NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investing in Fixed Income Securities (NISM XXI-A)

Bond Pricing and Yield Measures: How to Calculate Price and YTM

Q: What is the difference between current yield and YTM?

Current yield is annual coupon divided by market price. It ignores the gain or loss at redemption and the timing of cash flows. YTM is the rate that equates the present value of all remaining cash flows to the price, so it includes both.

Q: Why does bond price fall when yield rises?

The coupons are fixed. When the market demands a higher yield, those fixed cash flows are discounted at a higher rate, so their present value is lower. The price must fall to give buyers the higher return.

Q: When is yield to call used?

It is used for callable bonds, where the issuer may redeem early. You treat the call date as the end of the bond and the call price as the redemption amount. Investors often compare it with YTM and take the lower for a premium bond.

Q: Can I calculate YTM by hand in the exam?

Exact YTM needs trial and error. In practice, use the approximate formula or test the given options in the price formula. Knowing whether the bond is at par, premium or discount often narrows the answer.

Updated 11 October 2026 · Fact-checked

A bond's price is the present value of its future coupons and its face value, discounted at the required yield. Yield to maturity is the discount rate that makes that present value equal the market price. Current yield is annual coupon ÷ market price. Yield to call assumes the bond is redeemed at the call date.

Understand Bond Pricing and Yield Measures

A bond promises fixed cash flows: a coupon each period and the face value at maturity. A rupee received later is worth less than a rupee today. So the price of a bond is the sum of all its future cash flows, each discounted back to today.

The discount rate is the required yield, which is what the market demands for a bond of that risk and tenor. If the required yield equals the coupon rate, the bond trades at par. If the required yield is higher than the coupon rate, the price falls below face value (discount). If it is lower, the price rises above face value (premium). Price and yield move in opposite directions.

Yield measures answer the reverse question: given the market price, what return do you earn? Current yield looks only at the coupon income against the price. It ignores the gain or loss when the bond is redeemed at face value and ignores time value. Yield to maturity (YTM) is the single rate that discounts all remaining cash flows to equal the price. It assumes you hold to maturity, the issuer pays in full, and coupons are reinvested at the YTM itself.

A callable bond can be redeemed by the issuer before maturity. Yield to call (YTC) uses the call date and call price in place of maturity and face value. For a premium bond, the lower of YTM and YTC is the more cautious measure, often called yield to worst.

For a discount bond, the order is: coupon rate < current yield < YTM. For a premium bond, the order is reversed: coupon rate > current yield > YTM. For a par bond, all three are equal.

Key formulas to remember

Bond price: P = C ÷ (1+y) + C ÷ (1+y)² + … + (C + F) ÷ (1+y)ⁿ; C = coupon per period, F = face value, y = yield per period, n = number of periods.
Annuity form of price: P = C × [1 − (1+y)⁻ⁿ] ÷ y + F ÷ (1+y)ⁿ; Useful when there are many coupons.
Zero coupon bond price: P = F ÷ (1+y)ⁿ; No coupons. Only one cash flow at maturity.
Current yield: Current yield = Annual coupon ÷ Market price × 100; Uses market price, not face value.
Coupon rate: Coupon rate = Annual coupon ÷ Face value × 100; Fixed at issue. Do not confuse with current yield.
Par, premium, discount rule: Yield = coupon rate → par; yield > coupon rate → discount; yield < coupon rate → premium; Price and yield move in opposite directions.
Approximate YTM: YTM ≈ [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2]; A quick estimate only. The exact YTM needs trial and error or a calculator.
Semi-annual adjustment: Periods = years × 2; yield per period = annual yield ÷ 2; Apply when coupons are paid twice a year.

How to solve Bond Pricing and Yield Measures questions

Use this order for any bond pricing or yield question. It keeps the units consistent and avoids the usual traps.

1Identify what is asked: price, current yield, YTM, or YTC.
2List the face value, coupon rate, market price, years left and coupon frequency.
3Convert the coupon rate into a rupee coupon: face value × coupon rate ÷ frequency.
4Match the yield and the number of periods to the coupon frequency.
5For price: discount each cash flow or use the annuity form, then add the discounted face value.
6For current yield: divide the annual coupon by the market price.
7For YTM or YTC: test a rate, compare the resulting price with the market price, and adjust. For YTC, use the call date and call price.
8Check against the par, premium, discount rule. If the answer disagrees with it, recheck.

