CFA Level 1 Quant Methods
Great! Let’s continue with Reading 2: The Time Value of Money in Finance, covering all Learning
Outcome Statements (LOS 2.a – 2.c). These notes follow CFA exam style and tone, and are designed to
reinforce conceptual clarity with formulas, examples, and exam-focused insights.
📘 READING 2: The Time Value of Money in Finance
LOS 2.a: Calculate and interpret the present value (PV) of fixed-income and equity
instruments based on expected future cash flows.
🔑 Key Concepts:
Time Value of Money (TVM): A dollar today is worth more than a dollar tomorrow.
The present value (PV) is the discounted value of future cash flows using an appropriate rate of
return (discount rate).
📐 General Formula:
FV
PV =
(1 + r)n
F V : Future value
r: Discount rate per period
n: Number of periods
🧮 Financial Calculator Keys:
N = number of periods
I/Y = interest rate per period
PV = present value
PMT = periodic payment (for annuities or bonds)
FV = future value
💸 Applications in Finance:
1. Zero-Coupon Bond:
Face Value
PV =
(1 + r)n
2. Coupon Bond:
C
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FV 1/4
C FV
PV = ∑ +
(1 + r) t (1 + r)n
Where C = Coupon payment
3. Preferred Stock (Perpetuity):
D
P =
r
D: Annual dividend
r: Required rate of return
4. Equity Valuation:
Gordon Growth Model:
D1
P0 =
r−g
Where g is the dividend growth rate.
✅ Summary Box:
PV decreases as r increases.
Always use appropriate sign conventions in calculator (cash outflows = negative).
Perpetuity: constant payment with no end.
LOS 2.b: Calculate and interpret the implied return of fixed-income instruments and
required return and implied growth of equity instruments given the present value
(PV) and cash flows.
🔁 Rearranged TVM:
1. Yield to Maturity (YTM) for Bonds:
C FV
PV = + ⋯ +
(1 + r)1 (1 + r)n
→ Solve for r using calculator: IRR of bond’s cash flows.
2. Equity Required Return (from Gordon Model):
D1
r= +g
P0
3. Implied Dividend Growth Rate:
D1
g=r−
P0
📌 Common CFA Application:
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Given stock price and expected dividend growth, calculate investor's required return.
If given bond price and cash flows, calculate YTM (IRR).
✅ Summary Box:
Solve for return using cash flow + PV inputs.
CFA exam may give D1, P0, and g → ask for r.
Price up = yield down (inverse relationship).
LOS 2.c: Explain the cash flow additivity principle, its importance for the no-
arbitrage condition, and its use in calculating implied forward interest rates,
forward exchange rates, and option values.
💬 Cash Flow Additivity Principle:
The PV of a series of cash flows equals the sum of the individual PVs.
This is fundamental to valuation and arbitrage-free pricing.
🔄 Implications:
Used in replicating portfolios.
Supports no-arbitrage condition: Two assets with same cash flows must have the same PV.
📊 Applications:
1. Forward Interest Rates:
2 (1 + S2 )2
(1 + S2 ) = (1 + S1 )(1 + 1y1y) ⇒ 1y1y = −1
(1 + S1 )
2. Forward Exchange Rates:
1 + idomestic
F =S×( )
1 + iforeign
F : Forward rate
S : Spot rate
i: Interest rate
3. Options Pricing:
Based on replicating portfolios and binomial trees.
Cash flow additivity ensures consistent option pricing under no-arbitrage.
✅ Summary Box:
CF Additivity = PV of bundle = sum of parts.
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Core principle in fixed income, FX, derivatives.
Used to derive implied rates and enforce no-arbitrage.
🔚 READING 2 TAKEAWAYS:
LOS Concept Formula / Insight
2.a Present value of financial assets PV = FV
(1+r)n
D1
2.b Solve for return/growth using PV + cash flow r= P0
+g
2.c CF Additivity and no-arbitrage pricing Used in forward rates & options
Would you like me to continue next with Reading 3: Statistical Measures of Asset Returns (LOS 3.a–
3.d)?
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