Question $1$

You are operating a gold mine that will extract $10$ tons of gold per year for the next twelve years. You

expect to sell the extracted gold for a per$-$ton price of $$60$ million every year for the next six years. For the

final six years, you expect to sell the extracted gold for an uncertain per$-$ton market price of either $$30$M

$(50$ percent probability$)$ or $$90$M $(50$ percent probability$).$ Assume that the cost of extracting each ton of

gold is $$45$ million for all years.

a$)$ Suppose that the risk$-$free rate is $3$ percent and the market risk premium is $5$ percent. Retrieve

the beta of gold by looking up the primary gold exchange traded fund $($symbol: GLD$)$ on Yahoo!

Finance. What is the expected return on gold? This will be used as your discount rate on your gold

mining operations.

b$)$ What is the value of your gold mining operation? This is calculated as the present value of

expected future revenues minus the present value of future costs.

You will learn at t$=6$ whether the per$-$ton gold price for the last six years will be $$30$M or $$90$M$.$

c$)$ Now assume that you have the option at t$=6$ to ramp down gold production to three tons per year

for the last six years of operations. Illustrate why you would only ramp down production to three

tons per year if the gold price ends up being $$30$M per ton for the final six years.

d$)$ What is the value of your gold mining operation at t$=0,$ given that you have the option at t$=6$ to

ramp down gold production to three tons per year for the final six years of operations?

Question $2$

When a firm has cash flow problems, there are often negative feedback effects. For example, the firm

may need to cut capital expenditures and research and development activities that are necessary to

remain competitive in its industry.

Your firm, Goldmine Incorporated, is considering the purchase of a foreign technology firm called

ForeignTechs. Goldmine is considering this purchase because ForeignTechs tends to have a good year

when Goldmine has a bad year. If Goldmine purchased ForeignTechs, then Goldmine would not have cash

flow problems in its bad years because ForeignTechs can provide support in those years.

The following table outlines the possible cash flows produced by Goldmine and ForeignTechs each year:

State A State B State C

Probability $30\%40\%30\%$

Goldmine Cash Flow $$20$M $$60$M $$100$M

ForeignTechs Cash Flow $$50$M $$40$M $$30$M

Assume that Goldmine incurs an additional cost of $$15$M in State A because of the negative feedback

effects resulting from the cash flow problems in that state. If Goldmine purchases ForeignTechs, then

Goldmine would not incur this additional $$15$M cost in State A$.$ The annual expected return on Goldmine

assets is $10$ percent and the expected return on ForeignTechs assets is $12\mathrm{.}5$ percent. Both firms are allequity and will operate in perpetuity. Each firm has $10$M shares outstanding.

a$)$ Assume that no merger announcement has been made. What is the share price of each firm?

Goldmine announces it will purchase all of the shares in ForeignTechs. Following the purchase of

ForeignTechs, Goldmine announces to the public that it will no longer incur the additional $$15$M cost in

State A because of the implicit insurance provided by ForeignTechs.

b$)$ What is the value of the combined firm?

c$)$ Is the merger a good idea? For this, you will have to compare the value created from the merger

to the value of the stand$-$alone firms.

d$)$ If the merger is a good idea, why might Goldmine encounter resistance from ForeignTechs$$

national government?