Estimating Duration for a Bond with Refinancing and Amortization

Summary

The question considers how to estimate the duration of a ten-year, 12% bond that refinances at par after five years and has 20% amortization. The proposed approach discounts the first four coupon payments, treats the fifth-year payment as coupon plus principal, and uses a five-year payment schedule to model the cash flows. This effectively represents the financing as two successive five-year periods.

The calculation produces a lower Macaulay duration than for a comparable ten-year bond without refinancing, reflecting the earlier expected return of principal. The document is a question rather than a complete worked analysis: it does not clarify how the amortization is distributed across the term, what discount rate applies, or precisely how the refinancing and payment schedule interact. Those details are needed to validate the cash flows and duration estimate.

Key ideas

• Expected refinancing can shorten a bond’s weighted average cash-flow timing.
• The proposed method models the financing as two five-year periods.
• Duration depends on the assumed timing and amount of principal repayments.
• The question does not provide enough detail to confirm the amortization schedule or discounting assumptions.

Tags

# Question on bond pricing


# Question on bond pricing












Excuse my naivete, but I have a simple bond math question. I was asked to calculate the duration for a 10 year bond at 12%, with a refinance at year 5 at par, and 20% amortization.

I started by discounting the coupon (12) for years 1-4 and coupon+principal (112) for year 5. I used the excel pmt function (PMT (12, 5, -100, 0, 0)) to find the annual payments and discounted accordingly. So essentially I viewed this as 2 5-year bonds. Does this make sense to you? This yields a Mac duration of ~5.1, compared to a duration of ~6.1 for a 10 year bond at 12% with no refi.

Any insight would be greatly appreciated.

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