Question

A small company heats its building and will spend $8938 in year 1 on natural gas for this purpose. Cost increases of natural gas are expected to be 9​% per year starting year 2. Their maintenance on the gas furnace is going to be $391 in the first year and this expense is expected to increase by 15​% per year starting year 2. If the planning horizon is 13 years, what is the total annual equivalent expense for operating and maintaining the​ furnace? The interest rate is 18​% per year.

​(a) The total present worth of operating and maintaining the furnace is _______ thousands. (2 decimal place)

The total annual equivalent expense for operating and maintaining the furnace is ____________ thousands. (2 decimal place)

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Answer 1

A.

% increase in the cost of gas g1 = 9% per year

% increase in the cost of maintenance g2 = 15% per year

R = 18%

Time = 13 years

Present worth of O&M cost = (8938/(18% - 9%))*(1- (1.09/1.18)^13) + (391/(18% - 15%))*(1- (1.15/1.18)^13)

Present worth of O&M cost = $67613.23

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B.

Let, total annual equivalent expense = P

Then,

P = 67613.23 / ((1-1/1.18^13)/.18)

P = $13771.88

So, total annual equivalent expense is $13771.88.