## WACC: Comprehensive Problems with BV and MV Weights
These questions require computing all component costs from raw data before calculating WACC under both weight bases. This is the highest-difficulty WACC question type.
### Equity Cost (New Issue)
Ke = D₁ / NP_new + g
- NP_new = new issue price – flotation cost
- g from historical dividends: use (Dₙ/D₀)^(1/n) – 1
### Cost of Retained Earnings
Kr = D₁ / P₀ + g (market price P₀, no flotation deducted)
### Preference Share Cost (YTM approximation)
Kp = [D + (RV – NP)/n] / [(RV + NP)/2]
### Debenture Cost (YTM method)
When market yield differs from coupon rate, the yield on comparable instruments is the correct cost. Then apply tax: Kd = Yield × (1 – t).
Alternatively use approximation: Kd = [I(1–t) + (RV–NP)/n] / [(RV+NP)/2]
### BV Weights
Use balance sheet amounts including retained earnings as a separate line.
### MV Weights
Equity MV = shares × market price (absorbed retained earnings — do not add separately)
Pref MV = shares × market price per pref share
Debt MV = number of debentures × market price per debenture
### Example 1
Q43 — Three-part WACC: component costs, BV weights, MV weights (PYQ)
Capital: Equity 80,000 shares @₹100 FV (BV ₹80L, MV ₹200 each → MV ₹1,600L); 9% Pref BV ₹20L MV ₹24L; 11% Deb BV ₹60L MV ₹66L; RE BV ₹40L (no separate MV)
Last dividend = 25% on ₹100 = ₹25; g = 5%; Tax = 30%; Shareholder personal tax = 20%
Component costs:
Ke: D₁ = 25 × 1.05 = ₹26.25; Ke = 26.25/200 + 0.05 = 13.13% + 5% = 18.13%
Kr: 18.13% × (1 – 0.20) = 14.50% (personal tax adjustment)
Kp = 9% (perpetual, no tax)
Kd = 11% × (1 – 0.30) = 7.70%
(2) BV WACC: Total BV = 200L
WACC = (80/200)×18.13 + (40/200)×14.50 + (20/200)×9 + (60/200)×7.70
= 7.25 + 2.90 + 0.90 + 2.31 = 13.36%
(3) MV WACC: Total MV = 1,600 + 24 + 66 = 1,690L (RE absorbed in equity MV)
WACC = (1600/1690)×18.13 + (24/1690)×9 + (66/1690)×7.70
= 17.15 + 0.13 + 0.30 = 17.58%
### Example 2
Q46 — Full BV and MV WACC with new issuance data (PYQ)
Existing BV: Debentures ₹8L, Pref ₹2L, Equity ₹10L. Tax = 50%.
Market prices: Deb ₹110, Pref ₹120, Equity ₹22.
Component costs from new issuance terms:
Kd: 8% coupon, 20-year, 4% flotation, sale ₹100 → NP = ₹96, RV = ₹100
Kd = [8×0.50 + (100–96)/20] / [(100+96)/2] = [4 + 0.20]/98 = 4.29%
Kp: 10% div, 15-year, 5% flotation, sale ₹100 → NP = ₹95, RV = ₹100
Kp = [10 + (100–95)/15] / [(100+95)/2] = [10+0.33]/97.5 = 10.60%
Ke: Flotation ₹2, sale ₹22 → NP = ₹20; D₁ = ₹2; g = 5%
Ke = 2/20 + 5% = 10% + 5% = 15%
BV weights: Deb 8/20, Pref 2/20, Eq 10/20
WACC(BV) = (8/20)×4.29 + (2/20)×10.60 + (10/20)×15 = 1.72+1.06+7.50 = 10.28%
MV: Deb = 8,000/100×110 = ₹8,800; Pref = 2,000/100×120 = ₹2,400; Eq = 1,00,000×22 = ₹22L
Total MV = 8,800+2,400+22,00,000 ≈ ₹23,11,200
WACC(MV) = (8800/2311200)×4.29 + (2400/2311200)×10.60 + (2200000/2311200)×15
≈ 0.02 + 0.01 + 14.28 = 14.31%