Question

5-25 a new tennis court complex is planned. each of two alternatives will last 18 years, and the interest rate is 7%. use present worth analysis to determine which should be selected. construction annual cost o&m a $500,000 $25,000 b $640,000 $10,000 contributed by d. p. loucks, cornell university

Explanation:

Step1: Recall present - worth formula for alternatives

The present - worth (PW) of an alternative with initial cost $P$ and annual cost $A$ over $n$ years at interest rate $i$ is given by $PW = P+A(P/A,i,n)$, where $(P/A,i,n)=\frac{(1 + i)^{n}-1}{i(1 + i)^{n}}$. Here, $i = 0.07$ and $n = 18$.

Step2: Calculate $(P/A,0.07,18)$

$(P/A,0.07,18)=\frac{(1 + 0.07)^{18}-1}{0.07(1 + 0.07)^{18}}$.
First, calculate $(1 + 0.07)^{18}=1.07^{18}\approx3.37993$.
Then, $(1 + 0.07)^{18}-1\approx3.37993 - 1=2.37993$.
And $0.07(1 + 0.07)^{18}=0.07\times3.37993\approx0.236595$.
So, $(P/A,0.07,18)=\frac{2.37993}{0.236595}\approx10.059$.

Step3: Calculate present - worth of Alternative A

For Alternative A, $P = 500000$ and $A = 25000$.
$PW_A=500000+25000\times10.059=500000 + 251475=751475$.

Step4: Calculate present - worth of Alternative B

For Alternative B, $P = 640000$ and $A = 10000$.
$PW_B=640000+10000\times10.059=640000+100590 = 740590$.

Step5: Compare present - worths

Since $PW_B

Answer:

Alternative B should be selected.