Calculating Yield to Maturity for an Amortizing Bond

Summary

The document poses a fixed-income valuation problem: how to calculate yield to maturity for a semiannual coupon bond that repays principal in installments before its final maturity. It provides a coupon rate, day-count convention, clean price, valuation date, maturity date, and two scheduled amortization payments. The central issue is how those principal repayments change the cash flows used in the yield calculation.

The questioner outlines the usual approach of converting clean price to dirty price by adding accrued interest and solving for yield from discounted payments. For an amortizing bond, each scheduled principal payment reduces the outstanding nominal, so later coupon amounts depend on the remaining principal; principal repayments also belong in the discounted cash-flow schedule. The document contains no worked solution, computed yield, or explicit treatment of payment-date timing and accrued interest around the amortizations. It therefore identifies the modeling issue but does not establish a numerical result.

Key ideas

• Yield to maturity is found by discounting the bond’s scheduled cash flows to its dirty price.
• An amortization schedule adds principal repayments before final maturity.
• Coupon cash flows must reflect the outstanding principal after each repayment.
• The document poses the calculation but does not provide a solved yield or full cash-flow schedule.

Tags

# Yield to maturity of amortized bond


# Yield to maturity of amortized bond












I have an amortized bond with maturity at 30.04.2023, a semiannual frequency, 10% coupon rate, 30Е/360 day convention, and a clean price of 104.9367. Also, there are two amortization payments: 300 at 30.04.2018 and 300 at 30.04.2021. Assuming that today is 02.12.2019, what is yield to maturity?

My attempt:

I know that the formula is: $$P_{dirty} = \sum_i^N \frac{C/k}{(1+y/k)^i} + \frac{M}{(1+y/k)^N}$$ where y is yield to maturity, M is nominal of bond, N number of payment, k number of payments per year and C is yearly payment.

$P_{dirty}$ can be found using clean price and the accrued amount and then we can express y from this formula. But the question is, how to use it considering amortization payments. How do amortization payments affect C, M, and $P_{dirty}$?

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