If a corporation wanted to guarantee its long term costs of financing an investment project, it could:

a.) sell t-bill futures for when the funds were needed
b.) buy t-bill futures for when the funds were needed
c.) sell t-bond futures for when the funds were needed
d.) buy t-bond futures for when the funds were needed

To determine the correct choice, let's first understand what T-bill and T-bond futures are and how they can be used to guarantee the long-term costs of financing an investment project.

T-bill (Treasury bill) and T-bond (Treasury bond) are financial instruments issued by the U.S. Treasury to raise capital. They are considered relatively low-risk investments and are commonly used for hedging purposes.

Futures contracts are agreements to buy or sell an underlying asset (in this case, T-bills or T-bonds) at a predetermined price and date in the future.

If a corporation wants to guarantee its long-term costs of financing an investment project, it needs to ensure a fixed interest rate, which can be achieved through buying or selling T-bill or T-bond futures.

To lock in financing costs, the corporation would enter into a futures contract. By doing so, it would agree to buy or sell T-bill or T-bond futures at a set price at a specified future date. This helps the corporation eliminate the risk of interest rate fluctuations that could increase financing costs.

Now, let's analyze each option:

a.) Sell T-bill futures for when the funds were needed:
Selling T-bill futures means agreeing to sell T-bills at a predetermined price in the future. This action would not help the corporation guarantee its long-term costs since it would be receiving cash in exchange for the T-bills, rather than locking in a fixed interest rate.

b.) Buy T-bill futures for when the funds were needed:
Buying T-bill futures involves agreeing to purchase T-bills at a predetermined price in the future. This action would help the corporation guarantee its long-term costs as it secures a fixed interest rate on the T-bills.

c.) Sell T-bond futures for when the funds were needed:
Selling T-bond futures means agreeing to sell T-bonds at a predetermined price in the future. Again, this action wouldn't help the corporation guarantee its long-term costs as it does not involve locking in a fixed interest rate.

d.) Buy T-bond futures for when the funds were needed:
Buying T-bond futures involves agreeing to purchase T-bonds at a predetermined price in the future. This action would help the corporation guarantee its long-term costs as it allows them to lock in a fixed interest rate on the T-bonds.

Therefore, based on the analysis, the correct choice would be d.) buy T-bond futures for when the funds were needed.