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AFM Paper 3 — AFM Module C — Time Value of Money, Annuities, Bond Valuation & YTM Weightage: 10 to 12 Marks (Core Financial Management Numerical Set) 15 mins study
Bond Valuation: Current Yield, YTM, Duration & Sinking Fund
AFM Paper 3 (AFM Module C — Time Value of Money, Annuities, Bond Valuation & YTM) — 3 Solved Case Sets & Interactive Calculator
Master every Bond Math & Time Value of Money calculation tested in JAIIB AFM Module C: Intrinsic Value of a Bond, Current Yield vs Approximate Yield to Maturity (YTM), Semi-Annual Coupon Adjustment (2n periods at r/2), Bond Theorems (Discount vs Premium convergence to Par), and Sinking Fund / EMI Annuity Factors.
Switch JAIIB Workbook: Depreciation (SLM Bond Valuation: Current Yield Ratio Analysis Retail Banking: Home Loan LTV Slabs
All 4 Workbooks Step 1: Formula & Regulatory Cheat Sheet
Practice Dynamic AFM Paper 3 Case Studies Core Formulas, Accounting Rules & Examiner Traps
| Concept / Metric | Exact Mathematical Formula | Regulatory / Accounting Norm | Common IIBF Examiner Trap |
|---|---|---|---|
| Current Yield (CY) of a Bond | Current Yield (%) = (Annual Coupon Interest / Current Market Price) × 100 | Ignores capital gain/loss at maturity and time remaining to maturity | Never use Face Value in the denominator of Current Yield—always divide Annual Coupon by Current Market Price! |
| Approximate Yield to Maturity (YTM) | YTM ≈ [Annual Coupon + ((Face Value - Market Price) / Years to Maturity)] / [(Face Value + Market Price) / 2] | For a Discount Bond (Price < Par): YTM > Current Yield > Coupon Rate. For a Premium Bond (Price > Par): Coupon Rate > Current Yield > YTM. | If the bond is trading at a Premium (Market Price > Face Value), (Face Value - Market Price)/n is NEGATIVE (annual amortized capital loss)! |
| Semi-Annual Coupon Bond Valuation | Bond Price = ∑ [(C / 2) / (1 + y/2)^t] + [Face Value / (1 + y/2)^(2n)] | Divide annual coupon C by 2, divide annual discount rate y by 2, and double the number of years n to 2n half-years. | Forgetting to double n or halve y in semi-annual bond questions is the most common mistake in JAIIB AFM. |
CASE STUDY SET #1Moderate (IIBF Standard)10 Marks (5 × 2M)
Discount vs Premium Bond Valuation, Current Yield & Approximate YTM
Official IIBF Case Scenario & Financial Data:
A bank’s Treasury Investment Desk evaluates two corporate bonds (Bond X and Bond Y), each having a Face Value (Par Value) of ₹1,000 and a remaining maturity of 5 years:
| Bond Parameter | Bond X (Discount Bond) | Bond Y (Premium Bond) |
|---|---|---|
| Face Value (Redemption Value at Par) | ₹1,000 | ₹1,000 |
| Annual Coupon Rate | 8.00% p.a. (₹80/yr) | 11.00% p.a. (₹110/yr) |
| Current Market Price | ₹900 | ₹1,050 |
| Remaining Years to Maturity (n) | 5 Years | 5 Years |
Question 1.1 • 2 Marks
What is the Current Yield (%) of Bond X and Bond Y respectively?
A Bond X = 8.89%; Bond Y = 10.48%
B Bond X = 8.00%; Bond Y = 11.00%
C Bond X = 9.00%; Bond Y = 10.50%
D Bond X = 8.42%; Bond Y = 10.73%
Correct Answer: Option A — Bond X = 8.89%; Bond Y = 10.48%
Current Yield = (Annual Coupon / Current Market Price) × 100- Step 1: Bond X Current Yield = (₹80 / ₹900) × 100 = 8.888% (8.89%).
- Step 2: Bond Y Current Yield = (₹110 / ₹1,050) × 100 = 10.476% (10.48%).
IIBF Examiner Tip: Notice that for Discount Bond X, Current Yield (8.89%) > Coupon (8.00%); for Premium Bond Y, Current Yield (10.48%) < Coupon (11.00%).
Question 1.2 • 2 Marks
Calculate the Approximate Yield to Maturity (YTM %) of Discount Bond X.
