Problem 3:

Firm X is considering building a plant that will manufacture heaters powered by natural gas. The plant will cost $1 million to

build, which the firm must pay immediately if it builds the plant If built, the plant will produce 2,000 heaters this year It will

then become completely obsolete (with no salvage value) at year-end due to advancing technology In addition to the

expenditure to build the plant, the cost of manufacturing each heater will be $1,000 for labor and materials, payable at the end

of the year.

a) Suppose that there is a forward market for heaters with a forward price of $F per heater delivered in a

year. What is the minimum forward price $F for which building the plant is a posiuve NPV project for Firm X

Assume that the nsk-free rate is 4*

b) Suppose now that there is no forward market for heaters However, there is a spot market for natural

gas In particular, the price of natural gas is currently S2 per mm BTU (thousand Bntish Thermal Units). In a year,

the natural gas price will be either $4 per mm BTU or $1 per mm BTU Suppose that if the price of natural gas rises

to S4

. demand for natural gas heaters will be very low and the market price of your heaters will be S900. If the price

of natural gas falls to $1, demand for the heaters will be very high, and their market price will be $3,000 Assume

for simplicity that natural gas incurs no storage costs. The risk-free rate is 4V Suppose that Firm X leams next

year's natural gas pnces only after it decides to construct the plant and manufacture the heaters Find the NPV of

building the plant

c) Keep all the assumptions in part b, except assume now that firm X leams next year's natural gas price

after it decides to construct the plant but before actually manufacturing the heaters, and that it does not have to

manufacture the heaters. Find the new NPY of building the plant