Advanced Financial Management · Security Valuation

Bond Valuation and Yield Measures: YTM and Current Yield

Updated 5 October 2026 · Fact-checked

Bond value is the present value of all future coupons plus the redemption amount, discounted at the investor's required return. YTM is the discount rate that makes that present value equal the market price. Find it by trial at two rates and interpolate. Current yield is just annual coupon ÷ market price.

Understand Bond Valuation and Yield Measures

A bond is a promise to pay fixed coupons for some years and then repay the face value. Like any asset, it is worth the present value of the cash you will receive. So you list the cash flows, pick a discount rate, and add up the present values.

The discount rate is the required return (kd) for a bond of that risk. The coupon rate is only a number printed on the bond. It fixes the cash flow. It is not the discount rate. This is the most important idea in the topic.

Price and yield move in opposite directions. If the coupon rate equals the required return, the bond is worth its face value. If the coupon rate is higher, the bond sells at a premium. If it is lower, it sells at a discount. A zero coupon bond pays no coupon, so its value is just the redemption amount discounted back.

Yield measures work the other way round. You know the price and ask what return it gives. Current yield looks only at the coupon income against price. Yield to maturity (YTM) is the full return if you hold to maturity, including the gain or loss between price and redemption value. Yield to call (YTC) is the same calculation, but it assumes the issuer redeems at the call date and call price.

Key rules to remember

Value of a bond: V = Σ [C ÷ (1 + kd)^t] + M ÷ (1 + kd)^n, t = 1 to n; C is annual coupon (face value × coupon rate), M is redemption value, n is years to maturity, kd is required return.
Annuity-factor form: V = C × PVIFA(kd, n) + M × PVIF(kd, n); Use the table factors given in the question. This is the usual exam layout.
Zero coupon bond: V = M ÷ (1 + kd)^n; No coupons, so only one cash flow.
Perpetual (irredeemable) bond: V = C ÷ kd; Use only when the bond never matures.
Current yield: Current yield = Annual coupon ÷ Current market price × 100; Ignores redemption gain or loss and the time value of money.
Approximate YTM: YTM ≈ [C + (M − P) ÷ n] ÷ [(M + P) ÷ 2]; P is current price. A quick estimate and a good starting rate for the exact method.
Exact YTM by interpolation: YTM = L + [(PV at L − P) ÷ (PV at L − PV at H)] × (H − L); L is the lower trial rate and H the higher one. PV at L must be above P and PV at H below P.
Yield to call: Find the rate where C × PVIFA(r, nc) + Call price × PVIF(r, nc) = P; nc is years to the call date. Use the call price instead of M.
Semi-annual coupons: Coupon = C ÷ 2; periods = 2n; rate per period = kd ÷ 2; Effective annual yield = (1 + y ÷ 2)² − 1, where y is the annual nominal yield.

How to solve Bond Valuation and Yield Measures questions

Use this sequence for any bond question, whether it asks for value, yield or a buy decision.

1Write down face value, coupon rate, years to maturity, redemption value (par, premium or discount) and market price.
2Compute the cash flows: annual coupon = face value × coupon rate. Check whether coupons are annual or half-yearly and adjust the rate and periods.
3If the question asks for value, identify kd and discount the coupons and the redemption amount using the given factors.
4If the question asks for YTM, compute the approximate YTM first to choose two trial rates, one just below and one just above.
5Calculate the bond's present value at both rates. The price must fall between the two values. Then interpolate.
6For yield to call, replace maturity with the call date and redemption value with the call price.
7Compare intrinsic value with market price. Value above price means undervalued, so buy. Value below price means overvalued, so avoid or sell.
8State the answer with units and a one-line conclusion.

Quickest way: Approximate YTM first, then two-point check

When to use it: Use when the question asks for YTM and gives PV factor tables, and time is short.

Compute the approximate YTM with [C + (M − P) ÷ n] ÷ [(M + P) ÷ 2].
Round it to a whole percentage and test that rate and the next one that brackets the price.
Check the signs: PV at the lower rate must exceed P, and PV at the higher rate must be below P.
Interpolate once. If the exam only says 'approximate', stop at step 1 and show the working.
For zero coupon bonds there is no table work. Use YTM = (M ÷ P)^(1/n) − 1.

