Fundamentals of Transportation/Evaluation/Solution

Example

Solution:

Convert everything to Present Value and see just how great a deal this is.

For the present value of the $5,000,000 benefit (gas reduction):

$P=\frac{F}{{\left(1+i\right)}^n}=\frac{\mathrm{\$}5,000,000}{{\left(1+0.03\right)}^{10}}=\mathrm{\$}3,720,469.57$

The benefit in present-day value is $3,720,469.57.

For the money (cost) being sent to the contractor, a payment of $470,000 per year, the present value would be:

$P=A\left[\frac{{\left(1+i\right)}^n-1}{i{\left(1+i\right)}^n}\right]=\mathrm{\$}470,000\left[\frac{{\left(1+0.03\right)}^{10}-1}{0.03{\left(1+0.03\right)}^{10}}\right]=\mathrm{\$}4,009,195.33$

The cost in present-day value is $4,009,195.33. Therefore, this detail, while shiny in appearance at first, is NOT a wise decision, since costs exceed benefits.

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