Engineering Economics & ManagementLecture 3

FINANCIAL & MONETARY ANALYSIS

Time Value of Money Conceptually, time value of money means that the value of a sum of money received today is more than its value received after some time. Conversely, the sum of money received in future is less valuable than it is today.In other words, the present worth of a rupee received after some time will be less than a rupee received today. Since a rupee received today has more value, individuals, as rational human beings, would naturally prefer current receipt to future receipts.

Techniques In order to have logical and meaningful comparisons between cash flows that result in different time periods it is necessary to convert the sums of money to a common point in time. There are two techniques for doing this: CompoundingF = P (1 + I)n DiscountingP =

Techniques (Contd) Compounding TechniqueInterest is compounded when the amount earned on an initial deposit (the initial principal) becomes part of the principal at the end of first compounding period. The term principal refers to the amount of money on which interest is received.

Evaluation Techniques Net Present Value MethodPay Back MethodInternal Rate of Return MethodBenefit Cost Ratio

Net Present Value (NPV) The NPV method requires that all cash flows be discounted to their present value, using the firms required rate of return.It can be expressed as

Net Present Value (Contd) ExampleThe advantages of the net present value method are that it takes into account the time value of money, and regardless of the pattern of cash flows, a Single net present value is easily calculated.Cash flows from two rural income generation projects in Rs.:

Year 0 1 2 3Project A:-2,500 1,0001,5001,000Project B:-2,500 -1,0002,5002,000

Net Present Value (Contd) Project A involves an initial investment of Rs. 2,500 and expected cash flows for 3 years. Project B requires the same initial investment, an additional cash outlay of Rs. 1,000 in the first year, and positive cash flows in the second and third year Suppose the required rate of return is 10%. Then the NPVs of the projects are:

C P/F, 10, 1 P/F, 10, 2 P/F, 10, 3NPVA= -2,500+1,000(0.9091)+1,500(0.8264)+1,000(0.7513)= Rs. 400

NPVB= -2,500-1,000(0.9091)+2,500(0.8264)+2,000(0.7513)= Rs. 160

Net Present Value (Contd) Since the NPV of A is the larger of the two, project A is the better investment.When the cost of a project is spread over a number of years, the net present value of the investment is obtained as follows:

Evaluation of NPV MeritsRecognizes the time value of moneyConsiders the total benefits arising out of the proposal over its life-timeA changing discount rate can be built into the NPV calculation by altering the denominatorParticularly useful for the selection of mutually exclusive projectsThis method of the asset selection is instrumental in achieving the objective of financial management, which is, the maximization of the shareholders wealth

Evaluation of NPV(Contd) De-MeritsDifficult to calculate as well as understandCalculation of the required rate of return to discount the cash flows is a complex procedureThis method will favour the project which has higher present value (or NPV). But it is likely that this project may also involve a larger initial outlay.May also not give satisfactory results in the case of two projects having different effective lives

Payback Period Number of years required to recover the initial outlay of an investment.The payback period is found in two ways: conventionally, and by discounting the cash flows.Conventional paybackDiscounted payback

Payback PeriodProject cash flows ($)

Year A B C0-2,400-2,400-2,4001 600 800 5002 600 800 7003 600 800 9004 600 800 1,1005 600 800 1,300 Conventional payback (years):Discounted payback (years)Net present value(i=10%):

Payback PeriodProject cash flows ($)

Year A B C0-2,400-2,400-2,4001 600 800 5002 600 800 7003 600 800 9004 600 800 1,1005 600 800 1,300 Conventional payback (years): 4.0 3.0 3.3Discounted payback (years) 5.4 3.8 4.1Net present value(i=10%): -125 633 867

Internal Rate of Return The method most widely used in evaluating capital projects is the internal rate of return method, commonly known as IRR.The internal rate of return for an investment is the rate of return (i.e. interest rate) that makes the present value of the cash flows equal to the cost of the investment. Mathematically, it is calculated from:

Internal Rate of Return(Contd) where C0 is the initial capital outlay, At is the cash flow in period t, and r is the internal rate of return, IRR, of the investment.The initial investment is $100,000, and the expected cash flow is $30,000 annually for 5 years then

or

Internal Rate of Return(Contd) In other words, what interest rate makes the right side of the equation equal to the left side ? The unknown we must solve for is the P/A factor.

From the interest rate table interest rate is between 15% and 16%. 15.175% or about 15.2%. Note that if the cash flows were discounted at 15.2%, the NPV of this investment would be zero.

Internal Rate of Return Method Consider the time value of moneyIn the case of the present value method, the discount rate is the required rate of return and being a pre-determined rate, usually the cost of capital, its determinants are external to the proposal under considerationThe IRR on the other hand, is based on facts which are internal to the proposal of the projectIRR depends entirely on the initial outlay and the cash proceeds of the project which is being evaluated for acceptance or rejection. It is, therefore, appropriately referred to as internal rate of return.

