A construction company is bidding on a project to install a large flood drainage

Question

A construction company is bidding on a project to install a large flood drainage culvert from Dandridge to a distant lake. If they bid $1,900,000 for the job, what is thee benefit-cost ratio in view of the following data? Is this a wise investment? The MARR is 6% per year, and the project’s life is 30 years. (Hint: First find the EUAC.)

               Initial construction bid                   $1,900,000

               Right of way maintenance            $25,000 per year

               Major upkeep every six years,

starting at the present time      $45,000

               Annual benefit to the taxpayers   $140,000

Explanation / Answer

Life of Project is 30 years

So n = 30

Let us first find the Equivalent uniform Annual Cost - EUAC


EUAC = (A/P,i,n)

A or P = Annualized Payments or cost
i = Interest rate
n = life or service years

Right of way maintenance = $25000 per year so we have to discount it using 6% MARR

($25000,6%,30) = $25000*14.59 ( Working Note 1 given at the end of solution) = $364750

Now for markup cost

$45000*1

ADD : $45000*.747258 ( W N 1: Discounting factor year 6 and if we start fro base year which we have taken in W N 1 then Take discounting factor for year 5, which we have taken)
ADD : $45000*.526788
ADD : $45000*.371364
ADD: $45000*0261797
ADD: $45000*.184557

Equals to $4095000

Now for tax benefit Annual

$140000*13.59072 = $1902701

Note : tax benefit will from next year not from same year so base year NPV which is 1 have been removed

So EUAC = $364750 + $4095000 - $1902701 ( tax saving ) = $2557049

So benefit cost ratio will be

BENEFIT = $ 2557049- $1900000 = NEGATIVE $657049

W N 1

year discount factor 0 1 1 0.943396 2 0.889996 3 0.839619 4 0.792094 5 0.747258 6 0.704961 7 0.665057 8 0.627412 9 0.591898 10 0.558395 11 0.526788 12 0.496969 13 0.468839 14 0.442301 15 0.417265 16 0.393646 17 0.371364 18 0.350344 19 0.330513 20 0.311805 21 0.294155 22 0.277505 23 0.261797 24 0.246979 25 0.232999 26 0.21981 27 0.207368 28 0.19563 29 0.184557 Total 14.59072

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