Quickest way: Par, premium and discount shortcut

When to use it: Use this when the options are far apart or when a question asks which measure is higher or lower.

Compare the coupon rate with the required yield or price with face value.
If price is below face value, expect YTM above current yield and current yield above coupon rate.
If price is above face value, expect the reverse order.
For one-year or zero coupon bonds, compute directly: P = (F + C) ÷ (1+y) or F ÷ (1+y)ⁿ.
Eliminate options that break the order, then calculate only if two remain.

Common mistakes in Bond Pricing and Yield Measures

Dividing the coupon by face value and calling it current yield.
Coupon rate and current yield sound alike.
Fix: Current yield always uses the market price in the denominator.
Using the annual yield with semi-annual coupons.
Students skip the frequency adjustment.
Fix: Halve the yield and double the number of periods, and use half the annual coupon.
Thinking price rises when yield rises.
Confusing yield with price.
Fix: Remember the inverse relationship. Higher required yield means lower price.
Forgetting to discount the face value.
Focus stays on the coupons.
Fix: The final period has two cash flows: the last coupon and the face value.
Using YTM for a bond that will be called, without checking YTC.
Students assume holding to maturity always.
Fix: Use the call date and call price in the YTC calculation, and compare with YTM for a premium bond.
Believing current yield equals the total return.
It looks like the income return.
Fix: Current yield ignores the capital gain or loss at redemption and time value. YTM captures them.

Worked examples

Example 1

A bond has a face value of ₹1,000, a coupon of 10% paid annually and 2 years to maturity. The required yield is 12%. What is its price, to the nearest rupee?

Show the solution

Annual coupon = 10% × ₹1,000 = ₹100.
Year 1 cash flow discounted: 100 ÷ 1.12 = 89.29.
Year 2 cash flow = 100 + 1,000 = 1,100. Discounted: 1,100 ÷ 1.2544 = 876.91.
Price = 89.29 + 876.91 = 966.20.

Answer: About ₹966. It is below face value because the required yield (12%) exceeds the coupon rate (10%).

Example 2

A bond with face value ₹1,000 and a 9% annual coupon trades at ₹900. What is its current yield, and is the YTM higher or lower than the current yield?

Show the solution

Annual coupon = 9% × ₹1,000 = ₹90.
Current yield = 90 ÷ 900 × 100 = 10%.
The bond trades at a discount, so the holder also gains ₹100 at redemption.
That extra gain pushes the YTM above the current yield.

Answer: Current yield is 10%. The YTM is higher than 10%, because the bond sells at a discount.

Exam tips

Expect direct questions on the order of coupon rate, current yield and YTM for discount and premium bonds.
Read the coupon frequency before you calculate. Many wrong options come from the annual versus semi-annual trap.
For YTM numericals, test the options in the price formula rather than solving from scratch.
Remember that YTM assumes coupons are reinvested at the YTM and the bond is held to maturity.
Negative marking applies on this paper at 10% of the marks for a question, so eliminate options by direction before you guess.

Practice questions from Investing in Fixed Income Securities (NISM XXI-A)

Bond Pricing 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 Pricing and Yield Measures: frequently asked questions

What is the difference between current yield and YTM?

Current yield is annual coupon divided by market price. It ignores the gain or loss at redemption and the timing of cash flows. YTM is the rate that equates the present value of all remaining cash flows to the price, so it includes both.

Why does bond price fall when yield rises?

The coupons are fixed. When the market demands a higher yield, those fixed cash flows are discounted at a higher rate, so their present value is lower. The price must fall to give buyers the higher return.

When is yield to call used?

It is used for callable bonds, where the issuer may redeem early. You treat the call date as the end of the bond and the call price as the redemption amount. Investors often compare it with YTM and take the lower for a premium bond.

Can I calculate YTM by hand in the exam?

Exact YTM needs trial and error. In practice, use the approximate formula or test the given options in the price formula. Knowing whether the bond is at par, premium or discount often narrows the answer.