(if your solution is on paper, put it in my mailbox in 1721 or 720)
Problem 1.
You are a consultant who was hired to evaluate a new product line for Markum
Enterprises. The upfront investment required to launch the product line is $10 million. The product will generate free cash flow of $750,000 the first year, and this free cash flow is expected to grow at a rate of 4% per year. Markum has an equity cost of capital of 11.3%, a debt cost of capital of 5%, and a tax rate of 35%. Markum’s current debt-equity ratio of 0.40 and it plans to keep it the same. a.
What is the NPV of the new product line (including tax shields from leverage)? (to find PV simply use WACC to discount the cash flows) b.
How much debt will Markum initially take on as a result of launching this product line? ( hint : for simplicity you can assume that all $10 mln of the investment are raised from outside by issuing bonds and stock. V
L
will increase then by PV, and the market value of debt will increase exactly by the amount of debt you raise; now you just have to find how much new debt is needed to keep the debt-equity ratio constant). c.
How much of the product line’s value is attributable to the present value of interest tax shields?
( hint : look for the difference between the unlevered and levered value of the project; to find the unlevered value you should find r
U
, keeping in mind that the debt-equity ratio stays constant – see lecture slides)
Problem 2. Your company extracts oil from a field with the remaining reserves of 100 mln barrels.
The current price of oil is $60. Your capacity allows you to extract maximum 10 mln barrels per year. Your annual costs are bq t
where b = 40. The risk-free rate r is 5% p.a.
According to the estimations, the annual oil price follows a binomial process: p t+1
is either 1.4
 p t
or
(1/1.4)
 p t
. a.
Compute the risk-neutral probabilities for the oil price stochastic process.
Use Monte-Carlo simulations to do parts b) to e). b.
Estimate the PV of your cash flows (profits) assuming no flexibility (i.e., a fixed annual output of 10 mln). c.
Assume now you optimize your extraction according to the one-period optimization model (due to linearity of the cost it will be either 0 or 10 each year). What will be your PV now? Compare to part (b) d.
Assume you can expand your extraction capacity for a fixed cost of $700 mln. The expansion would allow you to extract 20 mln barrels per year. Assume you decide to do the expansion right now (assume for simplicity it takes zero time). Assume that after the expansion you will optimize your extraction according to the one-period optimization model. What is the PV of the future cash flows net of the expansion cost? Is it worthwhile doing the expansion? e.
Assume you can delay the expansion until up to year 2 (we are now in year 0). Assume that both after and before the expansion you optimize your extraction according to the one-period optimization model. Shall you wait at all? If yes, what are the thresholds for the oil price above which you should expand in year 1 and in year 2 (provided you did not expand in year 1)? f.
In your opinion, is it always optimal to do one-period optimization, i.e. is it necessarily optimal to fully utilize your annual capacity whenever p > b ? Do not do any computations, an informal argument would suffice.
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