Machine X and Y each sell for $1,000 000 and each has a life of 17 years.Machine X produces 5000 units per year,has an annual maintenance expense of $10,000 and a salvage value of $33,750.Machine Y produces U units per year,has an annual maintenance expense of $11,000 and no salvage value.If the interest rate is j₁ = 8%,what does the value of U have to be for the two machines to be equivalent?

Question

Quizplus · Accepted Answer

To find the value of U that makes the two machines equivalent, we calculate the present value (PV) of the costs associated with each machine over its life, including purchase cost, maintenance, and salvage value, and then solve for U. For Machine X:- Purchase cost: $1,000,000 (no need to discount as it's a year 0 expense)- Annual maintenance: $10,000 for 17 years, discounted at 8%- Salvage value: $33,750 at the end of 17 years, discounted at 8%For Machine Y:- Purchase cost: $1,000,000 (same as Machine X)- Annual maintenance: $11,000 for 17 years, discounted at 8%- No salvage valueThe formula for the present value of an annuity (for the maintenance costs) is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment per period, r is the interest rate per period, and n is the number of periods. The formula for the present value of a lump sum (for the salvage value) is PV = F / (1 + r)^n, where F is the future value, r is the interest rate, and n is the number of periods.After calculating the PVs of all costs and equating the total PVs of both machines, we solve for U, the number of units produced by Machine Y that makes its total PV of costs equivalent to Machine X's. Given the complexity of these calculations and the need for precision, the correct answer is found through detailed financial analysis or using financial calculators/software, which yields U = 5084 units per year for Machine Y to be equivalent to Machine X.

Machine X and Y Each Sell for $1,000 000 and Each