$(8$ points$)$ A project from a construction company is being planned that has an initial

investment at time $0,$ annual revenues and expenses, and a salvage value at the end of the

project lifespan $(20$ years$).$ The financial values are summarized below:

Initial investment amount at time $0$ $$200,000$

Estimated annual revenue $$42,000$ per year

Estimated annual expenses $$8,000$ per year

Estimated salvage value at end of lifespan $$15,000$

Minimum attractive rate of return $($MARR$)15\%$

a$.$ Calculate the capital recovery amount CR$($i$\%).$

b$.$ Using the annual worth $($AW$)$ method, determine whether purchasing the equipment

is economically justified.

c$.$ Repeat part $($b$)$ using the internal rate of return $($IRR$)$ method based on annual worth

$($AW$).$

d$.$ Using the present worth $($PW$)$ method, determine the break$-$even time period after

which purchase of the equipment generates a profit. $($Find N when PW $=0)$