Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $1,000, compounded semi-annually, and the current date is April 15, 2022.

Company (Ticker) Coupon Maturity Latest Price Last Yield EST Spread
IOU (IOU) 7.2 April 15, 2032 1,089.6 ? 468

What is the equivalent Government Bond Yield?

Hint, calculate first the Yield to Maturity of IOU bond.

Question

Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $1,000, compounded semi-annually, and the current date is April 15, 2022.

Company (Ticker)	Coupon	Maturity 	Latest Price	Last Yield	EST Spread
IOU (IOU)	7.2	April 15, 2032	1,089.6	?	468

What is the equivalent Government Bond Yield?

Hint, calculate first the Yield to Maturity of IOU bond.

BlackTom AI · Accepted Answer

Yield to maturity (nominal, compounded semi‑annually) of the IOU bond is 6.00%, so subtracting the quoted spread of 468 basis points (4.68%) gives the equivalent government bond yield 6.00% − 4.68% = 1.32%.

1) Relevant knowledge points
- Coupon rate 7.2% on $1,000 face means annual coupons $72, paid semi‑annually => $36 each period.
- Ten years to maturity with semiannual periods => 20 periods.
- Price = $1,089.60; solve PV = coupon annuity + redemption value to get the semiannual yield r; nominal annual YTM = 2·r.
- EST Spread = 468 basis points = 4.68% (spread over government yield). So Government yield = YTM − spread.

2) Step‑by‑step reasoning and calculations
- Set up the present value equation:
  1,089.60 = 36 * a_angle_20@r + 1000 / (1 + r)^20
- Test r = 3.00% (semiannual). Compute annuity factor and redemption PV:
  (1.03)^20 ≈ 1.806111234
  a_angle_20@3% = (1 − (1.03)^−20) / 0.03 = (1 − 1/1.806111234) / 0.03 ≈ 0.446325 / 0.03 ≈ 14.8775
  PV(coupons) = 36 * 14.8775 ≈ 535.59
  PV(redemption) = 1000 / 1.806111234 ≈ 553.68
  Total PV ≈ 535.59 + 553.68 = 1,089.27 ≈ quoted price 1,089.60 (rounding explains tiny difference).
- Therefore r ≈ 3.00% per semiannual period, so nominal annual YTM (semiannual compounding) = 2 × 3.00% = 6.00%.

3) Convert spread and compute government yield
- EST Spread = 468 bps = 4.68%.
- Government yield = YTM − spread = 6.00% − 4.68% = 1.32%.

4) Why the correct answer is correct
- The price above par implies YTM < coupon rate; solving the PV equation gives YTM = 6% (nominal, semiannual). Using the given spread over government yields, subtracting 4.68% yields 1.32%, matching the calculation.

5) Why other choices are incorrect
- 6% is the bond’s YTM, not the government yield. 3% is the semiannual rate, not an annual government yield. 6.39%, 2.57% are not consistent with the PV calculation and the given 468 bps spread.

6) Conclusion
- The equivalent Government Bond Yield is 1.32%, which matches the provided correct answer.

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