Lucy has farmed his patch of this green and pleasant land for $10$ generations. she looks forward to handing the mantle over to her daughter who is currently $4$ years old, when she retires. On her land is a low rolling hill known to the family as $$canapy hill$$ because it is always windy. She thinks this will make a great place for a wind turbine.

The wind turbine installation company 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.

Lucy decides that she 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, lucy estimates that she will achieve a $70\%$ self$-$consumption rate as his milking parlour and refrigeration on site offer a reliable demand spread across the day.

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

Lucy decides to set a discount rate of only $4\%.$ Her accountant points out that farmer lucy might not even live long enough to see out the end of the project lifetime and she 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 $15\%.$

i$.$Calculate the annual output of the turbine

ii$.$Calculate the annual savings on imported electricity

iii.Calculate the annual income from exports and hence the total annual income

iv$.$ Calculate the revenue costs paid each of the first $10$ years and each year of the years $1120$

$.$

$$ calculate the NPV of this project in the table below, 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

$($Hint$)$

Be careful you don$$t pay for the loan twice! There is more than one way you could fill in your table to avoid this, but be careful

Do not be confused by the use of the term $$discount rate$$ in the table. You should use the interest rate in this question.

this table is actually set up to calculate the annuitisation of loans and should be for interest rates, not discount rates. Do not be confused by the use of the term $$discount rate$$ in the table. You should use the interest rate in this question.