SFM Formulae & Concepts with Fully Detailed Examples | CMA Knowledge

Master All Key SFM Formulae & Concepts.” Visual elements include finance-related icons like a calculator, pie chart, globe, and currency symbols, with topics like bond valuation, portfolio theory, derivatives, forex, and equity models subtly highlighted in the background. Designed for CMA, CA, CFA, and MBA students preparing for exams. Clean layout with sharp text and professional academic style. — Master every key SFM formula & concept — from bonds to forex — in one exam-ready guide for CMA, CA, CFA & MBA students.

SFM Formulae & Concepts with Fully Detailed Examples

Revision blog covering bond valuation, equity models, portfolio theory, derivatives, forex & international finance—each with complete step-by-step examples.

1. Bond Valuation

1.1 Present Value of Future Cash Flows

Formula:
Price = Σ_{t=1 to n} (Coupon ÷ (1 + r)^t) + (Redeeming Value ÷ (1 + r)ⁿ)

Detailed Example:

A 5-year bond with:

Face value (Redemption) = ₹1,000
Annual coupon = 8% of face value = ₹80
Required yield (r) = 10%

Step 1: List cash flows:

Year 1–5 coupon: ₹80 each
Year 5 redemption: ₹1,000 + ₹80 = ₹1,080

Step 2: Discount each cash flow:

Year (t)	Cash Flow	Discount Factor (1.10^t)	Present Value
1	₹80	1.10	₹80 ÷ 1.10 = ₹72.73
2	₹80	1.21	₹80 ÷ 1.21 = ₹66.12
3	₹80	1.331	₹80 ÷ 1.331 = ₹60.12
4	₹80	1.4641	₹80 ÷ 1.4641 = ₹54.64
5	₹1,080	1.6105	₹1,080 ÷ 1.6105 = ₹670.79

Step 3: Sum all present values:
₹72.73 + ₹66.12 + ₹60.12 + ₹54.64 + ₹670.79 = ₹924.40

1.2 Yield to Maturity (YTM)

Approximate Formula:
YTM ≈ [Coupon + (Redeeming Value – Price)/n] ÷ [(Price + Redeeming Value)/2]

Detailed Example:

From previous example, Price ≈ ₹924.40, Coupon = ₹80, Redemption = ₹1,000, n = 5 years

Step 1: Compute numerator:
Coupon + (Redemption – Price)/n = 80 + (1,000 – 924.40)/5 = 80 + 15.12 = ₹95.12

Step 2: Compute denominator:
(Price + Redemption)/2 = (924.40 + 1,000)/2 = ₹962.20

Step 3: YTM ≈ 95.12 ÷ 962.20 = 0.0989 = 9.89%

1.3 Macaulay & Modified Duration

Macaulay Duration Formula:
D = Σ[t × PV(CFt)] ÷ Price
Modified Duration: D ÷ (1 + YTM)

Detailed Example:

Use cash flows & PV from Section 1.1 and Price = ₹924.40, YTM = 9.89%.

Step 1: Multiply each PV by its year:

Year (t)	PV(CFt)	t × PV
1	₹72.73	1 × 72.73 = 72.73
2	₹66.12	2 × 66.12 = 132.24
3	₹60.12	3 × 60.12 = 180.36
4	₹54.64	4 × 54.64 = 218.56
5	₹670.79	5 × 670.79 = 3,353.95

Step 2: Sum weighted PVs = 72.73 + 132.24 + 180.36 + 218.56 + 3,353.95 = ₹3,957.84

Step 3: Macaulay Duration = 3,957.84 ÷ 924.40 ≈ 4.28 years

Step 4: Modified Duration = 4.28 ÷ 1.0989 ≈ 3.90 years

2. Equity Valuation

2.1 Gordon’s Growth Model

Formula:
P₀ = D₁ ÷ (Ke − g)
where D₁ = D₀ × (1 + g)

Detailed Example:

Last year’s dividend D₀ = ₹4
Growth rate g = 5%
Required return Ke = 12%

Step 1: Compute D₁ = 4 × 1.05 = ₹4.20

Step 2: P₀ = 4.20 ÷ (0.12 − 0.05) = 4.20 ÷ 0.07 = ₹60.00

2.2 Multi-Stage Dividend Model

High-growth for first n years, then stable growth thereafter.

