Comparison & Review

As we have seen, Economic analysis of Engineering projects can be done by various methods. They are :

• Payback Period Method
• Worth based Methods (PW, FW, AW)
• ROR Method
•  BC Ratio Method

• Depends on the situation based on :
  • Type of industry.
  • Type of investment.
  • Length of study period.
  • Financial stability of company.
  • Audience for presentation.
• Method may be set by policy.
• All have advantages.
• May give conflicting results between methods.

Payback Period

• Best for uniform cash flow patterns.
• Best for same life options .
• Good for short life options (i % is not a big factor).
• Quick and Easy .
• Simple to understand.
• Avoids time value of money.
• Results may be "incorrect".

Worth Based Methods - ( PW, FW, AW )

• All methods give consistent results. Hence it allows the best method to fit the situation.
• Requires known i %.
• Allows for ease of multiple N option analysis.
• Results sometimes are less meaningful to understand.

• Direct investment options
• Annual expenditures
• Required sums

Rate of Return (ROR)

• Most meaningful results (Finds i %).
• It is the easiest to understand vs real world i %.
• Possibly difficult to calculate.
• May give multiple answers.
• Requires Incremental Analysis between options.
• Allows equal opportunity to invest all possible cash to beat MARR vs. finding the best worth option.(Such as in a case where high cost leads to a  lower worth)

BC Ratio

• Requires Incremental Analysis between options.
• Fairly simple to calculate.
• Easy for public to understand. (BC Ratio >1.0 is good).Hence good for public work projects.
• Good to use when benefits are obscure.

                   ie: Less O&M   = Benefit
                       Less Damage = Benefit
                       Less impact    = Benefit
                       Time Savings = Benefit

Close Results in Analysis

If the analysis gives very close final results, then consider the following :

• Option with lower first cost.
• Shorter life option.
  • Chance to re-evaluate.
  • Less impact due to technology.
  • Less impact of inflation.
• Possible lack of need of project in future.

These concerns, while not officially a part of any engineering economic analysis should be considered in tight decisions.

Bonds

• Bonds are  financial instruments, setting forth conditions under which money is borrowed.
• They are sold by government agencies and corporations to raise $ for projects.
• Bond Terms :
  • Face Value (V)- The amount for which the bond is redeemed at maturity. Sometimes it is the purchase price from the issuer.
  • Bond Rate (b)- The bonds interest rate which determines the regular premiums.
  • Interest per Period (I)- I = Vb/c where c = # of Payments/year 
• Bonds can be bought and sold before maturity.
• If the going interest rate < the bond rate, then the bond can be sold for more than the face value. Interest on government bonds is tax free.
• The Bond rate is greater for lesser solvent issuers, who have a greater risk of not paying back the face value (Junk Bonds).

Example :The current interest rate is 7%. Is it a good investment to buy a 6%, $1000 bond for $900 with semi-annual payments with maturity in 7 years?
      
I = Vb/c = 1000(0.06) / 2 = $30
$900 = $30(P/A, i, 14) + $1000(P/F, i, 14)

For  i = 4% ---> PW = $894
       i = 3% ---> PW = $1000

Thus interpolate to find the semi-annual i*.

i* = 3% + 1%(1000-900) = 3% + 0.94% = 3.94% per Semi-annual period.
                      (1000-894)

Nominal rate n = (3.94%)(2) = 7.88%
Effective Annual Rate = i _EFF = (1 + r/m)^m-1
                                            = (1 +0.0788 / 2)²-1
                                            = 8.04% > 7%

Hence the purchase appears to be a good investment.

• Don't confuse the bond rate (b) with the going, current interest rate(i).
• Don't forget to find or use an i for the correct compounding period (Usually assumed to be the same as the # of bond interest payments/year, but not always.)
• Use I = Vb/c first to help determine the cash flow. Use a cash flow diagram to help visualize the cash flow of the bond.
• Use PW, EAW, FW or ROR to analyze the bond's cash flow.

Added to the Web: May 20, 2002. Last updated: April 26, 2002. Web page design by Dan Solarek.	http://cset.sp.utoledo.edu/engt3600/