Economic Equivalence and Profitability
4.2 PROFITABILITY ANALYSIS
4.2.5 Scheduling a Loan Payment
A loan of $1,000,000 is borrowed with interest at 8% per year or 2% per quarter. The loan will be repaid over a scheduled period of 25 years. During the first 5 years, or 20 periods, only the interest will be paid. During the next If a corporation with a sales volume of $182,800,000 has a healthy net gain in sales of 12% for the year, or $21,936,000, an expenditure of only $150,000 for a nonproductive project would result in a reduction of
At times it might be advantageous to delay payments toward principal to maintain a better cash flow position, and the amount paid in interest for the delay period must be weighed in this decision. In this example, the interest for the 5 years is 49.38% of the interest of the remaining 20 years of the loan. The interest for the first 5 years is also 40% of the loan. If the loan was $50,000,000, the interest for the 5-year delay period would be $20,000,000, or quarterly payments of $1,000,000 totaling $4,000,000 per year.
The $20,000,000 paid over the 5-year period would then be an addition to the $50,000,000 cost of the project and for discounted cash flow calculations, the $20,000,000 would be paid by the profit from the project for the first 5 years. Any cash expended while the project was under construction would be included with the loan.
Example 4.14 Loan Schedule
For the installation of a paper machine and stock preparation area, the following data apply:
20 years, or 80 periods, the loan balance will be reduced uniformly and interest paid on the loan balance.
Here $1,000,000 is repaid uniformly over the last 80 periods at $1,000,000/ 80=$12,500. The payment schedule is:
The first part of the cash flow calculation is a restricted view to accentuate paying only interest on the loan for the first 5 years. The project is judged from a commitment of $20,000,000 in interest (5 years at $4,000,000/yr). Although it is true that the interest will not be due at zero time but will be spread out in the future, the view here is to consider the $20,000,000 as a present commitment of the project. For the first 5 years the calculation is:
The present worth will be zero at about 17.04%. This says in effect that if the total interest payments for the first 5 years, i.e., $20,000,000, were swapped for the first 5 years of the project, the discounted cash flow rate of return would be about 17.04%.
The second part of the cash flow calculation goes from years 6 through 25, and the reference point here is a $55,000,000 investment. All discounting is done with respect to the beginning of year 6. The calculation is:
The present worth will be zero at about 8.60%. This says that if the project is regarded as an investment of $55 million at the beginning of the sixth year, it will have a discounted cash flow rate of return of 8.60% from the period starting at the beginning of the sixth year and ending at the end of the twenty- fifth year.
One of the major advantages in the process of delaying the payments toward the loan principal is to take advantage of the cash flow realized from depreciating the capital assets during the time. There is a possibility, however, that the delay of payments will be a detriment if the debt position of the corporation is good (very few debts outstanding), and a major expansion or major maintenance program is contemplated within a 4- to 6-year period. A possibility exists under these circumstances that the credit rating of the corporation would be affected. The corporation may then be in a better position to repay the debt at a more accelerated rate to ensure a more advantageous position in credit rating and solvency. This may ensure the ability to borrow sufficient funds at a later date to allow expansions or maintenance at a critical time in the future.
When contemplating the life of a corporation, plans must be projected to allow the corporation to continue indefinitely and not be affected by changes in personnel or any other short-term occurrence. Cycles in the change of personnel or business climate (cost of money expenses, etc.) should be projected and planned so that the corporation will have a continual healthy growth.
Example 4.15 Profitability of a Paper Machine
A paper machine has a production rate of 375 tons/day for 350 days/yr with paper selling at a price of $281.50 per ton. Gross income per year is
375×350×$281.50=$36,946,875 per year
After expenses, but before taxes, only 15.16% remains or 0.1516×$36,946,875=$5,601,146 per year
After allowing $2,238,980 for taxes, the net income after taxes is $5,601,146-$2,238,980=$3,362,166 per year
The capital cost for the machine is $34,000,000. A 10% tax credit is available, and the machine will be depreciated at straight line depreciation over 16 years or at
The cash flow is the sum of net profit after taxes plus depreciation and is $3,362,166+$2,125,000=$5,487,166 per year
The return on original investment for the machine is
The payback time will be
All the calculations above have neglected a 10% tax credit which amounts to
$34,000,000×0.10=$3,400,000
When the 10% tax credit is considered, the return on original investment becomes
The payback time when considering the tax credit is
Thus venture worth of the project at 10% rate of return is $+12,036,000. The next problem departs from the usual assumptions of uniform costs and replaces it with realistic values that change each year. All this change means is that the calculation of present worth and rate of return is a bit more complex, but it does not change the approach.
Example 4.16 Energy Conservation
Three years ago a pipe manufacturing company built and installed a gas drying oven at a total cost of $20,000. Operating costs of the oven have been less than satisfactory, and a task force has been appointed to find ways to reduce the excessive fuel costs. A firm manufacturing drying ovens of a new and radically different design has approached the company with a model that sells for $40,000 and promises to reduce costs, particularly energy costs, very dramatically. The task force has been asked to determine whether this new oven can be justified by the potential savings in fuel and maintenance costs. Details of the alternatives are tabulated below:
and for the other years is
Assume that both ovens will last for 10 years and that the book value of the existing oven will be credited to the new oven, if acquired. The treatment of this write-off is identical to depreciation, i.e., since it is not a cash expense, it must be added back to the cash flow after taxes. Depreciation values are as follows:
Tables 4.1 and 4.2 show the respective cash flows for the new and existing
Example 4.17 Revenue Requirements—Electric Utility
An electric utility is planning to add a 350 MW generating plant that will have a coal-fired steam generator design ed to burn high sulfur coal shipped by unit train from a mine that is a wholly-owned subsidiary. The plant is to be designed for peaking service which means it will be at full load every weekday, down to furnaces, and Table 4.3 provides the incremental analysis.
