After extensive medical and marketing research, Pill, Inc., believes it can penetrate the pain reliever market. It is considering two alternative products. The first is a medication for headache pain. The second is a pill for headache and arthritis pain. Both products would be introduced at a price of $$8\mathrm{.}50$ per package in real terms. The headache$-$only medication is projected to sell $3$ million packages a year, whereas the headache and arthritis remedy would sell $4\mathrm{.}6$ million packages a year. Cash costs of production in the first year are expected to be $$4\mathrm{.}45$ per package in real terms for the headache$-$only brand. Production costs are expected to be $$5\mathrm{.}00$ in real terms for the headache and arthritis pill. All prices and costs are expected to rise at the general inflation rate of $2$ percent.

Either product requires further investment. The headache$-$only pill could be produced using equipment costing $$18$ million. That equipment would last three years and have no resale value. The machinery required to produce the broader remedy would cost $$27$ million and last three years. The firm expects that equipment to have a $$800,000$ resale value $($in real terms$)$ at the end of Year $3.$

The firm uses straight$-$line depreciation and has a tax rate of $22$ percent. The appropriate real discount rate is $6$ percent.

a$.$

Calculate the NPV for headache pain reliever only. $($Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to $2$ decimal places, e$.$g$.,1,234,567\mathrm{.}89.)$

b$.$ Calculate the NPV for headache and arthritis pain reliever. $($Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to $2$ decimal places, e$.$g$.,1,234,567\mathrm{.}89.)$