Question

A new rail car costs $100,000 and is expected to last for twenty years, assuming that $20,000 is spent on a major overhaul at the end of year 10. Routine servicing and maintenance are expected to cost $2,000 per year. The car is expected to be used in revenue service for 300 days per year. What is the equivalent cost per-day-in-use over the twenty-year life of the car, assuming a discount rate of 6%, 8%, 10%

Answer 1

Solution:-

New rail car costs=$1,00,000

After 6% discount price=$1,00,000*(1-6/100)
=$1,00,000*0.94
=$94,000(Per 20 Years Expense)
After 8% discount price=$1,00,000*(1-8/100)
=$1,00,000*0.92
=$92,000(Per 20 Years Expense)
After 10% discount price=$1,00,000*(1-10/100)
=$1,00,000*0.9
=$90,000(Per 20 Years Expense)

Major overhaul at the end of 10 years=$20,000 per 20 Years(Only one event per 20 Years)

Yearly Maintanance =$2000/ Year
=20*$2,000
=$40,000(Per 20 Years)

Total Expense over the period of 20 Years(Discounted rate 6%)=94000+20000+40000=$1,54,000
Total Expense over the period of 20 Years(Discounted rate 8%)=92000+20000+40000=$1,52,000
Total Expense over the period of 20 Years(Discounted rate 10%)=90000+20000+40000=$1,50,000

Per Year operating days in number=300 Days
Total Working /Operating days for 20 years=300*200=6000 Days(Per 20 Years)
Hence,
Cost per day (Discount rate 6%)=1,54,000/6000
=$25.7 Per Day
Cost per day (Discount rate 8%)=1,52,000/6000
=$25.3 Per Day
Cost per day (Discount rate 10%)=1,50,000/6000
=$25 Per Day