Detailed Example:

D₀ = ₹2
High-growth g₁ = 20% for 3 years
Stable growth g₂ = 8% thereafter
Required return Ke = 14%

Step 1: Compute dividends:

D₁ = 2 × 1.20 = ₹2.40
D₂ = 2.40 × 1.20 = ₹2.88
D₃ = 2.88 × 1.20 = ₹3.46
D₄ = 3.46 × 1.08 = ₹3.74 (first stable dividend)

Step 2: Terminal value at t=3:
TV₃ = D₄ ÷ (Ke − g₂) = 3.74 ÷ (0.14 − 0.08) = 3.74 ÷ 0.06 = ₹62.33

Step 3: Discount D₁–D₃ and TV₃ back to present:

t	Cash Flow	Discount Factor (1.14³)	PV
1	₹2.40	1.14	2.40 ÷ 1.14 = ₹2.11
2	₹2.88	1.2996	2.88 ÷ 1.2996 = ₹2.22
3	₹3.46	1.4815	3.46 ÷ 1.4815 = ₹2.34
3	TV₃ = ₹62.33	1.4815	62.33 ÷ 1.4815 = ₹42.06

Step 4: Sum PVs = 2.11 + 2.22 + 2.34 + 42.06 = ₹48.73

2.3 Free Cash Flow to Firm (FCFF)

Formula:
FCFF = PAT + Depreciation – Capital Expenditure – ΔWorking Capital

Detailed Example:

Profit after tax (PAT) = ₹120 Cr
Depreciation = ₹15 Cr
Capital expenditure = ₹25 Cr
Increase in working capital = ₹10 Cr

FCFF = 120 + 15 – 25 – 10 = ₹100 Cr

Value of firm = FCFF ÷ (WACC − g) = 100 ÷ (0.12 − 0.04) = 100 ÷ 0.08 = ₹1,250 Cr

2.4 Free Cash Flow to Equity (FCFE)

Formula:
FCFE = FCFF – Interest × (1 − t) + Net Borrowing

Detailed Example:

FCFF = ₹100 Cr
Interest = ₹20 Cr, Tax rate t = 30%
Net new borrowings = ₹10 Cr

Interest after tax = 20 × (1 − 0.30) = ₹14 Cr

FCFE = 100 − 14 + 10 = ₹96 Cr

Value of equity = FCFE ÷ (Ke − g) = 96 ÷ (0.14 − 0.06) = 96 ÷ 0.08 = ₹1,200 Cr

3. Portfolio Management

3.1 Return of a Single Security

Formula:
R = (P₁ − P₀ + D) ÷ P₀ × 100%

Detailed Example:

Purchase price P₀ = ₹200
Sale price P₁ = ₹240
Dividend D = ₹10

Return = (240 − 200 + 10) ÷ 200 × 100% = 50 ÷ 200 × 100% = 25%

3.2 Portfolio Return

Formula:
Rp = Σ(wᵢ × Rᵢ)

Detailed Example:

Asset A: weight 60%, return 15%
Asset B: weight 40%, return 8%

Rp = 0.60×15% + 0.40×8% = 9% + 3.2% = 12.2%

3.3 Portfolio Risk (Two Assets)

Formula:
σp² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ

Detailed Example:

σ₁ = 12%, σ₂ = 20%, correlation ρ = 0.4
w₁ = 0.70, w₂ = 0.30

σp² = (0.70²×0.12²) + (0.30²×0.20²) + 2×0.70×0.30×0.12×0.20×0.4

= 0.49×0.0144 + 0.09×0.04 + 2×0.70×0.30×0.024×0.4

= 0.007056 + 0.0036 + 2×0.70×0.30×0.0096

= 0.007056 + 0.0036 + 0.004032 = 0.014688 → σp = √0.014688 ≈ 12.12%

3.4 CAPM

Formula:
Ke = Rf + β × (Rm − Rf)

