Problem asks specifically for present worth of the COSTS - why would they include the residual value? The residual value is not a "cost", and it is not realized until the end of the design life. If an agency were trying to determine the amount of money that they needed to put away to cover all costs associated with a 20 year life (basically what the question is asking)... I would argue that the residual value should not be included in this analysis... if it were, the agency would run out of money prior to the 20 year term expiring.
In similar terms - if you buy a car that has $x cost in maintenance every year for 10 years... the fact that you may sell it for $y or $2y at the end of the 10th year has no bearing on the actual yearly maintenance cost, and certainly wouldn't make the total maintenance cost over the term lower... you still have to cover those COSTS before you realize a residual value. I mean your final overall economic standing would change... but not the cost.
Do you guys disagree?
In similar terms - if you buy a car that has $x cost in maintenance every year for 10 years... the fact that you may sell it for $y or $2y at the end of the 10th year has no bearing on the actual yearly maintenance cost, and certainly wouldn't make the total maintenance cost over the term lower... you still have to cover those COSTS before you realize a residual value. I mean your final overall economic standing would change... but not the cost.
Do you guys disagree?