Strategic Financial Management · Equity and Bond Valuation and Evaluation of Performance

Bond Valuation and Yield Measures for CMA Final

Updated 11 October 2026 · Fact-checked

Bond valuation finds a bond's price by discounting its coupons and redemption value at the investor's required return. Yield measures work backwards: given the price, they find the return. To solve a question, list the cash flows, discount them, and for YTM use trial rates with interpolation or the approximate formula.

Understand Bond Valuation and Yield Measures

A bond is a promise to pay fixed interest (the coupon) at regular intervals and to repay the face value at maturity. Its worth to you today is the present value of those promised cash flows. You discount them at the return you require, which depends on the risk of the issuer and on market interest rates.

A zero-coupon bond pays no interest. It is issued at a deep discount and repaid at face value. Its price is just the face value discounted for the number of years left, so there is only one cash flow to handle.

Price and yield move in opposite directions. When the required return rises above the coupon rate, the bond sells at a discount. When it falls below the coupon rate, the bond sells at a premium. When the two are equal, the price equals face value. As maturity approaches, the price moves towards face value.

Yield measures answer different questions. Current yield looks only at the annual coupon income against the price. Yield to maturity (YTM) is the single discount rate that equates the present value of all cash flows to the market price. Yield to call (YTC) does the same, but assumes the issuer redeems at the call date and call price. Realised yield (realised compound yield) measures what you actually earned, given the rate at which you reinvested the coupons.

YTM assumes you hold to maturity, the issuer does not default, and coupons are reinvested at the YTM itself. That last assumption is rarely true, which is why realised yield exists.

Key rules to remember

Price of a coupon bond: P = Σ C ÷ (1 + r)^t (t = 1 to n) + M ÷ (1 + r)^n = C × PVAF(r, n) + M × PVF(r, n); C = coupon per period, M = maturity (redemption) value, r = required return per period, n = number of periods.
Price of a zero-coupon bond: P = M ÷ (1 + r)^n; No coupons. The YTM is r = (M ÷ P)^(1/n) − 1.
Current yield: Current yield = Annual coupon ÷ Current market price × 100; Ignores the gain or loss at redemption and the time value of money.
Approximate YTM: YTM ≈ [C + (M − P) ÷ n] ÷ [(M + P) ÷ 2]; Quick estimate. Use it as the starting rate for trial and error, or when the question asks for an approximation.
YTM by interpolation: YTM = r1 + [(P1 − P) ÷ (P1 − P2)] × (r2 − r1); P1 and P2 are the bond values at the lower rate r1 and the higher rate r2. P is the market price, and it must lie between P1 and P2.
Yield to call: P = Σ C ÷ (1 + r)^t (t = 1 to k) + Call price ÷ (1 + r)^k; k = number of periods to the call date. Solve for r exactly as for YTM.
Realised compound yield: r = (Terminal value ÷ P)^(1/n) − 1; Terminal value = coupons compounded at the reinvestment rate to the end of the holding period + sale or redemption price.
Semi-annual bonds: Coupon per period = Annual coupon ÷ 2; periods = 2n; discount rate per period = annual rate ÷ 2; Follow the question's convention for annualising, usually multiplying the half-yearly rate by 2.

How to solve Bond Valuation and Yield Measures questions

Use this sequence for any bond question. It keeps your working clean and lets the examiner award method marks even if arithmetic slips.

1Write down the face value, coupon rate, price (if given), years to maturity, payment frequency and redemption value. Note whether redemption is at par, premium or on a call date.
2Compute the coupon in rupees: coupon rate × face value, not × price.
3Decide what is unknown: price (given a required return) or yield (given a price).
4For price, discount each cash flow with PVAF for the coupons and PVF for the redemption value, using the same rate and the same number of periods.
5For YTM, find the approximate YTM first. Test two rates on either side of it, compute the bond value at each, then interpolate.
6For current yield, divide the annual coupon by the market price. For YTC, replace maturity with the call date and the redemption value with the call price. For realised yield, compound the coupons first.
7State the conclusion in words: whether the bond is at a discount or premium, and whether to buy if the question asks. Compare intrinsic value with market price: buy if value is higher.

Quickest way: Approximate YTM first, then two trial rates

When to use it: Use this when you must find YTM or YTC in a numerical question and time is short. It saves you from random guessing of discount rates.

Calculate the approximate YTM using [C + (M − P) ÷ n] ÷ [(M + P) ÷ 2].
Round it to the nearest whole percent and use that and the next whole percent as your two trial rates, so that the market price falls between the two values.
If the price is below face value, the YTM must be above the coupon rate. If the price is above face value, it must be below the coupon rate. Use this as a check on your trial rates.
Compute the bond value at both rates, then interpolate. Keep the interpolated answer to two decimals.

