Finance Problem Set 2 Questions (2015)

Problem Set 2

1.

The money supply in Leutonia is $5 billion, and the public holds no cash. The Leutonian Central Bank decides that it wants to double the money supply. It is considering an open market operation. The required reserve ratio in the country is 10%, and banks hold no excess reserves.

Should the Central Bank buy or sell bonds? Explain.

How many dollars’ worth of bonds should the Central Bank buy or sell? Show your calculations.

If banks do hold excess reserves, and the public does hold some cash, would the total increase or decrease in the money supply be higher or lower than the figure the Central Bank wants? Explain your answer.

2.

Suppose the Fed decides to sell $3 billion in Treasury bonds. Assume that the reserve requirement is 5%, banks hold no excess reserves, and the public holds no cash.

What is the total increase or decrease in the money supply which would result from the Fed’s action? Explain your answer, and show your calculations.

3.

We saw in lecture that banks are currently holding a lot in excess reserves, thereby increasing total reserves held in the banking system. Explain whether and how the Fed could decrease the level of bank reserves in the system, while leaving the money supply unchanged.

4.

Find the PV of a stream of payments lasting 4 years. Each payment is for $300, and the discount rate is 5%. The payments are all received at the end of the year, starting with the first payment, received exactly one year from the present. Show your work.

5.

Find the PV of the following perpetuity:

Yearly payment = $5,000 (received at the end of each year)

Discount rate = 8%

Show your work.

6.

After graduation from Harvard Extension, you decide to stay in the Cambridge area and start your own business. You think you see a couple of opportunities.

Knowing first-hand the pressure Harvard students are under, you consider opening a business that allows them to let off steam and get rid of their aggression: A paintball center right in The Square.

The cost of the project would be $250,000, payable up front, while revenues are expected to be $13,000 per year, forever. Assume profits are always received at the end of the year, and the only cost of the project is its acquisition price, $250,000, payable immediately.

a.

If the rate of return on comparable projects is 4%, is this project worthwhile? Show your calculations.

b.

What is the project’s internal rate of return (IRR)? Show your calculations.

You are also considering a second business opportunity: Supplying fish, fresh from the bottom of the Charles River, to Harvard Dining Services, for the next three years. For this, they will pay you $35,000 immediately. You figure it will cost you $14,000 a year in supplies to provide this culinary joy.

So, the revenue and costs of the project can be summarized as follows:

Immediate and only revenue: $35,000

Costs in Year 1: $14,000

Costs in Year 2: $14,000

Costs in Year 3: $14,000

c.

Find this project’s internal rate of return (IRR). Show your calculations.