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You can repair your furnace for $500 and it will last 5 more years, but your heating bills will cost you about $1500 per year. Alternatively, a new furnace can be installed for $3000 that will reduce your annual heating bill to $1200. Suppose you sell the house in 5 years and receive an additional $1000 in the sales price of your home (salvage value) because of having a fairly new furnace. Should you replace it? Use a 5-year analysis period and a MARR of 5%

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Answer:

By present value old furnace should not be replaced, since  the new furnace costs more.

Explanation:

Solution

For the old furnace

Present value = - 500 - 1500 = (1 +i)^n-1/i (1+i)n

= - 500-1500 * 1.05^⁵/0.05 * 1.05^⁵

= -$6994.215

Now,

For the new furnace

The present value = - 3000 - 1200 *  1.05^⁵ - 1/0.05 * 1.05^⁵ + 1000/ (1.05)⁵

= -$7411.845

Therefore, As the new furnace costs more by present value old furnace should not be replaced

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