Please answer all questions (q1-3) in as much detail as possible, full working is required. Course text used can be found here:…


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1. A monopolist tech company is considering whether or not to introduce a new model of digital
assistant. A facility to produce the digital assistant can be built this year (2019) at a cost of Β£15000.
Potential sales are estimated by the demand curve 𝑸 = 𝟏𝟐𝟎𝟎 βˆ’ πŸ“π‘·, where Q is the quantity sold and
P is the price. At the same time, the Government is considering legislation to make suppliers of
equipment responsible for preventing harm to users. If the legislation passes, the Intercept of the
demand curve will rise by 50%; if the legislation is abandoned, the intercept will fall by 25%. The
plant will start producing in 2020 if the investment is made; the (constant) marginal cost will be Β£25;
if the law is passed, the cost will rise to Β£50 (to produce models compliant with the law). The risk
free interest rate is 10%. Assume that the law has a 25% chance of being enacted and that all price
risk is diversifiable. The plant, once built, will operate forever.
a. Should the firm build the plant now?
Now suppose that the firm can now (in 2019) acquire an option to conduct R&D on a cheaper way to
make the device. If they exercise the option, the firm will have to spend an additional Β£10000 on
R&D and the production cost will fall by 40%, with effect from 2021.
b. How much would the firm be willing to pay for this option?
Suppose that the firm can also opt to delay building the plant by one year. In other words, the firm
can purchase in 2019 an option to delay building the plant (for the same cost of Β£15000, payable in
2020) until after it is known whether or not the law has passed.
c. Assuming the firm did not have the option to do R&D, how much would it be willing to pay
for the option to delay?
d. How much would the firm be willing to pay for a package consisting of both options? (If
the firm decides in 2019 to purchase both options, it can choose in 2020 whether to invest
nothing, Β£15000 for the plant or Β£15000 for the plant + Β£10000 for the R&D if it delays
building the plant production will start in 2020)
e. Finally, suppose the firm could lobby to ensure that the law is enacted. If it does so, there
is no point in the other options, since there would be no uncertainty about the outcome (the
law would be in force). Assuming that the firm could still choose whether or not to invest in
R&D in 2020 if and only if it had invested in building the plant in 2019, how much would it be
willing to pay to guarantee that the law was enacted?
2. Imagine that at some future date, the High-speed railway operated by HS2 PLC. Will actually start
running. As of that date, HS2 PLC has 100,000 shares outstanding. Earnings will be Β£1,500,000 at the
end of year 1 and Β£2,400,000 at the end of year 2. An investment outlay of Β£600,000 at the end of
year 1 has already been decided upon. SBCH is all-equity financed with a required rate of return of
16%. The firm will be liquidated after 2 years. Assume that the firm operates in a world with perfect
capital markets. The firm’s policy is to pay out any surplus cash as dividends.
a. What is the current (year 1) share price of SBCH stock?
b. HedgeTrim Ltd. owns 10% of SBCH and wants an income from the firm of Β£45,000 at the
end of year 1. Show how they can achieve this (without a change in the firm’s dividend
policy). What percentage of the firm will they own after the end of year 1 following this
c. How can HedgeTrim obtain the same income as in part b through changing the current
dividend policy of HS2 PLC? How many shares will HS2 PLC have outstanding at the end of
year 1 under the new policy? What percentage of the firm will HedgeTrim own at that time?
3. A private investor is interested in taking over the Hinckley Point C reactor. The revenues of
operating the plant are determined by the electricity demand (a random parameter 𝝎 distributed
uniformly on [0, 1]) and by the quality of nuclear fuel 𝒅 provided by an overseas supplier. The
revenue function is πŽπ’…, the cost of fuel quality is
and the supplier’s outside option is 𝑼̅ > 𝟎. The
investor needs to specify a contract paying the supplier an amount 𝝅 (if the reactor produces
revenue 𝑹, the investor gets 𝑹 βˆ’ 𝝅 and the fuel supplier gets 𝝅. Suppose, moreover, that the fuel
supplier has to accept or reject the contract before observing 𝝎, but chooses the fuel quality after
observing it.
a. First assume that the investor can observe the revenue R but cannot separately
observe 𝒅 or 𝝎. You may assume that the contract takes the form 𝝅 = πœΆπ‘Ή where a
is a (not necessarily positive) parameter. Find the fuel supplier’s optimal quality as a
function of a, π‘ˆΜ… and R, and use this to compute the value of a that maximises the
investor’s expected utility. Also, find the optimised expected value of the reactor as
a function of π‘ˆΜ….
b. How (if at all) would your answer differ if the fuel supplier observed w before
accepting or rejecting the contract? (you should set up the problem, but do not have
to solve it explicitly).
c. Now suppose that the investor can choose a contract that depends on w (𝝅 = 𝜢𝝎)
or on d (𝝅 = πœΆπ’…) but not both. In other words, they must pay off the fuel supplier
before observing the value of revenue R. As before, the fuel supplier accepts or
rejects the offer before observing w. Which would the investor prefer to observe?
On Q1:
a. If the firm invests in the plant in 2019, costs are incurred in 2019 and production starts
in 2020, regardless of whether the law passes.
b. If the firm purchases (pays for) the R&D option in 2019, it will be exercised (if at all)
and the extra investment made in 2020. This will only affect costs starting from 2021.
c. If the firm only has an investment option, it will pay for the option in 2019, decide
whether to exercise it (and pay the investment cost) in 2020 and start production in
d. If the firm chooses to buy both options, it will pay for them in 2019, make the exercise
decision (a choice among three different courses of action) once it knows whether the
law has passed – in 2020 – and pay the investment cost(s) and start producing in 2021.
e. If the law is enacted, demand will shift as in the rest of the question, but R&D
investment may still be profitable. Investment must be paid for in 2019 affecting
production in 2020 and R&D may or may not be paid for in 2020, affecting cost in 2021.
The firm will behave optimally.
Less confusing than Brexit scenarios, I guess. Sorry again for any confusion. If you are still
unsure, make the most sensible assumption and indicate clearly what it is.
Also on Q1 β€’
Sales given by demand curve are per year.
The firm will have to choose its profit-maximising price. It will do this separately
in each circumstance (each period, taking into account what it knows and what its
costs are).

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