A 10.53%
B 10.00%
C 8.89%
D 11.11%
Correct Answer: Option A — 10.53%
Approx YTM = [Coupon + (FV - Price)/n] / [(FV + Price)/2]- Step 1: Annualized Capital Gain = (₹1,000 - ₹900) / 5 = ₹100 / 5 = +₹20 per year.
- Step 2: Numerator (Total Average Annual Return) = ₹80 (Coupon) + ₹20 (Capital Gain) = ₹100.
- Step 3: Denominator (Average Investment) = (₹1,000 + ₹900) / 2 = ₹950.
- Step 4: Approximate YTM = (₹100 / ₹950) × 100 = 10.526% (10.53%).
IIBF Examiner Tip: Verify Bond X hierarchy: YTM (10.53%) > Current Yield (8.89%) > Coupon Rate (8.00%).
Question 1.3 • 2 Marks
Calculate the Approximate Yield to Maturity (YTM %) of Premium Bond Y.
A 9.76%
B 11.71%
C 10.48%
D 10.00%
Correct Answer: Option A — 9.76%
Approx YTM = [Coupon + (FV - Price)/n] / [(FV + Price)/2]- Step 1: Annualized Capital Loss = (₹1,000 - ₹1,050) / 5 = -₹50 / 5 = -₹10 per year.
- Step 2: Numerator = ₹110 (Coupon) - ₹10 (Capital Loss) = ₹100.
- Step 3: Denominator = (₹1,000 + ₹1,050) / 2 = ₹1,025.
- Step 4: Approximate YTM = (₹100 / ₹1,025) × 100 = 9.756% (9.76%).
IIBF Examiner Tip: If you accidentally add ₹10 instead of subtracting on a premium bond, you get the trap option 120/1025 = 11.71%!
Question 1.4 • 2 Marks
Suppose the investor’s Required Rate of Return (Market Discount Rate) is 10.00% p.a. Given PVIFA(10%, 5 yrs) = 3.7908 and PVIF(10%, 5 yrs) = 0.6209, what is the exact Theoretical Intrinsic Value of Bond X (8% coupon)?
A ₹924.16
B ₹900.00
C ₹950.25
D ₹1,000.00
Correct Answer: Option A — ₹924.16
Intrinsic Value = (Annual Coupon × PVIFA) + (Face Value × PVIF)- Step 1: PV of 5 years of ₹80 Coupons = ₹80 × 3.7908 = ₹303.264.
- Step 2: PV of ₹1,000 Redemption Value at Year 5 = ₹1,000 × 0.6209 = ₹620.900.
- Step 3: Total Intrinsic Value = ₹303.26 + ₹620.90 = ₹924.16.
IIBF Examiner Tip: Since Bond X is trading in the market at ₹900 whereas its intrinsic value at 10% required return is ₹924.16, Bond X is undervalued and is a BUY!
Question 1.5 • 2 Marks
If market interest rates remain unchanged at 10.00% over the next 5 years, how will the market prices of Discount Bond X and Premium Bond Y behave as they approach maturity (Pull-to-Par theorem)?
A Bond X price will rise towards ₹1,000; Bond Y price will fall towards ₹1,000
B Bond X price will fall; Bond Y price will rise
C Both bond prices will remain constant at ₹924.16 and ₹1,037.91
D Both bond prices will rise
Correct Answer: Option A — Bond X price will rise towards ₹1,000; Bond Y price will fall towards ₹1,000
Pull-to-Par Bond Theorem: At maturity (t = N), Bond Price = Face Value (₹1,000)- Step 1: As time to maturity shrinks, the discount on Bond X narrows, pulling its price UP to ₹1,000 at maturity.
- Step 2: Conversely, the premium on Bond Y amortizes, pulling its price DOWN to ₹1,000 at maturity.
IIBF Examiner Tip: Classic Burton Malkiel Bond Theorem tested in both JAIIB AFM and CAIIB BFM.
CASE STUDY SET #2Advanced (High-Yield Numerical)10 Marks (5 × 2M)
Semi-Annual Coupon Bond Pricing, Effective Annual Yield (EAY) & Perpetuity
Official IIBF Case Scenario & Financial Data:
A 10% Coupon Corporate Bond of Face Value ₹1,000 pays interest SEMI-ANNUALLY (on 30th September and 31st March) and matures in 4 years. The market required yield is 12% p.a. compounded semi-annually. Given PVIFA(6%, 8 periods) = 6.2098 and PVIF(6%, 8 periods) = 0.6274.
| Bond Parameter | Annual Basis | Semi-Annual Adjusted Basis |
|---|---|---|
| Face Value | ₹1,000 | ₹1,000 |
| Coupon Payment | 10% of ₹1,000 = ₹100 / yr | 5% of ₹1,000 = ₹50 per half-year |
| Market Discount Yield | 12% p.a. | 6% per half-year |
| Number of Compounding Periods | 4 Years | 8 Half-Years |
Question 2.1 • 2 Marks
What is the Present Value of the 8 semi-annual coupon payments of ₹50 each discounted at 6% per half-year?
