Cost of Capital – CA Inter FM Study Material is designed strictly as per the latest syllabus and exam pattern.

## Cost of Capital – CA Inter FM Study Material

**Theory Questions**

Question 1.

Explain the significance of cost of capital. (4 Marks Nov. 2019)

Answer:

The cost of capital is one of the most important component to take financial decisions. The correct calculation of cost of capital helps in the following decision making:

(1) Evaluation of investment options:

Present value of all future benefit is calculated by discounting them with the relevant cost of capital. Different investment options have different cost of capital so we have to calculate cost of capital related to every project and then present value of future benefits related to these projects.

(2) Financing Decision:

Finance managers obtains funds from various sources with consideration of cost, risk and control. Finance manager can easily compare cost of different sources and select source with lowest cost.

(3) Designing of optimum credit policy:

In modern world firm has to sell its products or services on credit. For evaluation of credit period cost of capital is used, benefit though credit should be higher than cost of funds blocked in credit.

Question 2.

Distinguish between Unsystematic Risk & Systematic Risk. (2 Marla Nov. 2020)

Answer:

Unsystematic Risk :

Risk which is associated with performance of company is known as company specific risk or unsystematic risk. This risk can be reduced or eliminated by diversification of the securities portfolio. This is also known as diversifiable risk.

Systematic Risk:

Risk which is associated with macro-economic or market under which a firm is doing business is known as unsystematic risk. This risk cannot be eliminated by the diversification of the securities portfolio, it is also known as non-diversifiable risk. The examples are Center and State government policies, inflation, GDP, per capita income, interest rate etc. This risks are assessed in terms of beta coefficient (b or (3) and calculated through regression equation between return of a security and the return on a market portfolio.

**Practical Problems**

**Cost Of Debt**

Question 1.

A company issues 25,000,14% debentures of ₹ 1,000 each. The debentures are redeemable after the expiry period 5 years. Tax rate applicable to the company is 35%.

Calculate the cost of debt after tax if debentures are issued at 5% discount with 2% flotation cost. (5 Marks Nov. 2015)

Answer:

K_{d} = \(\frac{\mathrm{I}(1-\mathrm{t})+\left(\frac{\mathrm{RV}-\mathrm{NP}}{\mathrm{n}}\right)}{\frac{\mathrm{RV}+\mathrm{NP}}{2}}\) × 100

= \(\frac{140(1-0.35)+\left(\frac{1000-930}{5}\right)}{\frac{1000+930}{2}}\) × 100

Net Proceeds = 1,000 – 5% Discount – 2% Flotation cost = 930

Note: Flotation cost has been calculated on the basis of face value (i.e. 2% of ₹ 1,000 or ₹ 950 whichever is higher).

Question 2.

TT Ltd. issued 20,000,10% Convertible debentures of ₹ 100 each with a maturity period of 5 years. At maturity the debenture holders will have the option to convert the debentures into equity shares of the company in the ratio of 1 : 5 (5 shares for each debenture). The current market price of the equity shares is ₹ 20 each and historically the growth rate of the shares are 4% per annum. Assuming tax rate is 25%.

Compute the cost of 10% debentures using Approximation Method and Internal Rate of Return Method.

PV Factor are as under:

Year | 1 | 2 | 3 | 4 | 5 |

PV Factor @ 10% | 0.909 | 0.826 | 0.751 | 0.683 | 0.621 |

PV Factor (S’ 15% | 0.870 | 0.756 | 0.658 | 0.572 | 0.497 |

Answer:

(a) Calculation of Cost of Convertible debenture using Approximation Method:

K_{d} = \(\frac{\mathrm{I}(1-t)+\frac{\mathrm{CV}-\mathrm{NP}}{\mathrm{n}}}{\frac{\mathrm{CV}+\mathrm{NP}}{2}}\) × 100

= \(\frac{10(1-0.25)+\frac{121.67-100}{5}}{\frac{121.67+100}{2}}\) × 100 = 10.68%

