Forward prices of a generic asset The purpose of these problem is to guide you and introduce you the “no-arbitrage” condition required to compute forward prices. For the following problems, assume the following information: There is an asset A. The price of the asset today, denoted by ?0, is ?0 = $100. The CCIR (yearly) is 6%.

Problem 4: No storage cost, and a convenience yield. Assume that asset A has no storage cost and there is a convenience yield. Every 9 months, the holder of the asset receives 5% of the asset value as a payment (you can call that a dividend). Suppose that someone is willing to enter a forward contract of Asset A for delivery in one year from now at ?0,1 = $115

a. Suppose that in 9 months, the price of the asset is ? 9 12 . How much money does one receive at t=9 months from holding the asset? Assume you have ? shares.

b. If you spend the dividend to buy more of asset A, how many more units of A can you buy (assume you can buy fractions of the asset)

c. We don’t know a priori if there is a mispricing. Compute an arbitrage portfolio to exploit the potential mispricing. Hint: start by borrowing today to buy $100 1+5% units of asset A and reinvest the dividend to buy more of A to get one unit at t=1 year.

d. What would be the forward price that makes the profit in a) zero?

e. Now try to find the general pricing formula. Suppose that the rate is ?, the spot price is ?0 and someone is willing to enter a forward at a forward price of ?0,? for delivery at time t=T. Replicate your portfolio/strategy in a) using this new information. What is the no-arbitrage forward price? Assume that a dividend %? is paid at ?1,?2,?3, … ,?? < T

Use the following information on the supply and demand for oil in the hypothetical country Economica to answer the questions below. Assume that the demand and supply curves are linear. Questions 2a and 3 are worth 10 points. Each part of every other question is worth 5 points.

              Domestic           Domestic

Price ($)      Demand             Supply

60             460                 280

80             440                 320

100             420                 360

120             400                 400

140             380                 440

1. Assume that the world price of oil is $80 per barrel. Assume that Economica is a small country and that Economica imposes a $20 per barrel tariff on imported oil. Calculate the effect of the tariff on

a. Domestic producer surplus

b. Consumer surplus

c. Government tariff revenue

d. Consumption distortion loss

e. Production distortion loss

f. Total efficiency loss

g. Oil imports

2. Suppose that Economica is a large country. The export supply curve is as follows

Price     Quantity

60        60

80       120

100       180

120       240

Assume that Economica imposes a $20 tariff on imported oil. Assume that the world price of oil is initially $80.

a. Graph the import demand and export supply curves

Calculate

b. the price of oil in Economica

c. the price of oil in the Rest of the World

d. Domestic oil production

e. The change in producer surplus

f. The change in consumer surplus

g. Tariff revenue

h. Oil imports

i. the terms of trade effect

j. total deadweight loss

Bonus

k. effect on foreign welfare

l. effect on world welfare

PLEASE ANSWER QUESTION 2. All Parts.

1. Let’s think about a per unit production subsidy. Start with an initial equilibrium price of $5 and quantity of 100 million. Now provide producers with a $1 per unit subsidy. Shade in (the cost of) the subsidy, make up numbers for the new quantity exchanged, the price consumers face (P_c) and the price producers get (P_p). Ideally you can do this without simply copying it from the book... try it over several days until you can.

2. The goal of a subsidy to labor (such as the EITC) is to both raise wages and encourage employment to support low-income families. How does the wage elasticity of demand affect the success of achieving these goals? (That is, are the goals better met if demand for labor is elastic or inelastic?) Illustrate your answer by showing a wage subsidy in two scenarios: relatively inelastic demand for labor and relatively elastic demand for labor. Assume an initial equilibrium of $10 per hour and 100 mn hours of labor employed. Also, keep in mind that the supply curve in the labor market reflects workers (supplying labor) while the demand curve reflects firms (demanding labor).

3. Assume a $1 / pack excise tax is placed on the producers of grapes. This causes the price to rise from $3 / pack to $3.80 / pack and causes quantity demanded to fall from 470 million packs per year to 400 million packs per year.

1. • Illustrate this in a S&D graph
   • What price do the producers get after the tax?
   • What is the tax revenue for the government? (answer in $ and make a bold line around it)
   • What is the price elasticity of demand for grapes? (you will need a calculator)
   • Shade in the lost consumer surplus.

Q1/Imprudential, Inc., has an unfunded pension liability of $678 million that must be paid in 17 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8.7 percent, what is the present value of this liability? (Enter answer in millions. E.g., 100 million goes in as '100'.)

Q2/Assume a bronze sculpture sold in the year 2,010 at auction for a price of $10,424,744. Unfortunately for the previous owner, he had purchased it in year 1,996 at a price of $12,333,689. What was his annual rate of return on this sculpture? (Enter answer in percents, not in decimals.)

