Plastic trays last 8 years and cost $20 each.Metal trays last 24 years and cost $X.There is no salvage value for either type of tray.Trays need to be purchased today and are assumed to be needed forever.If the interest rate is j₁ = 6%,what value of X will the buyer be indifferent to purchasing plastic or metal trays?

Question

Quizplus · Accepted Answer

The buyer will be indifferent to purchasing plastic or metal trays when the present value of their costs is the same. For plastic trays, the cost is $20 every 8 years. For metal trays, the cost is $X every 24 years. Using the formula for present value of a perpetuity: PV = PMT / i, where PMT is the payment and i is the interest rate per period. However, since these are not perpetuities but rather repeating costs, we adjust the formula to account for the periodic nature of the costs.For plastic trays, the equivalent annual cost (EAC) can be calculated using the formula: EAC = PMT / [(1 - (1 + i)^-n) / i], where PMT is the payment ($20), i is the annual interest rate (6% or 0.06), and n is the number of years (8). This gives us an EAC for plastic trays.For metal trays, we do a similar calculation with PMT being $X, i = 0.06, and n = 24 years.To find the value of X that makes the buyer indifferent, we set the present value of costs for both types of trays equal to each other and solve for X. Given the complexity of the calculation and the specific numbers involved, the correct answer is found through financial calculation or formula manipulation, leading to the correct value of X that equates the present value of costs for both options. The correct answer is D) $40.42, which is the value of X that makes the present value of costs for plastic and metal trays equal, assuming a 6% interest rate and the given lifespans.

Plastic Trays Last 8 Years and Cost $20 Each