Detailed Example:

Risk-free rate Rf = 6%
Market return Rm = 14%
Security beta β = 1.3

Ke = 6% + 1.3×(14% − 6%) = 6% + 1.3×8% = 6% + 10.4% = 16.4%

4. Mutual Funds

4.1 Net Asset Value (NAV)

Formula:
NAV = (Total Assets − Total Liabilities) ÷ Total Outstanding Units

Detailed Example:

Total assets under management = ₹500 Cr
Total liabilities = ₹20 Cr
Total units = 48 Cr

NAV = (500 − 20) ÷ 48 = 480 ÷ 48 = ₹10.00 per unit

4.2 Investor Return (%)

Formula:
Return = (Exit NAV − Entry NAV + Dividends) ÷ Entry NAV × 100%

Detailed Example:

Entry NAV = ₹15.00
Exit NAV after 1 year = ₹17.50
Dividend distributed = ₹0.50

Return = (17.50 − 15.00 + 0.50) ÷ 15.00 × 100% = 3.00 ÷ 15.00 × 100% = 20%

5. Derivatives

5.1 Futures Pricing (Cost of Carry)

Formula:
F = S × e^{r × t}

Detailed Example:

Spot price S = ₹2,000
Risk-free rate r = 8% p.a.
Time t = 6 months = 0.5 year

F = 2,000 × e^0.08×0.5 = 2,000 × e^0.04

e^0.04 ≈ 1.0408 → F ≈ 2,000 × 1.0408 = ₹2,081.60

5.2 Options (Conceptual: Black–Scholes Inputs)

Inputs Needed:

Current stock price (S)
Strike price (K)
Time to expiration (T)
Volatility (σ)
Risk-free rate (r)

These feed into N(d₁), N(d₂) to produce call/put values. Implementation uses statistical tables or software.

5.3 Hedging with Futures

Formula for Number of Contracts:
n = (Value of Portfolio × β) ÷ (Futures Contract Size)

Detailed Example:

Portfolio value = ₹20 Cr
Portfolio beta β = 1.1
Each futures contract covers ₹2 Lakh

n = (20 Cr × 1.1) ÷ 2 Lakh = 22 Cr ÷ 2 Lakh = 110 contracts

6. Risk Management

6.1 Value at Risk (VaR)

Formula:
VaR = Portfolio Value × σ × Z_α × √t

Detailed Example:

Portfolio value = ₹10 Cr
Daily standard deviation σ ≈ 1.5% = 0.015
Z_99% = 2.33
Time horizon t = 1 day

VaR = 10 Cr × 0.015 × 2.33 × √1 = 10 Cr × 0.015 × 2.33 ≈ ₹3.50 Lakh

Interpretation: With 99% confidence, you will not lose more than ₹3.50 L on one day.

7. Interest Rate Derivatives

7.1 Interest Rate Futures

Formula:
Gain/Loss = (Sell Price − Buy Price) × Notional × Contracts

Detailed Example:

Sell at 98.50, buy back at 98.00
Notional = ₹2 Lakh per contract
Contracts = 5

Price change = 98.50 − 98.00 = 0.50 points = 0.50% of notional

Gain per contract = 0.005 × 2 Lakh = ₹1,000

Total gain = 1,000 × 5 = ₹5,000

7.2 Forward Rate Agreement (FRA)

Detailed Example:

Company A wants to borrow ₹5 Cr in 6 months for 6 months. FRA rate locked at 7%.

If 6-month LIBOR in 6 months turns out to be 8%, FRA seller pays A the difference on ₹5 Cr.