A ₹310.49
B ₹303.73
C ₹400.00
D ₹379.08
Correct Answer: Option A — ₹310.49
PV of Semi-Annual Coupons = (C / 2) × PVIFA(y/2, 2n)- Step 1: Semi-annual coupon (C/2) = ₹100 / 2 = ₹50.
- Step 2: Number of half-yearly periods (2n) = 4 × 2 = 8; Half-yearly discount rate (y/2) = 12% / 2 = 6%.
- Step 3: PV of Coupons = ₹50 × PVIFA(6%, 8) = ₹50 × 6.2098 = ₹310.49.
IIBF Examiner Tip: Always convert years to half-years (8) and annual rate to half-yearly rate (6%) before looking up the PV table!
Question 2.2 • 2 Marks
What is the Present Value of the ₹1,000 redemption value and the Total Fair Value of the semi-annual bond today?
A PV of Principal = ₹627.40; Total Bond Value = ₹937.89
B PV of Principal = ₹635.50; Total Bond Value = ₹945.99
C PV of Principal = ₹620.90; Total Bond Value = ₹931.39
D PV of Principal = ₹1,000.00; Total Bond Value = ₹1,310.49
Correct Answer: Option A — PV of Principal = ₹627.40; Total Bond Value = ₹937.89
Total Bond Value = PV of Coupons + [Face Value × PVIF(6%, 8)]- Step 1: PV of Redemption Principal = ₹1,000 × PVIF(6%, 8) = ₹1,000 × 0.6274 = ₹627.40.
- Step 2: Total Fair Value of Bond = ₹310.49 + ₹627.40 = ₹937.89.
IIBF Examiner Tip: Because the required yield (12%) exceeds the coupon rate (10%), the bond trades below ₹1,000 par (at ₹937.89).
Question 2.3 • 2 Marks
What is the Effective Annual Yield (EAY) corresponding to a nominal yield of 12% p.a. compounded semi-annually vs compounded quarterly?
A Semi-Annual = 12.36%; Quarterly = 12.55%
B Semi-Annual = 12.00%; Quarterly = 12.36%
C Semi-Annual = 12.25%; Quarterly = 12.68%
D Semi-Annual = 12.36%; Quarterly = 12.36%
Correct Answer: Option A — Semi-Annual = 12.36%; Quarterly = 12.55%
EAY = [1 + (r / m)]^m - 1- Step 1: For Semi-Annual (m = 2): EAY = (1 + 0.12/2)^2 - 1 = (1.06)^2 - 1 = 1.1236 - 1 = 12.36%.
- Step 2: For Quarterly (m = 4): EAY = (1 + 0.12/4)^4 - 1 = (1.03)^4 - 1 = 1.1255 - 1 = 12.55%.
IIBF Examiner Tip: As compounding frequency m increases, Effective Annual Rate increases!
Question 2.4 • 2 Marks
If the bank also issues a Perpetual Non-Cumulative Preference Share / Consol Bond paying ₹90 annual dividend forever and the market required return is 9% p.a., what is the Present Value of this Perpetuity?
A ₹1,000
B ₹900
C ₹810
D ₹1,090
Correct Answer: Option A — ₹1,000
PV of Constant Perpetuity = Annual Cash Flow (C) / Required Discount Rate (r)- Step 1: Annual Perpetual Cash Flow (C) = ₹90; Discount Rate (r) = 9% = 0.09.
- Step 2: PV of Perpetuity = ₹90 / 0.09 = ₹1,000.
IIBF Examiner Tip: If a perpetuity grows at a constant rate g per year (Growing Perpetuity / Gordon Model), PV = C1 / (r - g).
Question 2.5 • 2 Marks
Using the Rule of 72 and Rule of 69.3, approximately how many years will it take for a Zero-Coupon Deep Discount Bond to double in value at an implicit yield of 9% p.a.?
