Profitability index

A similar form of indicator is the Profitability Index (PI), where the denominator is the maximum exposure of the project, and is applicable where the company is sensitive to the maximum exposure e.g. 

Equation (9-54) may be solved for i either graphically or by an iterative trial-and-error procedure. The value of i given by Eq. (9-54) is known as the discounted-cash-flow rate of return (DCFRR). It is also known as the profitability index, true rate of return, investor s rate of return, and interest rate of return. 

Working capital can range from about 10 percent to almost 100 percent of the invested capital, depending on the industry, and is an important fac tor in the profitability index of a business. For this reason, it is best to compare the performance of an individual company with that of others that are as similar as possible. 

Fig. 76 shows the total profit index as bar column related to the left vertical axis. The profit index indicates the planned profit per period over the... 

Secondly, the profit volatility is mainly driven by sales and procurement value volatility and the respective ratio of sales turnover to procurement costs. The higher the ratio of sales turnover to procurement costs, the better the respective profit index. 

Fig. 85 shows the different exchange rate index experiments on the horizontal axis with the basis experiment indexed with 100. The total profit index is represented by the column bar related to the left vertical axis. The volume indices for sales, inventory, production and procurement as well as the value-added index are represented by the lines with markers related to the right vertical axis. This figure structure and the sequence of indices oriented at the value chain structure will be used also in the following experiments. 

I i Profit index —O— Inventory index HD— Procurement index -O— Sales index —Utilization index---Value-added index... 

A-Best profit index Sales quantity index... 

Average profit index -0-Worst profit index... 

Discounted cashflow rate of return (DCFRR). This method is called the investors return on investment, internal rate of return, profitability index, interest rate of return, or discounted cashflow. A trial-and-error solution is necessary to calculate the average rate of interest earned on the company s outstanding investment in the project. It can also be considered the maximum interest rate at which funds could be borrowed for investment in the project, with the project breaking even at the end of its expected life. 

An article by J. Linsley, Return on Investment Discounted and Undiscounted, Chern. Eng., 86(11) 201 (May 21, 1979), suggests that return on investment can be defined as net, after-tax profit plus depreciation divided by capital investment. This definition of return on investment where depreciation cash flow is included as part of the return is not used in this book, instead, this method of handling cash flow is included in the profitability methods reported for discounted-cash-flow Profitability Index and Net Present Worth. 

Example 3 Determination of profitability index with continuous interest compounding and prestartup costs. Determine the discounted-cash-flow rate of return (i.e., the profitability index) for the overall plant project described in the following, and present a plot of cash position versus time to illustrate the solution. 

Solution. The procedure for this problem is similar to that illustrated in Table 1 in that a trial-and-error method is used with various interest rates until a rate is found which decreases the net cash position to zero at the end of the useful life. Let r represent the profitability index or discounted-cash-flow rate of return with continuous cash flow and continuous interest compounding. 

Determination of cash position at zero time (i.e., at time of plant startup) in terms of unknown profitability index r. 

Determination of cash position at end of estimated useful life (i.e., ten years from zero time) in terms of profitability index r. At the end of the useful life with the correct value of r, the total cash position, taking into account the working-capital investment, the salvage value, and the land value, must be zero. 

Determination of profitability index r. Equating Eq. (B) toEq. (C) gives the following result with r as the only unknown, and a trial-and-error solution will give the profitability index r. 

Thus, the profitability index or discounted-cash-flow rate of return for this example is 26%. 

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