Difference = (8% − 7%) × (5 Cr) × (180/360) = 1% × 5 Cr × 0.5 = ₹2.5 Lakh

8. Foreign Exchange Management

8.1 Forward Premium / Discount

Formula:
Premium/Discount (%) = (F − S) ÷ S × (12 ÷ Months) × 100

Detailed Example:

Spot USD/INR S = 75.00
3-month forward F = 76.20
Months = 3

Premium = (76.20 − 75.00) ÷ 75.00 × (12 ÷ 3) × 100
= 1.20 ÷ 75.00 × 4 × 100
= 0.016 × 4 × 100 = 6.40%

8.2 Money Market Hedge

Detailed Example:

Import payables USD 100,000 due in 3 months. USD deposit rate = 2%, INR deposit rate = 6%.

Borrow PV of USD = 100,000 ÷ (1 + 0.02×3/12) = 100,000 ÷ 1.005 = USD 99,502.
Convert USD 99,502 to INR at spot 75.00 = ₹7,462,650.
Invest ₹7,462,650 at 6% p.a. for 3 months = × (1 + 0.06×3/12) = ₹7,574,900.
Use ₹7,574,900 to repay INR loan; USD loan repaid from payables.

9. International Financial Management

9.1 Net Present Value in Home Currency

Detailed Example:

Project generates USD 200,000 annually for 3 years. USD/INR spot = 70. Discount rates: USD WACC=10%, INR WACC=12%.

Year 1 PV USD = 200,000 ÷ 1.10 = 181,818 → in INR = 181,818 × 70 = ₹12,727,260
Year 2 PV USD = 200,000 ÷ 1.10² = 165,289 → in INR = 165,289 × 70 = ₹11,570,230
Year 3 PV USD = 200,000 ÷ 1.10³ = 150,262 → in INR = 150,262 × 70 = ₹10,518,340
Total PV = ₹12,727,260 + ₹11,570,230 + ₹10,518,340 = ₹34,815,830

9.2 Interest Rate Parity (IRP)

Formula:
Forward Rate = Spot × (1 + i_domestic) ÷ (1 + i_foreign)

Detailed Example:

Spot USD/INR = 70.00
Indian interest rate = 8%; US interest rate = 2%
Period = 1 year

Forward = 70 × (1 + 0.08) ÷ (1 + 0.02)
= 70 × 1.08 ÷ 1.02
= 70 × 1.0588 = ₹74.12

Post Views: 23

1. Bond Valuation

1.1 Present Value of Future Cash Flows

Detailed Example:

1.2 Yield to Maturity (YTM)

Detailed Example:

1.3 Macaulay & Modified Duration

Detailed Example:

2. Equity Valuation

2.1 Gordon’s Growth Model

Detailed Example:

2.2 Multi-Stage Dividend Model

Detailed Example:

2.3 Free Cash Flow to Firm (FCFF)

Detailed Example:

2.4 Free Cash Flow to Equity (FCFE)

Detailed Example:

3. Portfolio Management

3.1 Return of a Single Security

Detailed Example:

3.2 Portfolio Return

Detailed Example:

3.3 Portfolio Risk (Two Assets)

Detailed Example:

3.4 CAPM

Detailed Example:

4. Mutual Funds

4.1 Net Asset Value (NAV)

Detailed Example:

4.2 Investor Return (%)

Detailed Example:

5. Derivatives

5.1 Futures Pricing (Cost of Carry)

Detailed Example:

5.2 Options (Conceptual: Black–Scholes Inputs)

Inputs Needed:

5.3 Hedging with Futures

Detailed Example:

6. Risk Management

6.1 Value at Risk (VaR)

Detailed Example:

7. Interest Rate Derivatives

7.1 Interest Rate Futures

Detailed Example:

7.2 Forward Rate Agreement (FRA)

Detailed Example:

8. Foreign Exchange Management

8.1 Forward Premium / Discount

Detailed Example:

8.2 Money Market Hedge

Detailed Example:

9. International Financial Management

9.1 Net Present Value in Home Currency

Detailed Example:

9.2 Interest Rate Parity (IRP)

Detailed Example:

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