A Rule of 72 = 8.00 Years; Rule of 69.3 = 8.05 Years
B Rule of 72 = 9.00 Years; Rule of 69.3 = 7.70 Years
C Rule of 72 = 8.00 Years; Rule of 69.3 = 7.70 Years
D Rule of 72 = 6.00 Years; Rule of 69.3 = 6.35 Years
Correct Answer: Option A — Rule of 72 = 8.00 Years; Rule of 69.3 = 8.05 Years
Rule of 72: Doubling Time = 72 / r%; Rule of 69.3: Doubling Time = 0.35 + (69.3 / r%)- Step 1: Rule of 72 = 72 / 9 = 8.00 Years.
- Step 2: Rule of 69.3 = 0.35 + (69.3 / 9) = 0.35 + 7.70 = 8.05 Years.
IIBF Examiner Tip: Don’t forget the "+ 0.35" constant in the Rule of 69.3 formula!
CASE STUDY SET #3Moderate (IIBF Standard)10 Marks (5 × 2M)
Sinking Fund Debenture Redemption, Ordinary Annuity vs Annuity Due & Capital Recovery
Official IIBF Case Scenario & Financial Data:
M/s InfraCon Ltd. has issued ₹500 Lakhs of Debentures redeemable at par at the end of 5 years. To ensure smooth redemption, the company sets up an annual Sinking Fund earning 8% p.a. compounded annually. Given Future Value Annuity Factor FVIFA(8%, 5 yrs) = 5.8666 and Present Value Annuity Factor PVIFA(8%, 5 yrs) = 3.9927.
| Annuity Factor @ 8% p.a. (5 Years) | Factor Value | Application |
|---|---|---|
| FVIFA (8%, 5 Years) — Ordinary Annuity | 5.8666 | Sinking Fund (Target Future Corpus = ₹500 L) |
| PVIFA (8%, 5 Years) — Ordinary Annuity | 3.9927 | Loan Amortization (Present Loan = ₹500 L) |
| Compound Factor (1.08) | 1.0800 | Converts Ordinary Annuity to Annuity Due |
Question 3.1 • 2 Marks
How much must M/s InfraCon Ltd. invest at the END of each year (Ordinary Annuity) into the Sinking Fund so that the accumulated corpus reaches ₹500 Lakhs at the end of Year 5?
A ₹85.23 Lakhs per year
B ₹100.00 Lakhs per year
C ₹125.23 Lakhs per year
D ₹78.91 Lakhs per year
Correct Answer: Option A — ₹85.23 Lakhs per year
Annual Sinking Fund Payment (A) = Target Future Value (FV) / FVIFA(r, n)- Step 1: Target Future Value (FV) at Year 5 = ₹500 Lakhs.
- Step 2: FVIFA(8%, 5 yrs) = 5.8666.
- Step 3: Annual End-of-Year Sinking Fund Installment = ₹500 Lakhs / 5.8666 = ₹85.228 Lakhs (₹85.23 Lakhs).
IIBF Examiner Tip: Because the fund earns 8% compound interest, the company only puts in 5 × ₹85.23L = ₹426.15L of principal, and ₹73.85L comes from interest!
Question 3.2 • 2 Marks
If the company deposits the Sinking Fund installment at the BEGINNING of each year (Annuity Due) instead of at the end of each year, what will be the required annual installment?
A ₹78.91 Lakhs per year
B ₹85.23 Lakhs per year
C ₹92.05 Lakhs per year
D ₹75.00 Lakhs per year
Correct Answer: Option A — ₹78.91 Lakhs per year
FV of Annuity Due = FV of Ordinary Annuity × (1 + r); Therefore Payment (Annuity Due) = Ordinary Payment / (1 + r)- Step 1: FVIFA for Annuity Due = 5.8666 × 1.08 = 6.3359.
- Step 2: Required Annual Beginning-of-Year Installment = ₹500 Lakhs / 6.3359 (or ₹85.228 / 1.08) = ₹78.91 Lakhs.
IIBF Examiner Tip: Investing at the beginning of each year earns one extra year of 8% compounding on every installment, lowering the required contribution by ÷ 1.08.
Question 3.3 • 2 Marks
Instead of a Sinking Fund, suppose the company took a ₹500 Lakhs Term Loan today at 8% p.a. repayable in 5 equal End-of-Year Equated Annual Installments (Principal + Interest). What is the Equated Annual Installment?