Common mistakes in Bond Valuation and Yield Measures

Calculating the coupon as coupon rate × market price.
Students see a price in the question and apply the percentage to it.
Fix: The coupon is always coupon rate × face value, unless the question says otherwise. Compute it in rupees on the first line.
Using the same rate and years for half-yearly bonds without adjusting.
The annual layout from the annual bond problems is copied automatically.
Fix: For semi-annual payments, halve the coupon and the rate and double the periods. Then annualise as the question requires.
Forgetting to discount the redemption value, or discounting it with the annuity factor.
The coupons and the maturity payment look like one stream.
Fix: Use PVAF for the coupons and PVF for the one-time redemption value. Write them as two separate lines.
Confusing current yield with YTM and treating the current yield as the return on the bond.
Both are percentages worked out from the price and both involve the coupon.
Fix: Current yield ignores gain or loss at maturity and time value. YTM includes both. A discount bond has YTM above current yield, and a premium bond has YTM below it, when held to maturity.
Interpolating with a price that is not between the two trial values.
The trial rates are chosen without checking the direction of the price relationship.
Fix: Check the direction first. If the computed value at your higher rate is still above the market price, raise the rate again until the market price is bracketed.
Using call price as maturity value but keeping the original number of years in yield to call.
Students change one input and forget the other.
Fix: For YTC, change both: the redemption amount becomes the call price and the time becomes the years to the call date.

Worked examples

Example 1

A bond of face value ₹1,000 carries a 10% annual coupon and is redeemable at par after 5 years. Investors require a return of 12%. (a) Find the value of the bond. (b) The bond trades at that value. Find its current yield and say whether it sells at a discount or premium.

Show the solution

Annual coupon = 10% × ₹1,000 = ₹100.
PVAF(12%, 5) = [1 − 1.12^-5] ÷ 0.12 = 3.6048. PVF(12%, 5) = 1 ÷ 1.12^5 = 0.5674.
PV of coupons = ₹100 × 3.6048 = ₹360.48.
PV of redemption value = ₹1,000 × 0.5674 = ₹567.43 (using the more precise factor 0.567427).
Value of bond = ₹360.48 + ₹567.43 = ₹927.91, about ₹927.90.
Current yield = ₹100 ÷ ₹927.90 × 100 = 10.78%.
The required return (12%) exceeds the coupon rate (10%), so the bond sells at a discount to face value.

Answer: (a) Value ≈ ₹927.90. (b) Current yield ≈ 10.78%. The bond sells at a discount because the required return is higher than the coupon rate.

Example 2

(a) A 9% annual-coupon bond of face value ₹1,000, redeemable at par after 4 years, is priced at ₹920. Find its YTM. (b) A 5-year zero-coupon bond of face value ₹1,000 is priced at ₹600. Find its YTM.

Show the solution

(a) Annual coupon = ₹90. Approximate YTM = [90 + (1,000 − 920) ÷ 4] ÷ [(1,000 + 920) ÷ 2] = 110 ÷ 960 = 11.46%.
Try 11%: PVAF(11%, 4) = 3.1024 and PVF = 0.6587. Value = 90 × 3.1024 + 1,000 × 0.6587 = 279.22 + 658.73 = ₹937.95.
Try 12%: PVAF(12%, 4) = 3.0373 and PVF = 0.6355. Value = 90 × 3.0373 + 1,000 × 0.6355 = 273.36 + 635.52 = ₹908.88.
The market price ₹920 lies between ₹937.95 and ₹908.88.
Interpolate: YTM = 11% + [(937.95 − 920) ÷ (937.95 − 908.88)] × 1% = 11% + (17.95 ÷ 29.07) × 1% = 11% + 0.62% = 11.62%.
(b) Zero-coupon: YTM = (M ÷ P)^(1/n) − 1 = (1,000 ÷ 600)^(1/5) − 1 = 1.6667^0.2 − 1.
1.6667^0.2 = 1.1076 approximately, so YTM = 10.76%.

Answer: (a) YTM ≈ 11.62%. (b) YTM of the zero-coupon bond ≈ 10.76%.

Exam tips

In MCQs, use the price relationship to eliminate options: a bond at a discount has YTM above its coupon rate, and a premium bond has YTM below it.
For YTM questions in the written section, show the approximate YTM, the two trial values and the interpolation. Marks are given for method.
Read the redemption terms carefully. Redemption at a premium, or a call date earlier than maturity, changes M and n.
Check whether the question says annual or half-yearly interest and whether it wants the YTM annualised. Write your convention in one line.
End with a decision if the question hints at one: compare intrinsic value with market price and say buy, hold or avoid.

Practice questions from Equity and Bond Valuation and Evaluation of Performance

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 the annual coupon divided by the current price. It ignores any gain or loss at redemption and the timing of cash flows. YTM is the discount rate that makes the present value of all coupons and the redemption value equal to the price, so it captures both.

How do I calculate the YTM of a bond in the exam?

First compute the approximate YTM with the formula [C + (M − P) ÷ n] ÷ [(M + P) ÷ 2]. Then value the bond at two rates around that estimate and interpolate to match the market price. For a zero-coupon bond, use (M ÷ P)^(1/n) − 1 directly.

How is a zero-coupon bond valued?

It is the present value of the single redemption amount: P = M ÷ (1 + r)^n. There are no coupon cash flows, so no annuity factor is needed. The lower the required return and the shorter the time left, the higher the price.

Why does bond price fall when yield rises?

The bond's coupons and redemption value are fixed. When the required return rises, those fixed amounts are discounted at a higher rate, so their present value falls. A fall in the required return does the opposite.