You invest $800 in 1 year BraPetro Eurobonds at par yielding 7%. Your broker provides you with 75% financing against these bonds at a 5% interest rate p. a. Bases on $200 of capital and $600 of borrowing at the above terms, and assuming BraPetro repays their bonds as promised at maturity, how much money have you made or lost? What is your return on capital?

Question

You invest $800 in 1 year BraPetro Eurobonds at par yielding 7%.   Your broker provides you with 75% financing against these bonds at a 5% interest rate p. a.   Bases on $200 of capital and $600 of borrowing at the above terms, and assuming BraPetro repays their bonds as promised at maturity, how much money have you made or lost?  What is your return on capital?

BlackTom AI · Accepted Answer

We start by understanding the structure of the trade: you invest 200 of your own capital and borrow 600 secured against the BraPetro bonds, which have a par value of 800 and yield 7% annually.

Step 1: Calculate coupon income from the bonds.
- A 7% yield on par value means the annual coupon is 7% of 800 = 56.

Step 2: Determine the cost of borrowing.
- The loan is 600 at 5% interest, so annual interest due on the loan is 0.05 × 600 = 30.

Step 3: Compute net cash flow from the investment over the year.
- Coupon income: +56
- Interest on loan: -30
- Net cash flow from financing and coupon: 56 − 30 = 26, i.e., you keep 26 of the year’s cash in addition to the return of principal at the end.

Step 4: Consider the final payoff at maturity.
- At maturity, the bonds repay at par value, i.e., you receive 800 from the bonds.
- You must repay the loan principal of 600 at maturity. You also owe interest on the loan for the year, which we’ve already accounted for in step 3 as 30; this interest is typically paid during the year, but if we’re calculating total profit over the year, we can treat it as settled against the year’s coupon cash.
- After repaying the loan principal, you have 800 − 600 = 200 remaining from the bond payoff. Add the net coupon net of interest (26) from step 3 to get total cash after the year: 200 + 26 = 226.
- Your initial out-of-pocket capital was 200, so the overall monetary profit (or loss) over the year is 226 − 200 = 26.

Step 5: Compute return on capital (ROC).
- ROC = profit / initial capital = 26 / 200 = 0.13, i.e., 13%.

Summary of results based on the given terms:
- Net profit over the year: 26 dollars.
- Return on your capital: 13%.

Assumptions noted:
- The 7% yield refers to the annual coupon on the par value of 800.
- The 5% loan rate applies to the borrowed 600 and the interest is accounted for in the annual cash flow.
- At maturity, the bonds are redeemed at par (800), and you can use the 800 to repay the 600 loan principal; the remaining cash plus the net coupon constitutes your total profit for the year.

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