FIN435 • Financial Management

Chapter 10 — WACC (Weighted Average Cost of Capital)

Formulas • Excel functions • In-class problems • Case study • Reference links
WACC Calculator (Annual) WACC Calculator (Semiannual)

1) What is WACC and why do we care?

Discount rate for projects
Blends debt + equity costs
After-tax debt

The Weighted Average Cost of Capital (WACC) is the firm’s blended required return across all capital providers (debt holders + equity holders), weighted by their share in the firm’s capital structure. It is commonly used as the discount rate for valuing projects and firms (DCF).

Rule of thumb: Compare ROIC vs WACC. If ROIC > WACC, the firm is creating value on invested capital; if ROIC < WACC, it is destroying value.
2) Master formula (WACC) ▾
WACC = (D / (D + E)) * Kd_after_tax + (E / (D + E)) * Ke where: D = market value of debt (often proxied by book value in examples) E = market value of equity (market cap) Kd_after_tax = Kd * (1 - TaxRate) Ke = cost of equity (CAPM or Dividend Discount Model)
3) Cost of debt (Kd): bond yield, then after-tax ▾
Annual coupon bond
Kd_before_tax = RATE(nper, coupon*1000, -(price - flotation_costs), 1000) Kd_after_tax = Kd_before_tax * (1 - tax_rate)
Semiannual coupon bond
Kd_before_tax = RATE(nper*2, coupon*1000/2, -(price - flotation_costs), 1000) * 2 Kd_after_tax = Kd_before_tax * (1 - tax_rate)
Flotation costs: flotation_costs = flotation_percent × price. Use price − flotation_costs as the net proceeds.
4) Cost of equity (Ke): CAPM or Dividend Discount Model (DDM) ▾
Method Formula When to use
CAPM (beta given)
1 CAPM (Cost of Equity)
Ke = rRF + β * (Rm - rRF) Ke = rRF + β * MRP
 When β and a market risk premium assumption are available.
DDM (dividend given)
2 Dividend Discount Model (DDM)
Ke = D1 / (P0 - flotation_costs) + g flotation_costs = flotation_percent * P0
 Dividend-paying firms with stable growth assumptions.
5) Excel pricing toolbox (bond price, YTM, duration) ▾
Bond price (annual)
Price = ABS( PV(YTM, YearsToMaturity, CouponRate*1000, 1000) )
YTM (annual)
YTM = RATE(YearsToMaturity, CouponRate*1000, -Price, 1000)
Bond price (semiannual)
Price = ABS( PV(YTM/2, YearsToMaturity*2, CouponRate*1000/2, 1000) )
YTM (semiannual)
YTM = RATE(YearsToMaturity*2, CouponRate*1000/2, -Price, 1000) * 2
Duration (example)
=DURATION(DATE(2025,2,4), DATE(2035,2,4), 5%, 7%, 2, 0) → 7.80
Duration interpretation: If duration = 7.80, then a +1% rate shock implies an approximately −7.8% price change (and vice versa for a −1% rate move).
6) In-class exercises (ready to copy into Excel) ▾
Exercise 1 — IBM WACC (Question)
Debt: $10m, coupon 5%, 10 years, price $950, flotation 7% of price, tax 40%. Equity: $20m, D1 = $5, P0 = 50, g = 5%, flotation = 0. Task: Compute IBM’s WACC.
Show solution ▾
Answer (structure): Wd = 1/3, We = 2/3 Kd = RATE(10, 5%*1000, -(950 - 950*7%), 1000) * (1-40%) = 3.98% Ke = 5/(50-0) + 5% = 15% WACC = (1/3)*3.98% + (2/3)*15% = 11.33%
2) After-tax cost of debt (semiannual) Noncallable bond, 20 years to maturity, 9.25% annual coupon paid semiannually, price = 1075, par = 1000, tax = 40%. After-tax Kd = RATE(20*2, 9.25%*1000/2, -1075, 1000) * (1-40%) = 5.08% 3) Cost of equity (DDM with flotation) D1 = 1.25, P0 = 27.50, g = 5.00%, flotation = 6% of price. Ke = 1.25 / (27.5 - 0.06*27.5) + 5% = 9.84% 4) WACC from weights Total capital raised: $10m, debt $3m, equity $7m. WACC = (3/10)*Kd + (7/10)*Ke 5) Extra cost of new stock vs retained earnings P0 = 45, EPS1 = 2.75, payout = 70%, g = 6%, flotation = 8% D1 = 2.75*0.70 = 1.925 rs = D1/P0 + g re = D1/(P0*(1-F)) + g Difference = re - rs 6) Full WACC (bond + CAPM) Bond: 20 years, 8% annual coupon, price = 1050, tax = 40% CAPM: rRF = 4.5%, MRP = 5.5%, beta = 1.2 Weights: debt 35%, equity 65% Bond yield = RATE(20, 8%*1000, -1050, 1000) After-tax Kd = BondYield*(1-40%) Ke = 4.5% + 1.2*5.5% WACC = 0.35*Kd_after_tax + 0.65*Ke
7) Quick WACC calculator (optional, in-page) ▾
This is a quick check. For graded work, use Excel and/or the course calculators: annual • semiannual.

Assignments and resources

A) Chapter 10 deliverables ▾
Reminder: Use consistent units (percent vs decimal) and keep the bond coupon timing consistent (annual vs semiannual) across RATE / PV inputs.
B) Where to get market inputs (rates, bonds, data) ▾
C) “Interest rate risk” reading (SEC) ▾

Fixed-rate bond prices and market yields move in opposite directions; coupon and maturity influence interest-rate risk.

D) Damodaran + Interactive 4D chart ▾

Use this to compare typical WACC / cost of equity / leverage by industry. Useful for sanity-checking project discount rates.

Interactive 4D (rotate): x = D/E (%), y = Beta, z = WACC, color = Tax rate. Drag to rotate; hover for exact values.
Homework (Team) — Monte Carlo in Excel: Yield → WACC + Bond Price
This is a required Monte Carlo (simulation) homework. You will run at least 1,000 trials (recommended 5,000) in Excel using a Telecom. Services industry example, which has a much higher debt weight than Semiconductor. You will simulate market borrowing yield and study how it affects: (1) after-tax cost of debt, (2) WACC, and (3) the price of a 10-year, 7% coupon bond (semiannual). Keep cost of equity fixed so the interest-rate effect is easier to see. You must create a histogram of simulated WACC and report mean + P5/P50/P95.
Quizzes (Chapter 10 — WACC)
Take these after completing the Monte Carlo homework. Use them for practice and self-check.
E) Example: WACC in the wild (Hertz, FYI) ▾
Note: WACC can change over time as market cap, debt, betas, and rates move. Always note the date of the WACC estimate you cite.
Interpretation idea (for discussion): If a firm’s WACC rises, future cash flows are discounted more heavily → lower present value. If WACC falls (holding cash flows fixed), present value rises.
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