When a wind generator is installed there is a substantial in

When a wind generator is installed there is a substantial initial? cost, but daily operation requires no further cash payment.? However, to keep the generator in proper operating? condition, it must undergo maintenance once a year. Each maintenance cycle requires a cash payment of ?$10,000. The solid lines on the graph below show this situation. The stepped blue line shows the cost over time and the straight brown line shows the revenue derived from the generator. As the second yearly maintenance? approaches, you are informed by the manufacturer that a significant upgrade is available for additional cost. The upgrade will make the generator far more? efficient, thus the revenue would increase substantially. The yearly maintenance cost after the upgrade would still be ?$10,000. The dashed lines show the cost and revenue projections if the upgrade is installed.

?(a) What is the amount of revenue per year without the? upgrade? ?

(b) What is the initial cost of the wind? generator? ?

(c) How many years after the initial installation do you breakeven if the upgrade is? installed? List your answer as number of years? + number of months. ?

(d) What is the cost of the upgrade completed at the two year maintenance? cycle? Note that this figure includes the standard ?$10,000 maintenance fee.

(f ) How many years after the initial installation will you have made a profit of $25,000 if the upgrade is NOT installed? List your answer as number of years + number of months.

(g) If the upgrade results in increased reliability thus increasing the maintenance interval to two years, though still at a cost of $10,000 per maintenance, how many years after the initial installation will you breakeven after the upgrade? List your answer as number of years + number of months.

Solution

(a) We need to find revenue per year (without upgradation). This would is basically equal to change in revenue per year, which in other words is equal to the rate of change or revenue. Rate of change of revenue can be found by finding the slope of revenue graph. Revenue curve is the soid green line.

Slope of solid green line:

=(35-0)/(2-0) = 35/2 = 17.5 Dollars/Year

(b) Initial cost of the wind generator is the value of y-intercept of the Blue Stepped Curve. We can see that at t=0, Blue Stepped curve starts at $25000. Therefore, initial cost of the wind generator is $25000.

(c) We know that the breakeven occurs when Revenue equals Cost. Therefore, after installation of upgrade, breakeven will occur when black dotted line meets the red dotted stepped curve for the first time.

From the given graph, we can see that black dotted line meets the red dotted stepped curve after approximately 3 years and 7 months.

(d) Cost of upgrade completed at two year maintenance cycle is equal to the sum of standard maintenance fee and the additional amount paid for the upgrade. We can see that the cost changes from 45000 to 65000, Therefore, upgradation cost is 20000. Adding to with the standard maintenance cost of 10000, we get the total upgrade expanses equal to $30000.

(f) From the graph, we can see that the profit will become $25000 after 6 years because after 6 years, the difference between Blue Stepped curve and Solid Green line is $25000.

(g) If the upgrade results in increased reliability thus increasing the maintenance interval to two years, the red dotted line will meet the black dotted line after 3 years and 3 months. Therefore, breakeven will occur after 3 years + 3 months.