Using Yield to Maturity to Discount Bond Cash Flows

Summary

The note explains how a bond’s coupon rate and yield to maturity (YTM) relate to its market price. It values a ten-year bond by discounting its annual coupon payments and redemption value at a 4% yield. Since the 3% coupon is below that yield, the calculated price is below the 1,000 face value; buyers pay less so the bond’s cash flows can offer the required return.

This illustrates the standard present-value method for a fixed-rate bond. YTM can serve as the discount rate when comparing bonds with matching currency, maturity, credit risk, and cash-flow conventions, but it is not a universal rate for every bond with similar features. The calculation assumes the stated payments and redemption occur as scheduled and uses annual compounding. YTM is also a single rate summarizing cash flows, and its interpretation as an investment return depends on assumptions such as holding to maturity and reinvesting coupons at that yield.

Key ideas

• Bond price is the present value of coupon payments and redemption value discounted at the yield to maturity.
• When a bond’s coupon rate is below the required yield, its price is below face value under the stated assumptions.
• YTM is a useful discount rate for comparing bonds with similar risk and cash-flow characteristics.
• The YTM return interpretation depends on assumptions about holding period and coupon reinvestment.

Tags

# Yield to maturity as discount rate


# Yield to maturity as discount rate












Assume that face value of a bond is equal to 1000. The coupon rate is 3% and yield to maturity is 4%.How can we correlate coupon rate and YTM in order to explain the state of current bond price. (Maturity 10years-Redemption value is 1000).

My approach: $P_0=r C a(n,YTM) + \frac{P}{(1+YTM) ^{n}}= 0.03 * 1000 a(10,0.04) + \frac{1000}{(1+0.04) ^{10}}= 918.88 $ $.

The yield to maturity or equivalent the return that investors expect from the bond is 0.04. The bond price is less than the face value beacuse the coupon rate is 0.03. Investors are not interested in buying the bond at 1000 since they can earn 0.04 from a bond with the same characteristics and price. So the Market squizzes the price to 918.88

Can we generalize that YTM is the discount rate for bond with same duration and characteristics(coupon rate and risk)?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.