## Part (a): Cost of Capital — B Ltd.
**Total Capital:**
| Source | Amount (₹) | Weight |
|---|
| Equity Share Capital | 14,00,000 | 0.35 |
| Preference Share Capital | 10,00,000 | 0.25 |
| Debentures | 9,60,000 | 0.24 |
| Bank Loan | 6,40,000 | 0.16 |
| **Total** | **40,00,000** | **1.00** |
---
**(i) Cost of Equity (Ke) — CAPM**
\
K_e = R_f + \β(R_m - R_f) \
\
Ke=14
---
**(ii) Cost of Preference Shares (YTM / IRR Method)**
Face Value = ₹1,000, Annual Dividend = 10% × 1,000 = ₹100, Redeemable at ₹1,065.40 after 3 years.
Current Market Price = ₹1,000 (assumed at par/issue price).
Calculate NPV at 10% and 14%:
| Year | Cash Flow (₹) | PVF @ 10% | PV @ 10% (₹) | PVF @ 14% | PV @ 14% (₹) |
|---|
| 0 | (1,000) | 1 | (1,000) | 1 | (1,000) |
| 1–3 (Dividend) | 100 | 2.487 | 248.70 | 2.322 | 232.20 |
| 3 (Redemption) | 1,065.40 | 0.751 | 800.12 | 0.675 | 719.14 |
| **NPV** | | | **+48.82** | | **−48.66** |
\
textIRR=10\IRR=10\displaystyle \text{IRR} = 10IRR=10\\% + \48.8248.82+48.66\displaystyle \frac{48.82}{48.82 + 48.66}48.82+48.6648.82 \×\displaystyle \times× (14\\% - 10\\%) \textIRR=10
\
=10= 10\\% + \48.8297.48\displaystyle \frac{48.82}{97.48}97.4848.82 \×\displaystyle \times× 4\\% = 10\\% + 2\\% = \\boxed{12\\%} \=10
**Cost of Preference Shares (Kp) = 12%**
---
**(iii) Post-Tax Cost of Debentures (Approximation Method)**
NP (Net Proceeds) = ₹100 − ₹4 (flotation) = ₹96; RV = ₹100; n = 5 years.
Let interest rate on debentures = X, so annual interest = 100X.
Interest on bank loan = 1.3X (pre-tax).
Using WACC = 14% to find X:
\
\Kd\displaystyle \text{Kd}Kd = \I(1−t)+fracRV−NPnfracRV+NP2\displaystyle \frac{I(1-t) + \\frac{RV - NP}{n}}{\\frac{RV + NP}{2}}fracRV+NP2I(1−t)+fracRV−NPn = \100X(0.7)+frac45frac1962\displaystyle \frac{100X(0.7) + \\frac{4}{5}}{\\frac{196}{2}}frac1962100X(0.7)+frac45 = \70X+0.898\displaystyle \frac{70X + 0.8}{98}9870X+0.8 \
\
\Kd(Bank Loan)=1\displaystyle \text{Kd(Bank Loan)} = 1Kd(Bank Loan)=1.3X \×\displaystyle \times× (1 - 0.3) = 0.91X \
Setting up WACC equation:
\
×\displaystyle \times× 0.91X \̲" style="color:#cc0000">0.14 = 0.35(0.20) + 0.25(0.12) + 0.24 \
×\displaystyle \times× \
70X+0.898+0\displaystyle \frac{70X + 0.8}{98} + 09870X+0.8+0.16 \
×\displaystyle \times× 0.91X \
\
0.14 = 0.07 + 0.03 + \16.8X+0.19298+0\displaystyle \frac{16.8X + 0.192}{98} + 09816.8X+0.192+0.1456X \
\
0.04 = \16.8X+0.19298+0\displaystyle \frac{16.8X + 0.192}{98} + 09816.8X+0.192+0.1456X \
\
0.04 \×\displaystyle \times× 98 = 16.8X + 0.192 + 14.2688X \
\
3.92 - 0.192 = 31.0688X \
\
3.728=31.0688XRightarrowX=0.12textor123.728 = 31.0688X \\Rightarrow X = 0.12 \ or \displaystyle \text{ or } or 12\\% \3.728=31.0688XRightarrowX=0.12textor12
So, interest rate on debentures = **12%**.
\
K_d = \12(1−0.3)+frac45frac1962\displaystyle \frac{12(1 - 0.3) + \\frac{4}{5}}{\\frac{196}{2}}frac196212(1−0.3)+frac45 = \8.4+0.898\displaystyle \frac{8.4 + 0.8}{98}988.4+0.8 = \9.298\displaystyle \frac{9.2}{98}989.2 = \\boxed{9.39\\%} \
**Post-tax cost of debentures ≈ 9.39%**
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**(iv) Interest Rate of Bank Loan**
\
textInterestrateonbankloan=1.3timesX=1.3times12\Interest rate on bank loan=1\displaystyle \text{Interest rate on bank loan} = 1Interest rate on bank loan=1.3 \×\displaystyle \times× X = 1.3 \×\displaystyle \times× 12\\% = \\boxed{15.60\\%} \textInterestrateonbankloan=1.3timesX=1.3times12
---
## Part (b): Walter's Model — H Ltd.
**Given:** EPS (E) = ₹3, r = 20%, Ke = 15%
Since **r (20%) > Ke (15%)**, the firm is a **growth firm**. As per Walter's Model, value is maximised by retaining all earnings (D = 0) and minimised by distributing all earnings (D = E).
**Walter's Formula:**
\
P = \D+fracrKe(E−D)Ke\displaystyle \frac{D + \\frac{r}{K_e}(E - D)}{K_e}KeD+fracrKe(E−D) \
**(i) Maximum Price — when D = 0 (full retention):**
\
P_{max} = \0+frac0.200.15(3−0)0.15\displaystyle \frac{0 + \\frac{0.20}{0.15}(3 - 0)}{0.15}0.150+frac0.200.15(3−0) = \frac0.200.15times30.15\displaystyle \frac{\\frac{0.20}{0.15} \\times 3}{0.15}0.15frac0.200.15times3 = \40.15\displaystyle \frac{4}{0.15}0.154 = \\boxed{₹26.67} \
**(ii) Minimum Price — when D = E = ₹3 (full distribution):**
\
P_{min} = \3+frac0.200.15(3−3)0.15\displaystyle \frac{3 + \\frac{0.20}{0.15}(3 - 3)}{0.15}0.153+frac0.200.15(3−3) = \30.15\displaystyle \frac{3}{0.15}0.153 = \\boxed{₹20} \
**Maximum Price = ₹26.67 | Minimum Price = ₹20**