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Analyzing the given cost patterns

A University spent $1.8 million to install solar panels atop a parking garage. The panels will have a capacity of 500kw, have a life expectancy of 20 years and suppose the discount rate is 10%.
a. If electricity can be purchased for the cost of $0,10 per kwh, how many hours per year will the solar panels have to operate to make this project even?
b. If efficient systems operate for 2,400 hours per year, would the project break even?
c. The University is seeking a grant to cover capital costs. How big of a grant would make this project worthwhile (to the University)?

2. Last year a toy manufacturer introduced a new toy truck that was a huge success. The company invested $205 million for a plastic injection molding machine (which can be sold for $2.0 million) and $100,000 in plastic injection molds specifically for the toy ( not valuable to anyone else). Labor and the cost of materials necessary to make truck is about $3. This year a competitor has developed a similar toy that has significantly reduced demand for the toy truck. Now the original manufacturer is deciding whether they should continue production of the toy truck. If the estimated demand is 100,000 trucks what is the break even price for the toy trucks? Should you shut down?

3. Your Insurance firm processes claims through its newer, larger high tech facility and its older, smaller low-tech facility. Each month, the high-tech facility handles 10,000 claims, incurs $100,000 in fixed costs and $100,000 in variable costs. Each month the low-tech facility handles 2,000 claims, incur $16,000 in fixed cost and $24,000 in variable costs. If you anticipate a decrease in the number of claims, where will you lay off workers?

Solution Preview

A University spent $1.8 million to install solar panels atop a parking garage. The panels will have a capacity of 500kw, have a life expectancy of 20 years and suppose the discount rate is 10%.

a. If electricity can be purchased for the cost of $0,10 per kwh, how many hours per year will the solar panels have to operate to make this project even?

Let solar panels operate x number of hours per year.
Energy produced per year=500*x=500x
Revenue saved per= 500x*0.10=50x
Discount rate=r=10%
Number of periods=n=20 years

PV factor of annuity of $1=1/r*(1-1/(1+r)^n)=1/10%*(1-1/(1+10%)^20)= 8.5136

PV of revenue saved=50x*8.5136=425.68x
Cost of solar panels=$1,800,000

Put
Cost of solar panels=PV of revenue saved
1800000=425.68x
x=1800000/425.68 =4228.53 or ...

Solution Summary

There are 3 problems. Solution to first problem depicts the steps to calculate the minimum operating hours and the needed grant value. Solution to second problem calculates the break even point in the given case. Solution to third problem provides analysis of cost patterns given and determines the course of action needed in case of reduced demand.

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