Common mistakes in Bond Valuation and Yield Measures

Discounting cash flows at the coupon rate
The coupon rate is the only rate printed on the bond, so it looks like the natural discount rate.
Fix: Discount at the required return or market yield. Use the coupon rate only to calculate the coupon in rupees.
Leaving out the redemption value
Students discount the coupons and stop, especially in annuity-factor working.
Fix: Always write two lines: coupons × PVIFA and redemption × PVIF. Check the redemption value, which may be at a premium.
Ignoring half-yearly coupons
The word 'half-yearly' sits inside a long case and is missed.
Fix: Halve the coupon and the rate, and double the periods. Report the annual yield as stated in the question.
Treating current yield as YTM
Both are called yields and both use price in the denominator.
Fix: Current yield ignores the gain or loss on redemption. For a discount bond YTM is higher than current yield. For a premium bond it is lower.
Interpolating with the wrong bracket
Both trial rates are chosen on the same side of the price, so the answer lies outside the range.
Fix: Check that one PV is above the price and the other below it before interpolating.
Using maturity details for yield to call
Students reuse the YTM working to save time.
Fix: Use the call year and call price. The cash flows stop at the call date.

Worked examples

Example 1

Case: Riya is considering a ₹1,000 face value bond with a 10% annual coupon. It matures at par in 5 years. She requires a 12% return. The bond is quoted at ₹900. Find its intrinsic value and current yield at intrinsic value, and advise whether she should buy. Given: PVIFA(12%, 5) = 3.6048 and PVIF(12%, 5) = 0.5674.

Show the solution

Annual coupon = ₹1,000 × 10% = ₹100.
PV of coupons = ₹100 × 3.6048 = ₹360.48.
PV of redemption = ₹1,000 × 0.5674 = ₹567.40.
Intrinsic value = ₹360.48 + ₹567.40 = ₹927.88.
Current yield at intrinsic value = 100 ÷ 927.88 = 10.78%.
Compare: intrinsic value ₹927.88 is above the market price of ₹900, so the bond is undervalued.

Answer: Intrinsic value is ₹927.88 and current yield at that value is about 10.78%. Riya should buy at ₹900, because the price is below intrinsic value.

Example 2

Case: A ₹1,000 face value bond with a 10% annual coupon has 5 years left and is redeemable at par. It trades at ₹920. Find the approximate YTM and then the exact YTM by interpolation. Given: PVIFA(12%, 5) = 3.6048; PVIF(12%, 5) = 0.5674; PVIFA(13%, 5) = 3.5172; PVIF(13%, 5) = 0.5428.

Show the solution

Annual coupon C = ₹100; M = ₹1,000; P = ₹920; n = 5.
Approximate YTM = [100 + (1,000 − 920) ÷ 5] ÷ [(1,000 + 920) ÷ 2] = 116 ÷ 960 = 12.08%.
Trial at 12%: 100 × 3.6048 + 1,000 × 0.5674 = 360.48 + 567.40 = ₹927.88, which is above ₹920.
Trial at 13%: 100 × 3.5172 + 1,000 × 0.5428 = 351.72 + 542.80 = ₹894.52, which is below ₹920.
The price lies between the two values, so interpolate.
YTM = 12% + [(927.88 − 920) ÷ (927.88 − 894.52)] × 1% = 12% + (7.88 ÷ 33.36) × 1% = 12% + 0.24% = 12.24%.

Answer: Approximate YTM is about 12.08% and the exact YTM by interpolation is about 12.24%.

Exam tips

Write the cash flow line first (coupon, years, redemption). Examiners award marks for correct inputs even if the arithmetic slips.
Read the redemption terms carefully. Redemption at a premium or discount changes M and the whole answer.
If the question says 'approximate YTM', use the short formula and do not waste time on interpolation.
Add a one-line interpretation: undervalued or overvalued, buy or sell, premium or discount. Case-scenario MCQs often test only this.
Check whether coupons are paid annually or half-yearly, and whether the required return is a nominal annual rate.

Practice questions from Security Valuation

Bond Valuation and Yield Measures in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Bond Valuation and Yield Measures: frequently asked questions

What is the difference between current yield and YTM?

Current yield is annual coupon ÷ current price. It ignores the gain or loss at redemption and the timing of cash flows. YTM includes the coupons, the redemption value and the time value of money, so it is the fuller measure of return.

How do I value a zero coupon bond?

Discount the redemption amount alone. Value = M ÷ (1 + kd)^n. For example, a ₹1,000 zero coupon bond maturing in 4 years at a 10% required return is worth 1,000 ÷ 1.4641 = ₹683.01.

How do I calculate YTM when the exam gives PV tables?

Find the approximate YTM, then test two table rates that bracket the price. Interpolate between the two present values. Always check that the market price falls between them.

When does a bond sell at a premium or discount?

When the required return is below the coupon rate, the bond sells at a premium. When it is above the coupon rate, the bond sells at a discount. When the two are equal, it sells at face value, assuming redemption at par.

How is yield to call different from YTM?

Yield to call assumes the issuer redeems the bond on the call date at the call price. You shorten the period to that date and use the call price in place of the maturity value. The method is otherwise the same as for YTM.