Evaluation of IRR MeritsIt considers the time value of moneyIt takes into account the total cash inflows and outflowsThe IRR is easier to understandIt does not use the concept of the required rate of return (or the cost of capital)It is consistent with the over-all objective of maximizing shareholders, wealthDe-MeritsIt involves tedious calculationsIt produces multiple rates which can be confusing

Benefit - Cost RatioBenefits - Disbenefits - CostInvestment

BenefitsCosts

Benefit-cost analysis of three mutually exclusive proposals

A group 0f 600 summer-home owners on the Atlantic coast of the United States is concerned with the erosion of the shoreline and periodic flooding of their properties from the ocean. They engaged a consultant engineer to conduct a feasibility study to solve their problem. After establishing the objectives of the home-owners and the physical and zoning constraints of the area, the engineer prepared the following three proposals:

a) Reconstruct the shoreline and provide all necessary protection measures to prevent erosion for 20 years at a cost of $350,000. In return the insurance company would reduce its annual premium to each home-owner by an average amount of $100.

b) Combine the work of Proposal (a) with the construction of a beach suitable for swimming and sunbathing and construct a refreshment stand and toilet facilities at a total cost of $500,000. The expected annual income from the refreshment stand would be $30,000 and the maintenance cost of the beach $10,000 per year.

c) Combine the work of Proposal (b) with the construction of a beach suitable for swimming and sunbathing and construct a cafeteria, toilet facilities, and a parking lot to accommodate twice as many people as Proposal (b) and charge the non-residents an entrance fee, at a total cost of $950,000. The estimated annual income from the restaurant concession plus the entrance fees would be $80,000. The annual cost of operation and maintenance of the beach would be $35,000.

BCR = B-D-C I

Proposal (a):BCR = $510,816 = 1.46 $350,000

Proposal (b):BCR = $766,224-$85,136 = 1.36 500,000

Proposal (c):BCR = $1,191,904-$297,976 = 0.94 950,000

Benefits and costs of upgrading power substation (amounts in 1975 dollars). Source: U.S. Naval Facilities Engineering Command, Economic Analysis Handbook, 1978, pp. 53-4.

Case 1: Direct savings increaseA naval base has experienced repeated blackouts due to outmoded and over-loaded transformer transmissions. A technical feasibility study recommends that the only alternative is to upgrade the power substation because the local power company is unable to provide the power required by the base. Although this is the only alternative possible, the Public Works Officer recognizes certain benefits potentially occurring from this project and has decided to do a benefit-cost analysis.The estimated cost of upgrading the power substation is $500,000 for an economic life of 25 years. The result will be a reduction in maintenance costs by eliminating two positions costing the navy, in salary and fringe benefits, $10,000 per person/year. Operating costs will decline by $10,000 per year.

In this case, the benefit-cost ratio is:BCR = $30,000 =0.55 $500,000 (0.1102) The ratio indicates that the project amortizes 55% of its investment in savings relative to the current operations over its anticipated economic life.

The information is useful for decision making, even though it is the only alternative available.

Case 2: Efficiency or productivity increase The public works planners at the naval base of the previous case have identified additional efficiency or productivity benefits occurring from the upgrading of the power substation.Since the existing substation serves the industrial area of the base, every time a power blackout occurs most industrial functions of the base come to a standstill. An officer conducted a time and motion study to determine the impact of blackouts on industrial output.The study revealed that the economic impact of industrial downtime due to blackouts averaged 2.5 man-years per year. Given the existing work backlog, by eliminating the recurring blackouts, the upgrading of the substation would provide an additional 2.5 man-years of industrial capacity with no increase in personnel. The value of this benefit is equal to the cost of hiring additional workers to provide 2.5 man-years of work per year at $12,000 per worker or $30,000 per year.

Using the annual equivalent formulation of the benefit-cost ratio,

BCR= $60,000=1.09 $500,000(0.1102).The benefit-cost ratio indicates that the value of the proposed project's benefits is $1.09 per dollar invested.

Table 11.5 Benefits and costs of construction alternatives for naval facility (amounts in 1975 dollars). Source: U.S. Naval Facilities Engineering Command, Economic Analysis Handbook, 1978, pp. 55-4.

Case 3: Quantifiable output measure Due to a proposed regional consolidation, the Naval Air Rework Facility at a Naval Air Station has been assigned the responsibility of providing all the corrosion-control maintenance for Atlantic Fleet P-3 Orions in the Northeast. The public works planners have undertaken a detail feasibility and concept study and have determined that there exist only two reasonable alternative methods of satisfying this operational requirement:

(a) Modify existing non-used hangar space to accommodate the corrosion-control function. (b) Demolish old hangar space and construct new, highly efficient semi- automated corrosion control facility. The appropriate basis of comparison for the two alternatives is the ratio of annual output benefits to annual equivalent costs:

Modify hangar: BCR= 300 jobs =0.94 $2,000K (0.1102) + $100KNew hangar: BCR= 375 jobs =1.01 $2,600K (0.1102) + $85KNotice that even if both ratios were less than unity, the alternative with the larger BCR is acceptable, because the benefit output per equivalent annual, dollar expended is higher for the new facility. In this case the BCR ranks the alternatives in terms of completed maintenance jobs per year per $1,000.

THANK YOU