A bicycle manufacturer currently produces 300,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $2 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $250,000 and would be obsolete aer 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require $50,000 of inventory and other working capital upfront (year 0), but argues that this sum can be ignored because it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery aer 10 years are $20,000.If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?

QUESTION: Where did the 166,250 come from?

Question 12

Free Cash Flow = EBIT (1 - Tax Rate) + Depreciation & Amortization - Capital Expenditure - Change in Net Working Capital.

Outside supplier

= $ 2 * 300,000(1-0.35) = $ 390,000 per year.

NPV of Annuity = $ 390,000*1/0.15(1 - 1/1.15¹⁰

=$1.9573 Million

In - House

In year 0 = Capital Expenditure and Net Working Capital.

= -$250, 0000 -$50,000 = -$300,000

In Year 1-9

1.5 * -300,000 - 25,000 +166,250 +25,000

FCF= -$283,750

FCF in year 10

FCF= - 283,750 + 20,000(1 - 0.35) + 50,000 = 220,750

Scrap proceeds are taxed instead since the book value of the machinery is zero.

NPV = -300,000 + -$283,750(9 years annuity) + -220,750/1.15¹⁰

= -$300,000 - 283,750/0.15(1-1/1.15⁹) - $220,750/1.15¹⁰

= -$ 1.7085Million

Therefore producing it will be cheaper by $248,800 ($1.9573Million - $1.7085Million)