10. (10 points) Springfield Ironworks (SI) recently had their furnace break down

Question

10. (10 points) Springfield Ironworks (SI) recently had their furnace break down and they need to quickly purchase a new one to minimize the disruption in their production. They can either choose a high quality furnace (H) that costs $130,000 with $5,500 of annual maintenance costs for the 6-year life of the furnace, or a low quality furnace (L) that costs $75,000 with $9,000 in annual maintenance costs for the 3-year life of the furnace. Which furnace should SI choose? What is the annualized cost of their choice? Assume a discount rate of 4.0%, and ignore all taxes.

H, $30,299

L, $99,976

H, $158,832

L, $36,026

Explanation / Answer

H, $30,299

HIgh quality furnace should be choosen and which has $ 30,299 annual cost.

Working:

a. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.04)^-6)/0.04 i 4.0% =      5.2421 n 6 Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.04)^-3)/0.04 i 4.0% =      2.7751 n 3 b. Annual Cost of high quality furnace = (Initial Costs / Present value of annuity of 1)+Annual maintenance cost = (130000/5.2421)+5500 = $       30,299 Annual Cost of Low quality furnace = (Initial Costs / Present value of annuity of 1)+Annual maintenance cost = (75000/2.7751)+9000 = $       36,026

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