Valuation of Preference Shares and Debt Instruments
Price is the present value of promised cash flows at the yield the market demands for that credit.
A bond or a redeemable preference share is valued as the present value of its promised cash flows, discounted at a yield that reflects market rates and the issuer's credit risk. ICAI Valuation Standard 303 adds that observable market inputs are preferred where they exist, and that the instrument's terms (coupon basis, timing, put or call, lock-in, prepayment, conversion) must be read before choosing a method.
For the SFA exam this is the most purely numerical topic: price from yield, yield from price, duration, and how a callable or convertible feature changes the answer.
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Worked Example: Pricing a Bond
Illustrative. Face value ₹100, 8% annual coupon, 3 years to maturity, market yield for this credit 10%.
1
Cash flow (₹)
8
Discount factor at 10%
0.9091
Present value (₹)
7.27
Time × PV
7.27
2
Cash flow (₹)
8
Discount factor at 10%
0.8264
Present value (₹)
6.61
Time × PV
13.22
3
Cash flow (₹)
108
Discount factor at 10%
0.7513
Present value (₹)
81.14
Time × PV
243.43
Total
Cash flow (₹)
Discount factor at 10%
Present value (₹)
95.03
Time × PV
263.92
| Year | Cash flow (₹) | Discount factor at 10% | Present value (₹) | Time × PV |
|---|---|---|---|---|
| 1 | 8 | 0.9091 | 7.27 | 7.27 |
| 2 | 8 | 0.8264 | 6.61 | 13.22 |
| 3 | 108 | 0.7513 | 81.14 | 243.43 |
| Total | 95.03 | 263.92 |
- check_circlePrice ₹95.03: below par, because the coupon (8%) is below the market yield (10%). A coupon above the yield gives a price above par.
- check_circleMacaulay duration = 263.92 ÷ 95.03 = 2.78 years. Modified duration = 2.78 ÷ 1.10 = 2.53.
- check_circleA 1 percentage point rise in yield should cut the price by about 2.53%. Repricing at 11% gives ₹92.67, a fall of 2.48%; the gap is convexity.
Terms the Paper Uses
- Yield to maturity (YTM)
- The single discount rate that equates the price with all remaining cash flows to maturity.
- Yield to call / yield to put
- The same calculation to the first call or put date, using the call or put price in place of face value.
- Clean vs dirty price
- Dirty (full) price includes interest accrued since the last coupon; clean price excludes it. Quotes are usually clean; the buyer pays dirty.
- Spot and forward rates
- Spot rates discount each cash flow at its own maturity's zero-coupon rate; forward rates are rates implied for future periods.
- Security hierarchy
- Senior secured debt ranks ahead of unsecured and subordinated debt. Lower rank means higher credit risk and a higher yield (VS 303).
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Illustration: a 9% redeemable preference share of ₹100 face, redeemable at par in 5 years, where investors require 11%. PV of five ₹9 dividends plus ₹100 at year 5, at 11%, is about ₹92.61. For bonds that do not trade, the SFA syllabus lists FIMMDA's valuation circulars, covering non-traded rated and unrated, floating-rate, perpetual, deep-discount, callable and puttable bonds, security receipts and pass-through certificates.
How the Valuation Examination Tests This
Expect a bond price from a given yield, the direction of a price move when rates change, a duration figure, or a yield-to-call question for a callable bond. The traps: discounting at the coupon rate instead of the market yield, treating the dirty price as the clean price, using Macaulay duration where the question asks for the percentage price change (that needs modified duration), and pricing a callable bond to maturity when it is likely to be called.
FAQs
How do you value a redeemable preference share?expand_more
Discount the expected dividends and the redemption amount at the return investors require for that risk. Cumulative, participating or convertible features are then valued on top or reflected in the rate.
What is the difference between Macaulay and modified duration?expand_more
Macaulay duration is the weighted average time to receive a bond's cash flows, in years. Modified duration divides it by (1 + yield per period) and gives the approximate percentage price change for a 1 percentage point change in yield.
Why does a bond trade below face value?expand_more
Because its coupon is lower than the yield the market currently requires for that maturity and credit. The discount brings the effective return up to the market yield.
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