Question 4

Suppose 100,000 kilograms of gold can be obtained from a gold mine during its first year in operation. However, its subsequent yield is expected to decrease by 10% over the previous year’s yield. The gold mine has a proven reserve of 1,000,000 kilograms.

1. a) Suppose that the price of gold is expected to be $60 per gram for the next several years. What would be the present worth of the revenue earned at an interest rate of 12% per annum compounded annually over the next seven years?
2. b) Suppose that the price of gold is expected to start at $60 per gram during the first year, but to increase at the rate of 5% over the previous year’s price. What would be the present worth of the revenue earned at an interest rate of 12% per annum compounded annually over the next seven years?
3. c) Consider part b again, find the net worth of the revenues to be earned in the next 4 years at the end of year 3.

4) You are holding a bond in your investment account, and when you check the account today you find the value of the bond has increased since you first bought it. List all the possible reasons why the price of the bond went up, and explain why these factors would have resulted in a price increase.

5) A company issues two different types of bonds: callable bonds and puttable bonds. The bonds have the same maturity date. If the company went on to perform really well in the future, so that they were viewed by the market as significantly less risky than when these bonds were first issued, which of the bonds would experience the greater change in price? Explain why.

6) A company recently paid out a $4 per share dividend on their stock. Dividends are projected to grow at a constant rate of 5% into the future, and the required return on investment is 8%. If we buy the stock today and hold it for one year, what is our holding period return for that one year?

The price of a zero-coupon bond with maturity 1 year is $943.40. The price of a zero-coupon bond with maturity 2 years is $898.47. For this problem, express all yields as net (not gross) rates. Assume the face values of the bonds are $1000.

1.What is the yield to maturity of the 1 year bond?

2.What is the yield to maturity of the 2 years bond?

3.Assuming that the expectations hypothesis is valid, what is the expected short rate in the first year?

4.Assuming that the expectations hypothesis is valid, what is the expected short rate in the second year ?

5.Assuming the liquidity preference theory is valid and the liquidity premium in the second year is 0.01, what is the expected short rate in the second year?

6.Assuming that the expectations hypothesis is valid, what is the expected price of the 2 year bond at the beginning of the second year?

7.What is the rate of return that you expect to earn if you buy the 2 year bond at the beginning of the first year and sell it at the beginning of the second year?

1. Assume that the functional form for new homes in a community each year is as follows:

Q_d = 1025 – (10*P) + (3*P_e) + (.25*P_r) + (8*Y) + (25*F) - (.75*T)

            And take the following values as constant:

                        P_e = 100 (in thousands of $)

                        P_r = 700 (in dollars per month)

                        Y = 45 (in thousands of $ per year)

                        F = 2.8 (in persons per household)

                        T = 120 (in $ of tax per home per year)

(The demand equation requires variables in the units mentioned for each of the five variables)

Solve for the reduced form linear demand function.

2. Turning to supply, assume that the price of new housing (P), the price of building materials (P_m), the wages of construction workers (W), the price of undeveloped land (P_u), and the level of impact fees they must pay to build a new house (IF) all affect the amount firms are willing to supply new homes. Take the specific functional form to be:

Q_s = 100 + (12*P) – (8*P_m) – (20*W) – (8*P_u) – (10*IF)

And take the following values as constant and given:

P_m = 30 (in thousands of $ per house)

W = 18 (in $ per hour)

P_u = 15 (in thousands of $ per lot)

IF = 4 (in thousands of $ per new house)

(The supply equation requires variables in the units mentioned for each of the four variables)

Solve for the reduced form linear supply function.

3. Using the reduced form Linear Demand & Supply functions you found in problems 1 & 2, solve for the equilibrium price (P) and quantity (Q) in this market. If either does not turn out to be an integer, please round to one decimal point.

4. Mathematically derive an equation that shows how the price of new homes (P) varies with the price of existing homes (P_e). Assume all variables other than P_e are held constant at the values given in problems 1 & 2.

Sam is planning an office party. He has the following utility function for fruit and cheese:

U ( F , C ) = min { 6 F , 2 C }

He has an income equal to $ 50 to spend on cheese and fruit. He prices the fruit and cheese during the first week of October. At this time the price of fruit per pound $ 1 and the price of cheese per pound equals $ 3 .

During the second week of October the price of fruit increased to $ 5 . 5 per pound. If Sam purchases the fruit and cheese at this time what is the magnitude of the income effect of this price change measured in pounds of fruit? Round your answer to the fourth decimal point.

1. Explain why a monopolist’s profit when he price discriminates cannot be less than his profits when he does not price discriminate.

2. The efficiency loss under perfect price discrimination is very high. True or False?

3. Consider a monopolist selling into two markets. Demand in the first market is given by P₁ = 50 - 2Q₁, and demand in the second market is given by P₂ = 70 - 2Q₂. Total cost for the monopolist is 50 - 10(Q₁ + Q₂), so marginal cost is 10.

1. What are the quantities and prices sold in each of the two markets?
2. What condition must hold in order for the monopolist to practice this kind of price discrimination?

The Bradley family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210. The Bradleys’ have a budget of $52,500 for next year. The government limits the number of acres of tobacco that can be planted to 100. The profit from each acre of corn is $300; the profit from each acre of tobacco is $520. The Bradleys’ want to know how many acres of each crop to plant in order to maximize their profit.

a. Formulate the linear programming model for the problem and solve.

b. How many acres of farmland will not be cultivated at the optimal solution? Do the Bradleys use the entire 100-acre tobacco allotment?

c. The Bradleys’ have an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for $110 per acre. Should the Bradleys’ lease the land at that price? What is the maximum price the Bradleys’ should pay their neighbor for the land, and how much land should they lease at that price?

d. The Bradleys’ are considering taking out a loan to increase their budget. For each dollar they borrow, how much additional profit would they make? If they borrowed an additional $1,000, would the number of acres of corn and tobacco they plant change?

6.

The firm Kappa has just decided to undertake a major new project. As a result, the value of the firm in one year’s time will be either $120 million (probability 0.25), $250 million (probability 0.5) or $360 million (probability 0.25). The firm is financed entirely by equity and has 10 million shares. All investors are risk-neutral, the risk-free rate is 4% and there are no taxes or other market imperfections.

(a) What is the value of the company and its share price?

Kappa decides to issue debt with face value $146 million due in one year and use the proceeds to repurchase shares now. Assume now that bankruptcy costs will be 15% of the value of the firm’s assets in the event of default on debt repayment.

(b)What is the value of the debt now? What is its yield?

(c) What is the expected value of the firm and the price per share? How many shares will be repurchased?

(d) Assume Kappa decides instead to issue debt with face value $100 million due in one year and repurchase shares with the proceeds. What is the firm’s value now? Why? What is its share price?

(e) Explain how the presence of corporate taxes would influence Kappa’s restructuring decision. (100 words)

(Total = 25 marks)

You purchased 100 shares of IBM common stock on margin at $151 per share. Assume the initial margin is 50%, and the maintenance margin is 30%. Below what stock price level would you get a margin call?

Assume the stock pays no dividend; ignore interest on margin.

Round your answer to the nearest cent (2 decimal places).