a numerical example.