Arundel Partner

The questions in this sample exam are mostly quantitative, but you should also expect some qualitative ones, such as true/false questions, on the exam. I did not include any here, as each true/false will require a different reasoning than others.

Question 1:

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

t = 0 t = 1 t = 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