Question 1:

Consider a project with the following risk-free cash flows:

t = 0t = 1t = 2

-40 20 25

Suppose that one year zero-coupon bonds yield 6% and two year zero-coupon bonds yield 8%.

1a) Find the NPV of the project.

20/(1+6%)+25/(1+8%)^2-40=0.3014

1b) Describe the tracking portfolio for this project.

FV=25 and 20

1c) Describe how you could finance the project to make arbitrage profits at t = 0 (i.e., a sure cash inflow at t = 0 without any future obligation). Please be explicit about what assets you would invest in, how much each would cost at t=0, and what each would pay at t=1 or t=2. (Hint: You will have to consider investing in the project and a portfolio at the same time).

Short sell bond by 40.3014, 18.8679 and 21.4335

1d) Suppose now that instead of the zero coupon bonds described above, there are two risk-free bonds in the market (Bond A and Bond B) that can be described as follows:

a) Bond A pays a $10 coupon at t=1 and matures at t=2 when the bondholders will receive $110. Today (i.e., at t=0) the market price of the bond is Ba = $104.743.

b) Bond B pays a $20 coupon at t=1 and also matures at t=2 when the bondholders will receive $95. Its price today is Bb=$100.790.

Calculate the NPV of project X. (Hint: Note that the interest rates in the economy may have changed. To solve this question, you will need to form a tracking portfolio of the project).

Question 2:

A lot is suitable for either six or nine condominium units. Assume:

• Risk free rate is 10%

• Per unit construction costs (now or next year):

$100,000 for building with six units

$110,000 for building with nine units

• Assume that construction does not take any time; i.e., if we decide to build (either now or next year), we can do so and sell the condos immediately

• Current price of each unit is $140,000

• Per year rental rate is $10,000 per unit (to be received at the end of the year)

• Next year, if market conditions are:

Favorable, condos sell for $186,000

Unfavorable, condos sell for $116,000

2a) Suppose we decide to build this year and sell immediately. Should we build six or nine units? What is the value of the lot given that we build this year?

6*(140-100)=240 9*(140-110)=360 build 9 units

2b) Suppose we decide to wait and make the construction decision next year. Calculate the value of the lot now.

2c) Suppose that as in part a, we decide to build today, but we do not sell immediately. Instead, we rent out the condos for a year, and sell them next year. How does the value of the lot change relative to your answer in part a? Please answer without doing any calculations.

Question 3:

A gold mine will produce all of its output two years from now. The mine has a reserve of 100 pounds of gold. The gold can be extracted at no cost and sold in year 2. We have the following data: • The two-year forward price of gold is $10,000 per pound today. • In year 2, gold price will be either $14,000 per pound, or $8,000 per pound. • The one-year risk-free rate is 10%. The risk-free rate will remain at 10% next year too.

3c) Now suppose that there is some uncertainty about the reserves of the mine. The mine’s reserves are either 100 pounds or zero, with each outcome equally likely. In year 1, we will learn whether the reserves are 100 pounds or zero. We receive an offer today for the mine that is conditional on the reserves. The bidder offers $1.1 million if reserves prove to be 100 pounds, but only $55,000 if the reserve turns out to be zero. The...