Farmer Brown$$s family has farmed his patch of this green and pleasant land for $10$ generations. He looks forward to handing the mantle over to his daughter, who is currently $4$ years old, when the time comes to retire. On his land is a low rolling hill known to the family as $$brass monkeys hill$$ because it is always windy. He thinks this will make a great place for a wind turbine.

The wind turbine installation company agrees that the hill looks like the best place on his farm for a turbine and thinks they can install one of their $6$ kWp turbines on the site and it will achieve a $27\%$ capacity factor there. The cost they quote is $25,000.$ The equipment has a life expectancy of $20$ years. Over the first $10$ years they expect O&M costs of $300$ per year rising to $350$ per year in the second $10$ years.

Farmer Brown decides that he can raise $10,000$ from the family savings but will need to borrow $15,000$ for the project. The bank offers him a $10-$year loan at $8\%$ interest.

The farm has a smart meter and, based on the half$-$hour data available, farmer Brown estimates that he will achieve a $70\%$ self$-$consumption rate as his milking parlour and refrigeration on site offer a reliable demand spread across the day.

His electricity tariff is $30$p per kWh$,$ and he has a deal on offer for exported electricity of $6$p per kWh$.$

Because he feels his family has a long$-$term commitment to the land and the environment, farmer Brown decides to set a discount rate of only $4\%.$ His accountant points out that farmer Brown might not even live long enough to see out the end of the project lifetime and he should be more concerned about the poor milk prices being offered by the supermarket for this year$$s milk output, so she suggests a discount rate of $15\%.$

$$ Draw up a table as below and calculate the NPV of this project using the two suggested discount rates for its complete lifetime.

Year Income: NPV $4\%$ DR NPV $15\%$ DR Expenditure: NPV $4\%$ DR NPV $15\%$ DR

$0$

$1$

$2$

$3$

$4$

etc