A ₹125.23 Lakhs per year
B ₹85.23 Lakhs per year
C ₹140.00 Lakhs per year
D ₹115.95 Lakhs per year
Correct Answer: Option A — ₹125.23 Lakhs per year
Equated Annual Loan Installment = Present Loan Principal (PV) / PVIFA(r, n)- Step 1: Present Value of Loan Today (PV) = ₹500 Lakhs.
- Step 2: PVIFA(8%, 5 yrs) = 3.9927.
- Step 3: Equated Annual Installment = ₹500 Lakhs / 3.9927 = ₹125.228 Lakhs (₹125.23 Lakhs).
IIBF Examiner Tip: Crucial distinction: Sinking Fund accumulates towards a FUTURE ₹500L (use FVIFA = ₹85.23L); Loan Amortization repays a PRESENT ₹500L (use PVIFA = ₹125.23L).
Question 3.4 • 2 Marks
Notice that the Loan Amortization Installment (₹125.23 Lakhs) is exactly ₹40.00 Lakhs higher than the Sinking Fund Installment (₹85.23 Lakhs). What does this ₹40.00 Lakhs difference mathematically represent?
A Annual Interest on ₹500 Lakhs at 8% p.a. (₹500L × 8% = ₹40 Lakhs)
B Annual Principal Repayment
C Sinking Fund Management Fee
D Compound Interest Difference
Correct Answer: Option A — Annual Interest on ₹500 Lakhs at 8% p.a. (₹500L × 8% = ₹40 Lakhs)
Capital Recovery Factor (1 / PVIFA) = Sinking Fund Factor (1 / FVIFA) + Interest Rate (r)- Step 1: Mathematical identity: (1 / PVIFA) - (1 / FVIFA) = r.
- Step 2: Multiply by ₹500 Lakhs: ₹125.23 Lakhs - ₹85.23 Lakhs = ₹500 Lakhs × 8% = ₹40.00 Lakhs!
IIBF Examiner Tip: Knowing that (1/PVIFA) = (1/FVIFA) + r lets you find PVIFA from FVIFA (or vice-versa) in 5 seconds during the exam!
Question 3.5 • 2 Marks
In the ₹500 Lakhs Term Loan @ 8% p.a. with an Equated Annual Installment of ₹125.23 Lakhs, what is the breakdown between Interest and Principal in the Year 1 Installment, and what is the Opening Principal for Year 2?
A Interest = ₹40.00 L; Principal = ₹85.23 L; Year 2 Opening Balance = ₹414.77 Lakhs
B Interest = ₹25.23 L; Principal = ₹100.00 L; Year 2 Opening Balance = ₹400.00 Lakhs
C Interest = ₹40.00 L; Principal = ₹125.23 L; Year 2 Opening Balance = ₹374.77 Lakhs
D Interest = ₹33.18 L; Principal = ₹92.05 L; Year 2 Opening Balance = ₹407.95 Lakhs
Correct Answer: Option A — Interest = ₹40.00 L; Principal = ₹85.23 L; Year 2 Opening Balance = ₹414.77 Lakhs
Year 1 Interest = Opening Loan × r; Year 1 Principal = Installment - Year 1 Interest- Step 1: Year 1 Interest = 8% of ₹500 Lakhs = ₹40.00 Lakhs.
- Step 2: Year 1 Principal Repaid = ₹125.23 Lakhs - ₹40.00 Lakhs = ₹85.23 Lakhs.
- Step 3: Opening Principal for Year 2 = ₹500.00 Lakhs - ₹85.23 Lakhs = ₹414.77 Lakhs.
IIBF Examiner Tip: In Year 2, interest will be 8% of ₹414.77L = ₹33.18L, and principal repayment will rise to ₹125.23L - ₹33.18L = ₹92.05L.
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Annual Coupon Interest:₹80 / yr
Current Yield (Coupon / Market Price):8.51%
Annualized Capital Gain / (Loss):₹10 / yr
Approximate Yield to Maturity (YTM):9.28%
Frequently Asked JAIIB Exam Questions (AFM Paper 3)
What happens to a bond’s price when its Required Yield to Maturity (YTM) equals its Coupon Rate?
When Required YTM exactly equals the Coupon Rate, the bond trades at Par Value (Face Value = ₹1,000), regardless of how many years remain to maturity.
Which bond has higher interest rate price risk (higher Duration): a high-coupon bond or a low-coupon bond of the same maturity?
A low-coupon bond (or zero-coupon bond) has a higher Duration and greater percentage price volatility for a given change in interest rates because a larger proportion of its total cash flows arrives at final maturity.
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