Term Structure breakeven logic

Bird is evaluating two US Treasury instruments. The first is a newly issued 7.00% coupon bond with a 5-year maturity issued at a price of $101.15 ($100.00 face value) with a yield to maturity of 6.72%. The second is newly issued zero-coupon bond with a 5-year maturity issued at a price of $71.30 ($100.00 face value) with a yield to maturity of 7.00%. Current US Treasury spot rates and extrapolated forward rates are provided in Exhibit 1. Bird expects that the future path of interest rates will follow that which is implied by the forward curve.

Using the information provided in Exhibit 1 and assuming that Bird’s interest rate expectation materializes, the forward rate at which an investor would be indifferent to purchasing the US Treasury zero coupon note today or one year from today is closest to:

1. 8.02%.
2. 7.02%.
3. 11.10%.

Can someone help me understand what the question means and why the answer is 8.02% ??

The investor has 2 choices here:

  1. Buy the 5 year spot today OR
  2. Invest at 1 year spot and then reinvest at the then current 4 year spot

Under option 1, I earn a rate of r(5) = 7 %; under option 2, I invest for 1 year at r(1) = 3%, but then I need to reinvest at the 4 year spot rate 1 year from today = f(1,4) = 8.02 %. Under both approaches, the accumulated value will be identical.

P.S. I love your user name!! :laughing: