Chapter 12: Investment Decisions - Life Cycle Costing
Investment Decisions - Life Cycle Costing: Sample Problems
Complete solutions to three different versions of the problem used throughout this module are presented below. The versions differ only with respect to the identity of the investor. In the first version the investor is an individual homeowner. In the second the investor is a non-profit agency and in the third, a small corporation.
All solutions were prepared using the Lotus spreadsheet program. The spreadsheets are shown with the columns identified by letter and the rows by number. The formulas used to calculate the cash flows, interest factors, and investment criteria are included in the spreadsheets. The variables in these formulas are identified by their "cell" ,that is, column and row, locations.
The spreadsheet solutions are also presented in the Lotus worksheet file CBLCC.WK1 accompanying this module. Readers may copy this file on to their own disks and use it to conduct their own cost/benefit analyses. To do so, they should make a second copy of the file, changing the name and then enter the initial cost, future savings, future operating costs, and cost of capital data in the appropriate locations to insure that the figures for initial cost, future net cash flows, and cost of capital remain in their present locations (assuming that n = or < 20). The figures given in the spreadsheet for NPV, IRR, MIRR, etc. will automatically change to their new values.
VERSION 1: INDIVIDUAL HOMEOWNER
A homeowner is contemplating replacing an existing electric resistance baseboard heating system with an oil fired forced hot air system. At current electricity rates the all electric system costs $2000 to operate annually. Given current oil prices the oil fired system's annual fuel costs would be $750. In addition, maintenance of the oil furnace would amount to $40 annually. Electricity rates and oil prices are projected to increase at an annual compound rate of 0.2 and 0.5 percent above the expected 4.0 percent rate of inflation. Maintenance costs will increase at the rate of inflation. The initial cost of installing the oil system would be $6000, comprised of $4000 for the ductwork and $300 for the oil tank and components and $1700 for the furnace. The furnace is expected to last 20 years. The current 20 year T-bond rate is 5.75 percent. The variability of returns on the oil system investment are judged to be about equal to the variability of the returns on the stock market, but the correlation between these returns is considered to be only 0.5. The homeowner's marginal federal and state income tax rate is 33 percent.
VERSION 2: NON-PROFIT AGENCY
All facts are the same as in Version 1 above except that the investor is a non-profit agency or institution. Due to its tax status, the agency will have no tax savings on interest paid or tax liability on interest earned. Thus, the required rate of return, k, is before tax.
VERSION 3: TAXABLE BUSINESS
All facts are the same as in Version 1 except that the investor is a small corporation. Its marginal federal plus state income tax rate is assumed to be 40 percent. The depreciable basis of the oil heating system is $6000 and the MACRS depreciation percentages for 10 year life property will be used to calculate the annual depreciation charges. The electric baseboards are fully depreciated for tax purposes and have zero current market and future salvage values. The firm is financed fifty percent by equity and fifty percent by debt with a before tax annual interest cost of 8.0 percent.
SOLUTION - VERSION 1: INDIVIDUAL HOMEOWNER
SOLUTION - VERSION 2: NON-PROFIT AGENCY
SOLUTION - VERSION 3: CORPORATION
COST BENEFIT ANALYSIS - BIBLIOGRAPHY
Eckstein, O. 1958. Water Resource Development: The Economics of Project Evaluation. Cambridge, MA: Harvard University Press.
Harberger, A.C. 1972. Project evaluation. In A.C. Harberger, Collected Papers, London: Macmillan.
Layard, R. (ed.) 1976. Cost-Benefit Analysis, Selected Readings. Harmondsworth:Penguin.
Little, I.M.D. and Mirrlees, J.A. 1974. Project Appraisal and Planning for Developing Countries. London: Heinemann Educational Books.
Kornai, J. 1979. Appraisal of project appraisal. In Economics and Human Welfare, ed. Michael J. Boskin, New York: Academic Press.
Prest, A.R. and Turvey, R. 1965. Cost-benefit analysis: a survey. Economic Journal 75, December, 683-735.
Sen, A.K. 1972. Control areas and accounting prices: an approach to economic evaluation. Economic Journal 82, Supplement, March, 486-501.
Willig, R.D. 1976. Consumer's surplus without apology. American Economic Review 66(4), September, 589-97.
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