My question is as follows:
1.) An earth compactor costs $38,000 and has an economic life of 9 years. However, the purchaser needs it for only 1 project that will be completed in 3 years. At the end of the project, it can be sold for 1/2 its purchase price. What is the annual cost to the owner if the required rate of return is 12%? Economics for Engineers has been the bane of my existence.
Thank you so much for any help you can provide.
On
Let $P\ $ ($=\$\ 38'000$) be the initial price of the machine and $p$ ($=0.12$) be the interest rate. At the beginning the purchaser has to take the amount $P$ out of his bank account, so after three years the total amount $(1+p)^3 P\ $ is missing there. On the other hand from the sale of the machine he then can pay back the amount ${P\over 2}$. It follows that the total cost per year is $${1\over3}\bigl((1+p)^3-{1\over2}\bigr) P\ ,$$ which amounts to $11'462$ dollars and $42$ cents.
At the end of 3 years, it can be sold for $19000$. So $$P \left(\frac{(1.12)^{3}-1}{0.12} \right) = 19000$$ So $P \approx 5630$.