Three different plans were presented to the GAO by a tech facility manager for o

Question

Three different plans were presented to the GAO by a tech facility manager for operating an identity-theft scanning facility.Plan A involves renewable 1 year contracts with payments of $1million at the beginning of each year.Plan B is a 2 year contract that requires four payments of $600,000 each with the first one made now and the other at 6-month intervals. Plan C is a 3 year contract that entails a payment of $1.5million and a second payment of $500,000 2 years from now.Assuming that the GAO could renew any of the plans under the same payment conditions . Which plan is the best on the basis of a present worth analysis at an interest rateof 6% per year compounded semiannually?

Explanation / Answer

PLAN A

FiRST OF ALL we need to calculate the effecttive annual rate of interest rate, since interest rate is compounded semiannually and cash flow is yearly,

EAR = (1+.06/2)^2-1 = 6.09%

Now, cash flow diagram = 1+1/(1.0609^1)+1/(1.0609^2)+1/(1.0609^3)+1/(1.0609^4)...upto infinity

= (1+1/.0609) = $17.4203 million

PLAN B

here, ssemi annual interest rate = 6/2 = 3%, as payment is also made semi annual

Now, cash flow diagram = .6+(.6/1.03^1)+(.6/1.03^2)+(.6/1.03^3)+(.6/1.03^4).....uotp infinity

= .6+.6/.03 = $20.6million

PLAN C

THIS PART IS SOME WHAT TRICKY,

FIRST OF all , since part of payment is made after every 3 years and part of payment is made after every 2 years

we need to calculate Effective interest rate for 3 years and for 2 years of semi annual ccompounding

Effective Rate for 3 year payment = (1+.06/2)^6-1 = 19.40523%

Effective Rate for 2 year payment = (1+.06/2)^4-1 = 12.5509%

CASH FLOW = 1.5+(.5/1.125509)+(1.5/1.1940523)+(.5/1.125509^2)+(1.5/1.1940523^2).......upto infinnity

CASH FLOW = 1.5+(1.5/.1940523)+(.5/.125509) = $31.21 MILLION

minimum cost is of Plan C, so Plan C should be chosen,

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