Question

A factory costs $970,000. You reckon that it will produce an inflow after operating costs of $187,000 a year for 15 years.

a. If the opportunity cost of capital is 11%, what is the net present value of the factory?

b. What will the factory be worth at the end of eight years?

Answer 1

a)NPV

$NPV = \frac{CF_{1}}{r} * \left [ 1 - \frac{1}{(1+r)^{n}} \right ] - Initial\ Investment$

$NPV = \frac{187,000}{0.11} * \left [ 1 - \frac{1}{(1+0.11)^{15}} \right ] - 970,000$

$NPV = 1,700,000 * 0.7909956533 - 970,000$

$NPV = \$374,692.61061$

b) At the end of eight years, the factory's worth is equal to the present value of future cash flows from year 9 to 15. A total of seven cash flows.

$PV_{8} = \frac{CF_{9}}{r} * \left [ 1 - \frac{1}{(1+r)^{n}} \right ]$

$PV_{8} = \frac{187,000}{0.11} * \left [ 1 - \frac{1}{(1+0.11)^{7}} \right ]$

$PV_{8} = 1,700,000 * 0.5183415891$

$PV_{8} = \$881,180.70147$

This is the worth of the factory at the end of 8 years.

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