Jeremy Stein's Gold -Mining Firm Requires Financing to Develop Its Gold Reserves

Answers

a) The value of the firm prior to the expansion project and prior to raising new funds is equal to:

asset*expected price of gold-expected bankruptcy costs (1)

First we need to calculate the expected price of gold:

The prices of gold are uniformly distributed over the range 100,500, therefore

Eprice of gold=100+5002=300$oz (2)

Second we need to calculate the expected bankruptcy costs:

* The firm will face bankruptcy when it cannot service its senior debt which has the face value of $ 500m, in that case the firm will face bankruptcy cost of $ 50m. This will happen when the value of the firm’s asset is below the level of its senior debt:

(1.973m oz×price of gold $)≤$500m (3)

pricedefault = 500m 1.9732m$oz=253.39$oz (4)

* The probability that the price of gold is less than $ 253.39 per oz is:

we know that prices of gold are uniformly distributed over the range 100,500, therefore

Px≤253.39=100253.39dx(500-100)=38.3% (5)

* The expected bankruptcy cost is equal to:

probability that the gold price is less than $253.39 per oz ×bankruptcy costs

Ebankruptcy cost=38.3475%×$50m=$19.17m (6)

Now, we can go back to the equation (1) and can calculate the value of the firm prior to the expansion and prior to rising new funds:

asset*Eprice of gold-Ebankruptcy cost

Vfirm=1.973m ×$300-$19.17m=$572.8m≈$573m (7)

The split of the value of the firm between (senior) debt-holders and equity-holders

From the above calculation we know that the value of the firm is $ 573m.

The senior debt-holders will be reimbursed if the gold price is above $253.39 per oz. In that case, the senior-debt holders are reimbursed and the equity-holders will get rest of the value of the firm.

If the gold price is below $253.39 per oz, then the firm is facing bankruptcy, $50m bankruptcy cost incurs and equity-holders get nothing.

Hence, we have that the value of the senior debt is:

Vsenior...