Question

Consider the following contract, where you agree to pay somebody $200 per year, each year, for five years, beginning one year from now. On the final year of repayment (the fifth year), you are also expected to pay an additional $400 on top of the $200, making your full payment in the fifth year equal to $600. Assume that the interest rate is equal to 8%. Round all answers to two decimal places.

1. What is the Present Value (PV) of the total payments that you will need to make as part of this contract?
2. Suppose that somebody offers you $1,000 today to sign this contract. Would signing this contract yield a positive totally Net Present Value for you?

Suppose that you could buy these contracts from people. You could pay a certain amount of money, and in return, you would own this contract which would make these payments to you.

3. What would we expect the be the market price for these contracts under efficient financial markets? \
Suppose finally that there is a large increase in the Government Budget Deficit due to an increase in Government Spending.
4. What would you expect to happen to long-term interest rates as a result of this increase in the Budget Deficit? Explain your answer using our I-NS figure from class.
5. How would this change in the interest rate affect the market price for these contracts? Explain your answer.

Answer 1

The Present Value of the contract's payments is calculated using a discount rate of 8%, and if the PV is less than the offer of $1,000, it yields a positive Net Present Value. Market price for these contracts equals the PV of future payments and would decrease if long-term interest rates increase due to a higher Government Budget Deficit.

Step-by-step explanation:

To calculate the Present Value (PV) of the total payments for the contract, we must discount each payment at the given interest rate of 8%. The payments are $200 per year for the first four years and $600 in the fifth year. Using the formula PV = P / (1 + r)^n, where P is the payment, r is the interest rate, and n is the number of years, we calculate the present value of each payment and sum them up to get the total PV.

If someone offers you $1,000 today to sign this contract, you need to compare this with the PV of the contract to determine if it yields a positive Net Present Value (NPV). If the PV of the contract is less than $1,000, then you have a positive NPV.

In efficient financial markets, the market price for these contracts would equal the PV of the future payments. As interest rates are a key factor in determining the PV, any change in interest rates would affect the contract prices. If there is a large increase in the Government Budget Deficit leading to higher long-term interest rates, the PV of these future payments would decrease, and therefore, the market price for these contracts would also be expected to decrease.