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Formula sheet/NISM Series X-A: Investment Adviser (Level 1)/Investment Products
[ INVESTMENT PRODUCTS ]

Bond Pricing, Duration & Yield Formulas

Bond Price:Price=∑[Ct/(1+y)t]+[M/(1+y)n]∣Dirty Price:Clean Price+Accrued Interest\text{Bond Price}: Price = \sum [ C_{t} / (1 + y)^{t} ] + [ M / (1 + y)^{n} ]\quad\Big|\quad \text{Dirty Price}: \text{Clean Price} + \text{Accrued Interest}
Coupon Yield:(Coupon/Face Value)×100∣Current Yield:(Annual Coupon/Current Market Price)×100\text{Coupon Yield}: (Coupon / \text{Face Value}) \times 100\quad\Big|\quad \text{Current Yield}: (\text{Annual Coupon} / \text{Current Market Price}) \times 100
Zero-Coupon Bond Yield:YTM=[(100−P)/P]×[365/Days to Maturity]×100\text{Zero-Coupon Bond Yield}: YTM = [ (100 - P) / P ] \times [ 365 / \text{Days to Maturity} ] \times 100
Macaulay Duration:DMac=[∑(t×Ct/(1+y)t)]/Bond Price\text{Macaulay Duration}: D_{\text{Mac}} = [ \sum ( t \times C_{t} / (1 + y)^{t} ) ] / \text{Bond Price}
Modified Duration:DMod=DMac/(1+y)  ⇒  %ΔPrice≈−DMod×Δy\text{Modified Duration}: D_{\text{Mod}} = D_{\text{Mac}} / (1 + y) \;\Rightarrow\; \% \Delta Price \approx - D_{\text{Mod}} \times \Delta y
Variables

Day Count Conventions: 30/360 for G-Secs and corporate bonds in India; Actual/365 for Money Market T-Bills. CtC_{t}: Coupon cash flow at period t; M: Par / redemption maturity value; y: Yield per period; n: Total periods to maturity.

Exam note

Bond prices move inversely to interest rates. A higher Modified Duration implies greater interest rate price volatility.

Worked examples
Economic Value Added (EVA) and Market Value Added (MVA)

Godrej Consumer reports EBIT of Rs 2,400 Cr, Effective Corporate Tax Rate of 25%, Total Capital Employed (Debt + Equity) of Rs 10,000 Cr, and Weighted Average Cost of Capital (WACC) of 11.5%. Total Market Capitalization of Equity is Rs 28,000 Cr, Market Value of Debt is Rs 2,000 Cr, and initial capital contributed by investors is Rs 6,000 Cr. Calculate EVA and MVA.

Equity Multiples & PEG Ratio Valuation

Infosys trades at CMP of Rs 1,500 with TTM EPS of Rs 60.00, Book Value per Share of Rs 250.00, and Annual Dividend per Share of Rs 36.00. Consensus forecasts long-term earnings growth (g) of 15.0% p.a. Calculate P/E Ratio, P/BV Ratio, Dividend Yield, Earnings Yield, and PEG Ratio.

Semi-Annual Bond Pricing and YTM Calculation

An 8.0% p.a. coupon Government Bond has a Face Value of Rs 1,000, semi-annual coupon payments (Rs 40 every 6 months), and 4 years to maturity (8 semi-annual periods). If the market required Yield to Maturity (YTM) is 7.0% p.a. compounded semi-annually (3.5% per half-year), calculate the theoretical Bond Fair Price.

Macaulay Duration, Modified Duration & Price Sensitivity

A 3-year annual coupon bond with Face Value Rs 100 and coupon rate 8.0% trades at Par (YTM = 8.0%, Price = Rs 100). Cash flows: Year 1 = Rs 8, Year 2 = Rs 8, Year 3 = Rs 108. Compute Macaulay Duration, Modified Duration, and estimate the percentage price change if market yields increase by 75 bps (+0.75%).

Spot-Futures Arbitrage Return % Calculation

On 3rd March, Tata Steel spot shares trade on NSE at Rs 150.00. March futures expiring on 30th March (27 days to expiry) trade at Rs 152.00. Calculate the cash-and-carry arbitrage profit in Rs and express it as an annualized percentage return.