Chapter 4
Table 4.1 New Furnace
Present worth @ 15%=-$45,362; total cash flow=(62,796).
1
0
9
Table 4.2 Existing Furnace
Present worth @ 15%=-$40,448; Total cash flow=(84,935).
20% at night, and offline on weekends. The following data provide the information for the financial calculations:
Table 4.3 Incremental Approach
Present worth @ 15%=-$4,914; DCFRR=10.97%.
Energy generated at 50% capacity factor:
kWh/yr=350 MW×50%×8760 hr/yr×1000kW/MW =1,533,000,000 kWh/yr Fuel consumption: Fuel cost: =606,813 ton/yr×$25/ton =$15,170,313/yr
Example 4.18 Risk Analysis—Capital Cost Estimate*
The basic procedure used in this example was originally introduced by Cooper and Davidson (1976) and is fully explained in a paper presented by Piekarski (1984). Given the generation plant investment in Example 4.17, a construction firm has been awarded the job of erecting the power plant. A definitive estimate of capital cost was made as shown below along with the probable range of variation to the estimate:
* The manual risk analysis approaches described in Example 4.18 and 4.19 give approximate estimates of the probability of achieving project objectives. Excellent software programs are now available which greatly simplify the estimation of overrun probability and of the amount of required contingency to reduce the overrun probability to an acceptable level. This software is preferred to the manual approaches and provide more reliable answers. Chapter 9 discusses computerized risk analysis and contingency determination using Monte Carlo techniques.
Management wishes to determine the contingency that needs to be added in order to insure that there is no more than a 30% probability that the project will overrun the bid.
Solution The cost estimate on the project utilizes the following equations to calculate the contingency:
To calculate the mean of each line item: Mean=(H+2×ML+L)/4
where
H=highest anticipated value ML=most likely value
L=lowest anticipated value
To estimate the standard deviation of each line item: SD=(H-L)/2.65
To calculate the overall mean and standard deviation:
Table 4.4 summarizes the computations of risk parameters.
The results are best explained by charts. The risks incurred in Example 4.17 are profiled in Fig. 4.1. The diagonal line of the chart is a cumulative probability distribution of the range of values calculated in Table 4.4. The crux of the chart is how it serves as a means to respond to the requirement that there be no more than a 30% chance that the project would overrun. A
Table 4.4 Risk Parameters
dashed line is superimposed at the 30% probability point which intersects the cumulative probability curve at 5% contingency (about $15M).
Example 4.19 Risk Analysis—New Product Evaluation
An electronic manufacturer is considering the introduction of a new product with the following financial characteristics:
As can be seen from the financial results, the project has a healthy net present value residual after 20% cost of money is deducted. Furthermore the rate of return of 33% is significantly above the hurdle rate of 20%.
Risk Analysis Using the Parameter Method If we calculate the net present value of the revenues, variable costs, and fixed investment after taxes at 20% hurdle rate, the following values are obtained:
The cash flow table for the project is:
All this does is set the stage for the risk calculation using the parameter method. It can be seen that the net present value at this cash flow position corresponds to the previous calculation (except for minor differences due to rounding error). The following calculations utilize the formulas from Example 4.17.
The risk profile is plotted in Fig. 4.2. This chart plots the probability of producing a positive or negative cash flow. It is evident that the project has a little more than 30% chance that it will yield negative results. This situation is quite normal for most new product developments and does not necessarily mean that management should turn down the project; on the average, only one out of three new product attempts is successful.
REFERENCES
Cooper, D.O. and Davidson, L.B. (1976). The parameter method for risk analysis.
Chemical Engineering Progress, Nov.:73–78.
Piekarski, J.A. (1984). Simplified risk analysis in project economics. 1984 AACE
Transactions, Morgantown, WV: AACE International, Paper D.5. Figure 4.2 Risk profile.
RECOMMENDED READING
Blank, L.T. and Tarquin, A.J. (2002). Engineering Economy. 5th ed. New York: McGraw-Hill Inc.
Canada, J.R., Sullivan, W.G. and White, J.A. (1996). Capital Investment Analysis for
Engineering and Management. 2nd ed. Englewood Cliffs, NJ: Prentice-Hall Inc.
Collier, C.A. and Glagola, C.R. (1998). Engineering Economic and Cost Analysis. 3rd ed. Berkeley, CA: Peachpit Press.
Sullivan, W.G., Wicks, E.M. and Luxhoj, J. (2002). Engineering Economy. 12th ed. Englewood Ciffs, NJ: Prentice-Hall Inc.
Thorne, H.C. and Piekarski, J.A. (1995). Techniques for Capital Expenditure Analysis. New York: Marcel Dekker Inc.