John is a farmer in the midwest who currently uses fossil fuels to dry his corn crop. He currently has a high$-$speed, high$-$temperature drying system, and to reduce his fuel costs, he wishes to switch to a combination of high$-$temperature and low$-$temperature drying system that allows him to use natural solar energy for part of the drying process. John will run $15,000$ bushels$/$day for $40$ days through the new drying system and estimates the solar drying will save him $$0\mathrm{.}015/$bushel$,$ therefore increasing his net returns. The initial cost of the system is $$80,000,$ has a real terminal value of $$30,000$ and has an investment life of $8$ years. John has a required rate of return of $10\%,$ a marginal tax rate of $30\%$ and the system will be depreciated using a straight$-$line method over $15$ years. Assume an inflation rate of $2\%$ and a risk premium of $1\%.$

What is the after$-$tax, risk adjusted discount rate?

a$\mathrm{.}10\%$

b$\mathrm{.}7\mathrm{.}7\%$

c$\mathrm{.}9\%$

d$\mathrm{.}7\%$

What are the pre$-$tax real net returns?

a$.$$$9,000$

b$.$$$12,000$

c$.$$$6,000$

d$.$$$7,560$

What is the yearly allowable depreciation using the straight$-$line method?

a$.$$$5,000$

b$.$$$5,333\mathrm{.}33$

c$.$$$4,000$

d$.$$$4,285\mathrm{.}71$

What is the capital gain$/$loss$?$

a$.$$$5,333\mathrm{.}33$

b$.($$$2,183\mathrm{.}55)$

c$.($$$7,333\mathrm{.}33)$

d$.$$$2,142\mathrm{.}86$

What is the life of the investment?

a$\mathrm{.}5$ years

b$\mathrm{.}8$ years

c$\mathrm{.}4$ years

d$\mathrm{.}7$ years

What is the accumulated depreciation after $8$ years?

a$.$$$40,000$

b$.$$$41,333\mathrm{.}33$

c$.$$$42,666\mathrm{.}67$

d$.$$$50,000$

What is the NPV$?$

a$.($$$11,848\mathrm{.}36)$

b$.($$$4,456\mathrm{.}89)$

c$.($$$11,152\mathrm{.}93)$

d$.($$$14,086\mathrm{.}05)$