Question

A small company heats its building and spends ​$7,800 per year on natural gas for this purpose. Cost increases of natural gas are expected to be 9​% per year starting one year from now​ (i.e., the first cash flow is ​$8,502 at EOY​ one). Their maintenance on the gas furnace is ​$345 per​ year, and this expense is expected to increase by 15​% per year starting one year from now​ (i.e., the first cash flow for this expense is ​$396.75 at the EOY​ one). If the planning horizon is 15 ​years, what is the total annual equivalent expense for operating and maintaining the​ furnace? The interest rate is 20​% per year.

The total annual equivalent expense for operating and maintaining the furnace is ?

Answer 1

Let us first estimate the present worth of natural gas expenses

Flow at the end of year 1=P=7800*1.09=$8502

Growth rate of expenses=g=9%

Time period=n=15 years

Rate of interest=i=20%

PW of expenses on natural gas is given by

6 PV g(1) = (1+g" (1+i)n) * 1. 2011

PV g(1) = 8502 0.20 – 0.09 (1 + 0.09) 15 (1 +0.2015)

PV g(1) = 77290.909091 * 0.763583 = 59018.02 (dollars)

Let us first estimate the present worth of maintenance expense

Flow at the end of year 2=P=345*1.15=$396.75

Growth rate of expenses=g=15%

Time period=n=15 years

Rate of interest=i=20%

PW of maintenance expenses is given by

6 PV g(2) = 2 (1+g" (1+i)n) 2 - 0

PV g(2) = 396.75 0.20 – 0.15" (1 + 0.15) 15 (1 +0.2015)

PV g(1) = 7935*0.471860 = 3744.21 dollars)

Present worth of total expanses=59018.02+3744.21=$62762.23

Total annual equivalent expense=62762.23*(A/P,0.15,15)

(A/P,1,n) = 1 -

0.20 (A/P,0.20,15) = 1 1-21 (1+0.2015 = 0.213882

Total annual equivalent expense=62762.23*0.213882=$13423.71