GB550 Unit 3 Bond Valuation Example

What the Barge Line's Debt Is Worth: A Unit 3 Bond Valuation of Unsecured and Secured Notes

[Student Name]

Purdue University Global

GB550: Financial Management

Unit 3 Bond Valuation

[Instructor Name]

[Date]

The barge operator, its notes and every price and yield are composite and illustrative; the methods and sources cited are real.

Part 1: Pricing the Unsecured Notes

Inputs. Face value $1,000; coupon 6.125 percent paid semiannually, $30.625 every six months; eight years to maturity, 16 periods; market yield 7.05 percent, 3.525 percent per period.

Formula. Price = C × [1 − (1 + i)^−n] / i + F / (1 + i)^n.

Coupons. 30.625 × [1 − 1.03525^−16] / 0.03525 = $369.69.

Principal. 1,000 / 1.03525^16 = $574.48.

Price. $944.17, or 94.42 percent of face. The 6.125 percent coupon was set when rates were lower, so the notes sell below face until they mature.

Current yield. Annual coupons of $61.25 divided by $944.17 = 6.49 percent, below the 7.05 percent yield to maturity because the current yield ignores the gain from the discount as the notes approach maturity.

Spreadsheet. PV(3.525%, 16, −30.625, −1000).

Part 2: What the Yield Says About Credit

The 7.05 percent yield can be read as a Treasury yield of about 4.35 percent for a similar maturity plus a credit spread of 270 basis points. That spread is what investors charge for the chance that the operator cannot pay. It is consistent with the Unit 1 figures: interest covered 3.47 times and debt at 2.68 times EBITDA place the company in the lower investment-grade or upper speculative-grade range, where spreads of that size are common. Koller et al. (2020) note that spreads reflect both default risk and liquidity, and notes from a mid-sized issuer trade less often than large issues, which adds a little to the spread.

A 270-basis-point spread is the market's own summary of the company's coverage and debt load, expressed as a price.

Bond prices for a real issuer would come from trade data published by FINRA or from a library database; these figures are illustrative.

Part 3: Interest Rate Risk

Rates up one point, to 8.05 percent. Price falls to $888.05, a drop of 5.94 percent.

Rates down one point, to 6.05 percent. Price rises to $1,004.70, a gain of 6.41 percent.

Modified duration. Macaulay duration is 6.39 years, and dividing by 1.03525 gives a modified duration of 6.17, which predicts a change of about 6.17 percent for a one-point move in either direction.

The actual changes straddle the estimate: the price rises more than duration predicts and falls less. That asymmetry is convexity, and it means duration slightly overstates losses and understates gains for large moves. Brealey et al. (2023) describe duration as a first approximation that works best for small rate changes, and the repricing here shows its limits at a full point.

Part 3b: A Wider Spread Instead of Higher Rates

Interest rate risk is not the only way the notes' value can change. If a drought year pushed coverage down and debt toward the covenant, investors might demand a wider credit spread even with Treasury yields unchanged. A 100-basis-point widening has the same arithmetic effect as a one-point rise in rates: the price falls to $888.05, and the market value of the $250.0 million issue drops from about $236.0 million to about $222.0 million. The company would not pay that loss in cash, since the coupon is fixed, but any new unsecured borrowing would cost about 8.05 percent rather than 7.05. That is why the financing choices in Units 9 and 10 pay close attention to coverage in a low-water year: the cost of the next loan depends on how the last bad year looked to lenders.

Part 4: The Secured Equipment Notes

Inputs. Price 99.10 percent of face, $991.00; coupon 5.40 percent paid semiannually, $27.00; five years to maturity, 10 periods.

Solution. Solving 991.00 = 27.00 × [1 − (1 + i)^−10] / i + 1,000 / (1 + i)^10 gives i = 2.805 percent per period, a yield to maturity of 5.61 percent.

Spreadsheet. RATE(10, 27, −991, 1000) × 2.

Comparison. With a five-year Treasury near 4.20 percent, the secured notes carry a spread of about 141 basis points, against 270 for the unsecured notes, a gap of 129 basis points. Most of the gap reflects the barges pledged as collateral: barges hold resale value, so lenders with a claim on specific vessels expect to recover more in a default. The shorter maturity also contributes, since five years of credit risk is less than eight.

What Carries Forward

Market value of unsecured notes: $250.0 million face at 94.42 percent, about $236.0 million.

Market value of secured notes: $110.0 million face at 99.10 percent, about $109.0 million.

Yields for the cost of debt: 7.05 percent unsecured, 5.61 percent secured.

Unit 6 uses these market values and yields to weight the cost of debt. Brigham and Ehrhardt (2020) stress that the cost of debt for capital budgeting is the yield on new borrowing, not the coupon on old debt, which is why the 7.05 percent yield, not the 6.125 percent coupon, carries forward.

References

Brealey, R. A., Myers, S. C., & Allen, F. (2023). Principles of corporate finance (14th ed.). McGraw Hill.

Brigham, E. F., & Ehrhardt, M. C. (2020). Financial management: Theory and practice (16th ed.). Cengage.

Koller, T., Goedhart, M., & Wessels, D. (2020). Valuation: Measuring and managing the value of companies (7th ed.). Wiley.