Q3/Suppose you are committed to owning a $228,233 Ferrari. If you believe your mutual fund can achieve a 14.76 percent annual rate of return, and you want to buy the car in 10 years on the day you turn 30, how much must you invest today?

Q4/Twenty years ago, you deposited $5,398 into an account. Fifteen years ago, you added an additional $8,009 to your account. You earned 5.68 percent, compounded annually, for the first 5 years and 9.81 percent, compounded annually, for the last 15 years. What is the value of your account today?

Q5/You are expecting to receive $300 at the end of each year in years 3, 4, and 5, and then 500 each year at the end of each year in years 10 through 25, inclusive. If the appropriate discount rate is 6.4 percent, for how much would you be able to sell your claim to these cash flows today?

Q6/You expect to receive 1000 bucks every year at the end of each year, starting in year 7 and ending in year 21. If you expect the rate of return is 10.2 percent, and you invest all your cash flows at the going rate as soon as you receive them, how much money will you have at the end of year 25?

There is a market with an equal number of Type A consumers and Type B consumers. Type A consumers value iphones at $100 and Apple earpods at $30. Type B consumers value iphones at $120 and Apple earpods at $10. Apple cannot identify Type A and Type B consumers and so must charge the same price for all consumers. A) If Apple wants to sell to both Type A and Type B consumers and packages each product separately, what price would Apple charge for iphones? What price would Apple charge for earpods? B) If Apple wants to bundle the two products together, what price would Apple charge for the bundle? C) How much profit per consumer can Apple make from bundling iphones and earpods together relative to selling them separately?

Cassiopeia inc. is currently trading at $100 per share. After examining the stock of Cassiopeia, you have determined that in each 3 month period its price will either increase to 25% or decrease by 20%. The interest rate is 3% every 3 months.

a) A six month European call option on Cassiopeia has an exercise price of $90. What is the value of this call option?

b) What is the value of a six month European put option on Cassiopeia with an exercise price of $90?

c) Verify that put-call parity holds.

d) Now suppose that Cassiopeia pays a dividend equal to $25 in three months. What is the value of a six month American call option on Cassiopeia with an exercise price of $90? Would you ever want to exercise this option early?

Cassiopeia inc. is currently trading at $100 per share. After examining the stock of Cassiopeia, you have determined that in each 3 month period its price will either increase to 25% or decrease by 20%. The interest rate is 3% every 3 months.

a)A six month European call option on Cassiopeia has an exercise price of $90.What is the value of this call option?

b)What is the value of a six month European put option on Cassiopeia with anexercise price of $90?

c)Verify that put-call parity holds.

d)Now suppose that Cassiopeia pays a dividend equal to $25 in three months.What is the value of a six month American call option on Cassiopeia with anexercise price of $90? Would you ever want to exercise this option early?

The market demand curve is P = 90 − 2Q, and each firm’s total cost function is C = 100 + 2q²

(a) (7 points) Suppose there is only one firm in the market. Find the market price, quantity, and the firm’s profit.

(b) (5 points) Show the equilibrium on a diagram, depicting the demand function D (with the vertical and horizontal intercepts), the marginal revenue function MR, and the marginal cost function MC. On the same diagram, mark the optimal price P, the quantity Q, and the average total cost ATC. Illustrate the firm’s profit. Hint: You don’t need to draw the ATC curve.

(c) (5 points) Using the demand function, find the elasticity of demand at the monopoly price and quantity.

(d) (2 points) Verify that the monopoly price and quantity satisfy the monopolist’s rule of thumb for pricing.

The mean selling price of senior condominium in Green Valley over a year was $215,000. The population standard deviation was $25,000. A random sample of 100 new unit sales was obtained

a. What is the probability that the sample mean selling price was more than $210,000?

b. What is the probability that the sample mean selling price was between $213,000 and $217,000?

c. What is the probability that the sample mean selling price was between $214,000 and $216,000?

d. Without doing the calculations, state in which of the following ranges the sample mean is most likely to lie: $213,000–$215,000; $214,000–$216,000; $215,000–$217,000, or $216,000–$218,000.

e. Suppose that, after you had done these calculations, a friend asserted that the population distribution of selling prices of senior condominiums in Green Valley was almost certainly not normal. How would you respond?

The Saunders Investment Bank has the following financing outstanding. What is the WACC for the company?

1. Debt: 50,000 bonds with $1000 par value, a coupon rate of 4.7 percent, and a current price quote of 103.5 (103.5% of par value); the bonds have 20 years to maturity. 200,000 zero coupon bonds with $1000 par value, with a price quote of 17.5 and 30 years until maturity.

2. Preferred Stock: 125,000 shares of 4 percent preferred stock with a current price of $89, and a par value of $100.

3. Common Stock: 2,300,000 shares of common stock; the current price is $55, and the beta of the stock is 1.40.

Market: The corporate tax rate is 40 percent, the market risk premium is 7 percent, and the risk-free rate is 4 percent.