System Documentation

CFA® Level II Topic: Corporate Finance & Equity Valuation (Cost of Capital)

Disclaimer: CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

01. From Static Discount Rates to a Macro-Linked WACC

Traditional valuation models treat the Discount Rate ($r$) as a static cell in Excel. In reality, the cost of capital is a dynamic variable driven by macro-liquidity and risk appetite. When the yield curve shifts, your Weighted Average Cost of Capital (WACC) should move with it.

The WACC Macro-Auditor (MVP v1.2) attaches your valuation to a live macro anchor: the 10-Year US Treasury Yield ($R_f$). It answers a single question: “If the Fed keeps rates higher for longer, how does my intrinsic value and duration profile change?”

02. Pricing Logic: Equity, Debt and Constant Spread WACC

All internal calculations are performed in decimals (not percentages) to avoid unit mismatch. The engine models both the equity and debt legs of the capital structure.

Equity Leg: Capital Asset Pricing Model (CAPM)

$$r_e = R_f + \\beta \\times ERP$$

$R_f$: Risk-Free Rate (10Y U.S. Treasury, from FRED)
$\\beta$: Levered Beta (asset sensitivity vs. market)
$ERP$: Equity Risk Premium (user-controlled)

Debt Leg: Constant Credit Spread Assumption

At the base case, the user provides a pre-tax Cost of Debt ($r_d$). The system infers a credit spread over the risk-free rate:

$$Spread = r_d - R_f$$

Under any macro scenario, the new cost of debt is locked by this spread:

$$r_d^{new} = R_f^{new} + Spread$$

This avoids arbitrage-inconsistent configurations where borrowing costs fall below the sovereign curve (i.e., $r_d < R_f$), and better reflects how corporate yields move with the risk-free term structure.

Combining both legs, the after-tax WACC is:

$$WACC = w_d \, r_d (1 - t) + w_e \, r_e$$

where $w_d$ and $w_e$ are the market value weights of debt and equity. The engine also continuously checks the stability condition $WACC > g$ (terminal growth). When $WACC \\le g$, the model flags an inversion and surfaces “N/A / Broken” instead of misleading valuation numbers.

03. OSINT Data Pipeline

To reduce manual errors and bring the model closer to live markets, the WACC Macro-Auditor integrates open-source intelligence (OSINT) into its baseline inputs. All fields remain fully editable for analyst override.

Source A: Federal Reserve (FRED)

Pulls the latest DGS10 (10-Year Constant Maturity Rate) to pin the Risk-Free Rate ($R_f$) to real-time macro conditions.

Source B: Equity Reference Data

For a given ticker, the system fetches live price, company name, and (where available) 5-year adjusted Beta ($\\beta$). These values seed the macro block and the Reverse DCF kernel, but can be overwritten by the user at any time.

When APIs are unavailable or rate-limited, the interface degrades gracefully to a manual input mode while preserving all valuation logic.

04. Sensitivity Matrix & Valuation Impact Engine

The 5 × 5 heat map is the core of the auditor. Each cell represents a joint shock to macro rates and risk appetite, and reports the percentage change in intrinsic value relative to the base case.

Axis	Description	Risk Dimension
X-Axis ($\\Delta R_f$)	Interest rate shocks from the Fed (e.g., -100 to +100 bps on the 10Y). This flows into both $r_e$ and $r_d$ via CAPM and the constant spread rule.	Systematic Rate Risk
Y-Axis ($\\Delta ERP$)	Shifts in the Equity Risk Premium capturing fear/greed cycles. This tilts the required return on equity at constant $R_f$.	Sentiment / Risk Premium Risk

For each cell, the engine computes the new WACC and then applies a Gordon Growth model to approximate the change in intrinsic value relative to the base case:

Valuation Kernel (Single Source of Truth)

Let $W_0$ be the base WACC, $W_1$ the shocked WACC, and $g$ the terminal growth rate (all in decimals). Under a constant FCF-per-share assumption:

$$P_0 = \\frac{FCF}{W_0 - g}, \\quad P_1 = \\frac{FCF}{W_1 - g}$$

$$\\text{Valuation Impact \\%} = \\left(\\frac{P_1}{P_0} - 1\\right) \\times 100 = \\left(\\frac{W_0 - g}{W_1 - g} - 1\\right) \\times 100$$

If $W_1 \\le g$, the denominator collapses and the cell is marked as “Broken / N.A.” instead of producing unstable numbers.

Both the heat map and the natural language interpretation card read from the exact same matrix object. There is no duplicated formula path, enforcing a strict Single Source of Truth for all outputs.

05. Reverse DCF, Duration Proxy and Input Guardrails

The auditor exposes two additional diagnostics on top of the sensitivity grid.

Reverse DCF Implied Growth

Given an observed price and a user-specified free cash flow per share, the tool backs out the growth expectations embedded in the market:

$$\\text{FCF Yield} = \\frac{FCF}{Price}$$

$$g_{implied} = WACC - \\text{FCF Yield}$$

This value is displayed as “Implied Growth” and can be directly compared against the analyst’s own terminal growth input $g$.

Equity Duration Proxy

As a rough measure of interest rate sensitivity, the system reports a duration-like multiple:

$$\\text{Duration Proxy} \\approx \\frac{1}{WACC - g}$$

A higher value indicates a longer-duration equity: small changes in discount rates lead to large changes in present value.

The interface surfaces guardrails when inputs become economically inconsistent. For example, if a user enters a Cost of Debt below the risk-free rate ($r_d < R_f$), the system highlights a negative credit spread and prompts the analyst to review the assumptions rather than silently accepting them.

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Warning: Long-duration assets (for example, deep tech, nuclear and AI infrastructure) embed a large share of their value far into the future. A seemingly small increase in WACC can destroy a disproportionate amount of present value. The WACC Macro-Auditor is designed to stress-test this margin of safety against a hawkish Fed and shifting risk premia. It is a diagnostic tool, not investment advice.