Valuing a Quarterly Coupon Bond with the Correct Discount Periods

Summary

This question concerns valuing a four-year coupon bond purchased at the start of its tenth quarter. The attempted calculation discounts only the remaining six quarterly payments, using a quarterly rate derived from the stated annual discount rate, but produces a value below the stated answer. The response points to two errors: cash flows should be discounted using the relevant yield, and quarterly coupons require discounting every remaining quarterly payment rather than skipping coupon dates.

The discussion illustrates how payment frequency and discount-period alignment affect present value. It does not show the corrected calculation, explain how the quoted annual rate should be compounded, or clarify bond price conventions such as accrued interest. The brief answer therefore identifies likely sources of error but does not fully derive or validate the quoted value.

Key ideas

• Bond valuation discounts each future cash flow using a rate consistent with the relevant yield.
• Quarterly coupons must be included at each remaining payment date.
• The discount period and coupon frequency need to align.
• The response does not provide a full calculation supporting the quoted price.

Tags

# Bond Fair Value


# Bond Fair Value












Im trying to learn bond valuations and working out problems I find online, but I come up with the wrong answer for this one.

Im buying a four year coupon bond for 963.54. The coupon is 5.172% paid quarterly. The bond is offered to me at the beginning of the 10th quarter. Im using a discount rate of 6.9%. I calculate sum the future values

(12.93)/(1.01725)^1 + (12.93)/(1.01725)^2 + ... + (12.93+1000)/(1.01725)^6 = 975.5756342

the answer is 977.97 without much explanation.

Can anyone see what I did wrong?

## Answer by vanguard2k (score 3, accepted)

https://quant.stackexchange.com/a/37214

- You have to discount the future cash flows with your discount rate (= yield)

- The coupon is paid quarterly, yet you discount annually. You will miss all other coupons in your calculation.

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