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Unformatted text preview: CE 395
Engineering Economics
Spring 2005
W. Hitchcock Basic Financial Analysis #2 Bonds Present Worth Analysis or Net Present Value Methodology Determine the complete cash flow Positive (receipts or benefits) Negative (investment, operating costs, other expenses) Put in table or graphic form Establish the MARR for analysis Determine the present worth or net present value of
the cash flow Present worth of benefits = PWB Present worth of costs = PWC Present Worth = Net Present Worth (NPW)= PWB PWC If the Present Worth is positive the investment is
considered profitable (attractive) Net Present Value
Example
The cash outlays and projected benefits for a proposed project that has a five year life are shown in the table below:
Year 0 1 2 3 4 5 Investment $1000 $2000 0 0 0 0 Net Income 0 0 $2,500 $3,000 $4,000 $4,000 What is the net present value of the project if the MARR for the company is 12% ? Assume all costs and benefits occur at the end of the interest period (year) Bonds
Example Types of Bonds Treasure Securities Agency Bonds Municipal Bonds Corporate Bonds Zero Coupon Bonds Bond Fundamentals A bond is a loan typically longer than 10 years Generally (but not always) interest is paid annually,
semiannually or quarterly The coupon rate is the annual interest paid on the bond by the issuer (if paid semiannually divide by 2 for semiannual payment amount) The maturity date is the date the loan ends and the borrower repays the face value of the bond. The face value or par value is the amount paid at maturity, but is not necessarily the amount paid for a bond at the time of purchase. Reading a Bond Quote
UAB Corp: 8 Jun30/15 Close 102.25 Bond issuer is UAB Corp 8 % is the annual interest paid on the face value of
the bond (typically $1,000 increments) The total annual interest paid would be .0825 X 1,000 = $82.50 The maturity date is June 30, 2015 Closing price is 102.25% of the par value Bond Value The future cash flow from a bond includes interest
payments and principal paid at the maturity date. At any point in time the value or price of a bond is the present value of the future cash flow produced by the bond. The price a willing buying would pay for a bond depends on the desired rate of return (MARR) as viewed by the buyer. Another way to look at a bond is the bond yield. If the price of the bond is fixed by the seller and the future cash flow is known the return on the bond is fixed. The bond yield is the interest rate such that:
Fixed Price of Bond = Present Value of Future Cash Flow Bond Examples The bond coupon rate is 8% with interest paid semi annually. The bond par value is $1,000. The bond maturity date is 5 years from now. If your MARR is 10% annual interest rate compounded semi annually, what would you pay for the bond today? If your MARR is 6% annual interest rate compounded semi annually, what would you pay for the bond today? What conclusion can you draw about the price of bonds and the prevailing MARR? Future Worth Analysis Instead of converting cash flows to equivalent present
values for analysis, the same conclusions can be drawn if the cash flows are converted to future values. Future Worth Analysis: Future worth of benefits = FWB Future worth of costs = FWC Future Worth = Net Future Worth (NFW)= FWB FWC If the Present Worth is positive the investment is
considered profitable (attractive) Financial Concepts
Equivalent Uniform Annual Benefit/Cost The project benefits can be converted to an
equivalent uniform annual benefit (EUAB) for the life of the project typically using MARR for "i". Similarly convert project costs to an equivalent uniform annual cost (EUAC). If the equivalent net uniform annual cash flow is positive, the project is acceptable. Therefore, if EUAB EUAC > 0, the project is acceptable. Example
Given: UAB Company pays $200/month for wastepaper to be hauled away. The material could be recycled if the company purchased a $6,000 compactor and spend $3,000/yr operating costs and $200/yr for strapping material. The compactor would produce 500 bales/yr and the estimated useful life of the compactor is 30 years with no salvage value. A wastepaper company will pick up the bales and pay $2.30/bale. Question: You were asked to determine if the compactor would be economic for the business. You selected 8% as the MARR.. Would the compactor selected 8% as the MARR.. Would the compactor be economic? Annual Cash Flow Analysis
Criteria Application
Case Fixed Input Fixed Output Situation Input Fixed Fixed use requirement or benefits Neither the input or other costs or the benefits are fixed Choice Criteria Maximize EUAB Minimize EUAC Neither Fixed Maximize EUAB  EUAC Internal Rate of Return Method IRR Method Probably the most widely used method. To use the method: Both benefits and costs must be present in the projected cash flow. The simple sum of the benefits must exceed the simple sump of the costs The IRR is the interest rate such that the benefits are
equivalent to the costs. IRR can be determined using PW, FW or Equivalent Annual Worth IRR Method Cash Flow Sign Change Caution An annual net cash flow table is a projected net cash flow for
each year of the project (i.e. only one net number + or for each year) When using the IRR method for evaluation ALWAYS develop an annual net cash flow table. If the sign on the net cash flow table changes more than one time, it is possible to have multiple solutions to IRR. [Descartes'Rule: number of positive roots = number of sign changes 2k (where k is a positive integer or 0)] In cases where multiple solutions are possible, it might be best to used another methodology for evaluation, including the External Rate of Return Method. External Rate of Return Method IRR Analysis may not be valid because it
inherently assumes that net annual benefits received by the company can be reinvested at the IRR. The multiple root possibility is also a constraint The External Rate of Return Method is an alternative We select a known external rate of return to use in the analysis to offset the distortions of IRR External Rate Of Return Analysis 3 Step Process To perform ERR a net cash flow table must be developed. Analysis is in three steps:
1. Discount all net cash outflows to the present using the known external rate of return. 2. Compound all net cash inflows to the future (end of the last period of the analysis) 3. Determine the rate of return such that the PW of the outflows equals the FW of the inflows. ...
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 Summer '05
 Hitchcock

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