Chapter 6, Problem 58P

To determine

The EUAC of the inn.

Answer to Problem 58P

The EUAC of the inn is $\$336264$.

Explanation of Solution

Given:

Initial cost of the land is $\$3.4\text{M}$.

Annual operation and maintenance cost is $\$25000$ for $20\text{years}$.

Painting cost is $\$15000$ after every $4$ year.

Exterior painting cost is $\$60000$ after every $5\text{years}$.

Furniture replacement cost is $\$100000$ every 6 years.

Parking and Paving cost is $\$80000$ every $8$ years.

Net demolition cost is $\$100000$ at end of $20\text{years}$.

MARR is $5\%$.

Calculation:

Draw the cash flow diagram to compute the EUAC.

Figure (1)

Write the expression to calculate the present worth of the cash flow shown in Figure (1).

$PW=\left(\begin{array}{l}\$3400000+\$15000\left(\frac{1}{{\left(1+i\right)}^4}\right)+\$60000\left(\frac{1}{{\left(1+i\right)}^5}\right)\\ +\$100000\left(\frac{1}{{\left(1+i\right)}^6}\right)+\$95000\left(\frac{1}{{\left(1+i\right)}^8}\right)+\$60000\left(\frac{1}{{\left(1+i\right)}^{10}}\right)\\ +\$115000\left(\frac{1}{{\left(1+i\right)}^{12}}\right)+\$60000\left(\frac{1}{{\left(1+i\right)}^{15}}\right)\\ +\$95000\left(\frac{1}{{\left(1+i\right)}^{16}}\right)+\$100000\left(\frac{1}{{\left(1+i\right)}^{20}}\right)+\$175000\left(\frac{1}{{\left(1+i\right)}^{20}}\right)\end{array}\right)$ ...... (I)

Here, the present worth is $PW$ and the interest rate is $i$.

Substitute $5\%$ for $i$ in Equation (I).

$\begin{array}{c}PW=\left(\begin{array}{l}\$3400000+\$15000\left(\frac{1}{{\left(1+0.05\right)}^4}\right)+\$60000\left(\frac{1}{{\left(1+0.05\right)}^5}\right)\\ +\$100000\left(\frac{1}{{\left(1+0.05\right)}^6}\right)+\$95000\left(\frac{1}{{\left(1+0.05\right)}^8}\right)\\ +\$60000\left(\frac{1}{{\left(1+0.05\right)}^{10}}\right)+\$115000\left(\frac{1}{{\left(1+0.05\right)}^{12}}\right)\\ +\$60000\left(\frac{1}{{\left(1+0.05\right)}^{15}}\right)+\$95000\left(\frac{1}{{\left(1+0.05\right)}^{16}}\right)\\ +\$100000\left(\frac{1}{{\left(1+0.05\right)}^{20}}\right)+\$175000\left(\frac{1}{{\left(1+0.05\right)}^{20}}\right)\end{array}\right)\\ =\left(\begin{array}{l}\$3400000+\$15000\left(0.8227\right)+\$60000\left(0.7835\right)\\ +\$100000\left(0.7462\right)+\$95000\left(0.6768\right)+\$60000\left(0.6139\right)\\ +\$115000\left(0.5568\right)+\$60000\left(0.4810\right)\\ +\$95000\left(0.4581\right)+\$100000\left(0.4155\right)+\$175000\left(0.3769\right)\end{array}\right)\\ =\left(\begin{array}{l}\$34000+\$12341+\$47010+\$74620+\$64296\\ +\$36834+\$64032+\$28860+\$43520+\$41550+\$65958\end{array}\right)\\ =\$3879021\end{array}$

Write the expression to calculate the EUAC.

$EUAC=P\left(\frac{i{\left(1+i\right)}^n}{{\left(1+i\right)}^n-1}\right)+A_{OM}$ ...... (II).

Here, the equivalent uniform annual cost is $EUAC$, the present worth of the cash flow is $P$, the interest rate is $i$, the number of period is $n$ and the annual operation and maintenance cost is $A_{OM}$.

Substitute $\$3879021$ for $P$, $\$25000$ for $A_{OM}$, $5\%$ for $i$ and $20$ for $n$ in Equation (II).

$\begin{array}{c}EUAC=\$3879021\left(\frac{0.05{\left(1+0.05\right)}^{20}}{{\left(1+0.05\right)}^{20}-1}\right)+\$25000\\ =\$3879021\left(0.080243\right)+\$25000\\ =\$336264\end{array}$.

Conclusion:

Thus, the EUAC of the inn is $\$336264$.