Question

the mwatex textile company is considering two mutually - exclusive electronic control systems for its textile machines. the investment period is 7 years (equal lives), and the marr is 8% per year. data for the systems are given below. based on the pw method, which alternative should the company select?

alternative	capital investment	net annual revenue
y	$16,000	$6,400

a) the net pw of the alternative x is $ (round to the nearest dollar.)
the net pw of the alternative y is $ (round to the nearest dollar.)
which alternative should the company select? choose the correct answer below.
a. alternative x
b. alternative y

b) what if the marr was 18%, instead of 8%?
the net pw of the alternative x is $ (round to the nearest dollar.)
the net pw of the alternative y is $ (round to the nearest dollar.)
which alternative should the company select? choose the correct answer below.
a. alternative y
b. alternative x

Explanation:

Step1: Recall the present - worth formula

The present - worth (PW) formula for an investment with initial cost $P$, annual net revenue $A$, and interest rate $i$ over $n$ years is $PW=-P + A(P/A,i,n)$, where $(P/A,i,n)=\frac{(1 + i)^n-1}{i(1 + i)^n}$.

Step2: Calculate $(P/A,i,n)$ for $i = 8\%$ and $n = 7$

For $i=0.08$ and $n = 7$, $(P/A,0.08,7)=\frac{(1 + 0.08)^7-1}{0.08(1 + 0.08)^7}=\frac{1.713824 - 1}{0.08\times1.713824}=\frac{0.713824}{0.137106}\approx5.20637$.

Step3: Calculate the net - PW of alternative X at $i = 8\%$

For alternative X, $P = 8000$ and $A = 4000$.
$PW_X=-8000+4000\times(P/A,0.08,7)=-8000 + 4000\times5.20637=-8000+20825.48\approx12825$.

Step4: Calculate the net - PW of alternative Y at $i = 8\%$

For alternative Y, $P = 16000$ and $A = 6400$.
$PW_Y=-16000+6400\times(P/A,0.08,7)=-16000+6400\times5.20637=-16000 + 33320.77\approx17321$.

Step5: Select the alternative at $i = 8\%$

Since $PW_Y>PW_X$, the company should select alternative Y.

Step6: Calculate $(P/A,i,n)$ for $i = 18\%$ and $n = 7$

For $i = 0.18$ and $n = 7$, $(P/A,0.18,7)=\frac{(1 + 0.18)^7-1}{0.18(1 + 0.18)^7}=\frac{3.18543 - 1}{0.18\times3.18543}=\frac{2.18543}{0.573377}\approx3.81156$.

Step7: Calculate the net - PW of alternative X at $i = 18\%$

For alternative X, $P = 8000$ and $A = 4000$.
$PW_X=-8000+4000\times(P/A,0.18,7)=-8000+4000\times3.81156=-8000 + 15246.24\approx7246$.

Step8: Calculate the net - PW of alternative Y at $i = 18\%$

For alternative Y, $P = 16000$ and $A = 6400$.
$PW_Y=-16000+6400\times(P/A,0.18,7)=-16000+6400\times3.81156=-16000+24394.00\approx8394$.

Step9: Select the alternative at $i = 18\%$

Since $PW_Y>PW_X$, the company should select alternative Y.

Answer:

A) The net PW of the alternative X is $\$12825$.
The net PW of the alternative Y is $\$17321$.
The company should select alternative Y.
B) The net PW of the alternative X is $\$7246$.
The net PW of the alternative Y is $\$8394$.
The company should select alternative Y.