## Part (a):
##
barrels_produced = c(80, 70, 50, 30, 10)
print(sum(barrels_produced))

gross_revenue = 20*barrels_produced

net_income = c(1200, 1000, 500, 200, 50)
option_1 = pmin(0.22 * gross_revenue, 0.5 * net_income)
option_2 = 5 * barrels_produced

depletion_allowance = pmax(option_1, option_2)

taxable_income = net_income - depletion_allowance

tax = 0.45 * taxable_income

after_tax_income = net_income - tax

T = data.frame(BP=barrels_produced,
               GR=gross_revenue,
               NI=net_income,
               Option_1=option_1, Option_2=option_2,
               DA=depletion_allowance, TI=taxable_income, tax, ATI=after_tax_income)
print(T)

print(sum(T$DA) )


## Part (b):
##
r= 0.2
PV = -1000 + sum( after_tax_income *((1+r)^(-seq(1, 5)) ))
print(sprintf('PV= %f', PV))

cs = polyroot( c(-1000, after_tax_income) )
rs = 1/cs - 1
print(rs)