Question

Yearly labor costs of a highway maintenance group are currently $420,000/year. If labor rates escalate at a 12% rate and general inflation increases at 9%, determine for each of the next 6 years the labor cost in then-current and constant worth dollars. (3.3) of the next be ars 129 rate and Question: In a new, highly automated factory, labor costs are expected to decrease at an annual compound rate of 5%; material costs are expected to increase at an annual compound rate of 6%; and energy costs are expected to increase at annual compound rate of 3%. The labor, material and energy costs the first year are $3million, $2 million, and $1,500,000. What will be the value of each cost during the fifth year?

Answer 1

In the highway maintenance scenario, after 6 years, the labor cost would be approximately $727,823 in then-current dollars and $600,000 in constant dollars. For the automated factory, the labor cost in the fifth year would decrease to $2,297,274, material costs would increase to $2,551,707, and energy costs would rise to $1,627,420.

Highway Maintenance Scenario:

The yearly labor costs are subject to a 12% escalation rate, and general inflation is at 9%. After 6 years, the labor cost in then-current dollars can be calculated using the formula:

Future Value=Present Value×(1+escalation rate)ⁿ

here, n is number of years

Future Labor Cost=$420,000×(1+0.12)⁶ ≈$727,823

To find the labor cost in constant dollars, we adjust for inflation:

Constant Labor Cost= Future Labor Cost / (1+inflation rate)ⁿ

where, n is number of years

Constant Labor Cost = $727,823 / (1+0.09)⁶≈$600,000

Automated Factory Scenario:

Labor costs decrease at a 5% annual compound rate, material costs increase at a 6% rate, and energy costs increase at a 3% rate. The costs during the fifth year are calculated similarly to the highway maintenance scenario. After 5 years:

Fifth Year Labor Cost = $3,000,000 × (1 − 0.05)⁵ ≈ $2,297,274

Fifth Year Material Cost=$2,000,000×(1+0.06)⁵ ≈$2,551,707

Fifth Year Energy Cost=$1,500,000×(1+0.03)⁵ ≈$1,627,420

In summary, the labor cost in the fifth year for the automated factory would decrease, while material and energy costs would increase due to their respective compound rates.