Assume a passenger bus was purchased two years ago by the Cold Fusion Transport Ltd$.$ for $$200,000.$ Today, it is announced that a similar bus can be purchased for $$175,000.$ The old bus uses $$80,000$ of fuel each year. If the new bus is purchased, the amount of fuel used will not change. However, fuel prices are expected to rise by $10\%$ at the end of next year. The newest bus will save the company $$10,000$ per year in other operational costs compared to the bus purchased two years ago. Each bus has an estimated useful life of five years and will be used $100,000$ kms$.$ per year. They will have no resale value at the end of their useful lives. If the new bus is purchased, the maintenance contract with the seller will be reduced from $$20,000$ per $100,000$ km$.$ of use to $$18,000.$ The old bus can be sold for $$140,000$ in one year$’$s time. In the meantime, it will be used as a temporary replacement vehicle for out$-$of$-$service buses.

Calculate the maximum purchase price that the company would be willing to pay for the new bus if the discount rate is $10\%.$ Assume the corporate income tax rate is $20\%$ but income taxes only apply to maintenance and operational costs. Assume all expenses are paid at each year$-$end. State any additional assumptions you make.