Question

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 $8.45 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 4.6 million packages a year. Cash costs of production in the first year are expected to be $4.20 per package in real terms for the headache-only brand. Production costs are expected to be $4.75 in real terms for the headache and arthritis pill. All prices and costs are expected to rise at the general inflation rate of 3 percent.

Either product requires further investment. The headache-only pill could be produced using equipment costing $20 million. That equipment would last three years and have no resale value. The machinery required to produce the broader remedy would cost $29 million and last three years. The firm expects that equipment to have a $1,000,000 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 7 percent.

a.	Calculate the NPV for headache pain reliever only.
b.	Calculate the NPV for headache and arthritis pain reliever

Answer 1

Resale value and discount rate are given in real terms. so, project cash flows should also be in real terms.

NPV = Present value of cash inflows - initial investment

a. NPV for headache pain reliever only

	Years	0	1	2	3	Total
	Cost of equipment	-$20,000,000	0	0	0	-$20,000,000
	Sales quantity	0	3000000	3000000	3000000
	Sales price/unit	0	$8.45	$8.45	$8.45
	Production cost/unit	0	$4.20	$4.20	$4.20
	Sales	$0	$25,350,000	$25,350,000	$25,350,000	$76,050,000
Less:	Production cost	$0	$12,600,000	$12,600,000	$12,600,000	$37,800,000
Less:	Depreciation	$0	$6,666,667	$6,666,667	$6,666,667	$20,000,000
	Pre-tax cash flow	$0	$6,083,333	$6,083,333	$6,083,333	$18,250,000
Less:	Taxes @22%	$0	$1,338,333	$1,338,333	$1,338,333	$4,015,000
	After-tax cash flow	$0	$4,745,000	$4,745,000	$4,745,000	$14,235,000
Add back:	Depreciation	$0	$6,666,667	$6,666,667	$6,666,667	$20,000,000
Add:	Sale of equipment	$0	$0	$0	$0	$0
Less:	Tax on equip. sale	$0	$0	$0	$0	$0
	Operating cash flow	-$20,000,000	$11,411,667	$11,411,667	$11,411,667	$14,235,000
	NPV	$9,947,820

Formulas

b. NPV for headache and arthritis pain reliever

Tax on resale value of equipment = (sale value - book value)*tax rate

Book value = cost of equipment - total depreciation

depreciation = (cost of equipment - resale value)/life of equipment

	Years	0	1	2	3	Total
	Cost of equipment	-$29,000,000	0	0	0	-$29,000,000
	Sales quantity	0	4600000	4600000	4600000
	Sales price/unit	0	$8.45	$8.45	$8.45
	Production cost/unit	0	$4.75	$4.75	$4.75
	Sales	$0	$38,870,000	$38,870,000	$38,870,000	$116,610,000
Less:	Production cost	$0	$21,850,000	$21,850,000	$21,850,000	$65,550,000
Less:	Depreciation	$0	$9,333,333	$9,333,333	$9,333,333	$28,000,000
	Pre-tax cash flow	$0	$7,686,667	$7,686,667	$7,686,667	$23,060,000
Less:	Taxes @22%	$0	$1,691,067	$1,691,067	$1,691,067	$5,073,200
	After-tax cash flow	$0	$5,995,600	$5,995,600	$5,995,600	$17,986,800
Add back:	Depreciation	$0	$9,333,333	$9,333,333	$9,333,333	$28,000,000
Add:	Sale of equipment	$0	$0	$0	$1,000,000	$1,000,000
Less:	Tax on equip. sale	$0	$0	$0	$0	$0
	Operating cash flow	-$29,000,000	$15,328,933	$15,328,933	$16,328,933	$17,986,800
	NPV	$12,044,264

Formulas