(b) Calculation of Cost of Convertible debenture using IRR Method Calculation of NPV at two discount rates:

Year | Cash Flow | Present Value | Present Value | ||

10% | DCF | 15% | DCF | ||

0 | (100) | 1.000 | (100) | 1.000 | (100) |

1 – 5 | 7.50 | 3.790 | 28.43 | 3.353 | 25.15 |

5 | 121.67 | 0.621 | 75.56 | 0.497 | 60.47 |

NPV | +3.99 | -14.38 |

IRR/K_{d} = LR + \(\frac{\mathrm{NPV}_{\mathrm{L}}}{\mathrm{NPV}_{\mathrm{L}}-\mathrm{NPV}_{\mathrm{H}}}\) × (H – L)

= 10% + \(\frac{3.99}{3.99-(-14.38)}\) × (15% – 10%)

= 11.09%

Determination of Convertible value:

Higher of

(i) The cash value of debentures = ₹ 100

(ii) Value of equity shares = 5 shares × ₹ 20 (1 + 0.04)^{5}

= 5 shares × ₹ 24.333 = ₹ 121.67

₹ 121.67 will be taken as redemption value as it is higher than the cash option and attractive to the investors.

**Cost of Preference Share Capital**

Question 3.

A company issued 40,000,12% Redeemable Preference Shares of ₹ 100 each at a premium of ₹ 5 each, redeemable after 10 year at a premium of 110 each. The flotation cost of each share is ₹ 2.

You are required to calculate cost of preference share capital ignoring dividend tax. (5 Marks May 2013)

Answer:

K_{ρ} = \(\frac{\mathrm{PD}+\left(\frac{\mathrm{RV}-\mathrm{NP}}{\mathrm{n}}\right)}{\frac{\mathrm{RV}+\mathrm{NP}}{2}}\) × 100

= \(\frac{12+\left(\frac{110-103}{10}\right)}{\frac{110+103}{2}}\) × 100

= 11.92%

**Cost of Equity**

Question 4.

JC Ltd. is planning an equity issue in current year. It has an earning per share (EPS) of ₹ 20 and proposes to pay 60% dividend at the current year end with a P/E ratio 6.25, it wants to offer the issue at market price. The flotation cost is expected to be 4% of the issue price.

You are required to determine rate of return for equity share (cost of equity) before the issue and after the issue. (5 Marks May 2018)

Answer:

Market price of share (MPS/P_{0}) = EPS × PE = ₹ 20 × 6.25 = ₹ 25

Net proceeds = 125 – 4% = ₹ 120

Return on Equity (ROE) = 1/PE = 1/6.25 = 16%

Growth rate = r × b = 1696 × 40% = 6.40%

K_{e} (before issue) = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{60 \% \text { of } 20}{125}\) + 6.40% = 16%

K_{e} (after issue) = \(\frac{\mathrm{D}_1}{\mathrm{NP}}\) + g = \(\frac{60 \% \text { of } 20}{120}\) + 6.40% = 16.40%

Question 5.

ABC Company’s equity share is quoted in the market at ₹ 25 per share currently. The company pays a dividend of ₹ 2 per share and the investor’s market expects a growth rate of 6% per year.

You are required to:

(i) Calculate the company’s cost of equity capital.

(ii) If the anticipated growth rate is 8% per annum, calculate the indicated market price per share.

(iii) If the company issues 10% debentures of face value of ₹ 100 each mid realises ₹ 96 per debenture while the debentures are redeemable after 12 years at a premium of 12%, what will be the cost of debenture? Assume Tax Rate to be 50%. (5 Marks Nov. 2016)

Answer:

(i)

Note: Thc cost of equity can be calculated with taking the effect of growth on dividend (i.e. D_{1} = 2.12).

(ii) P_{0} = \(\frac{D_1}{\mathrm{Ke}-\mathrm{g}}\) = \(\frac{2}{14 \%-8 \%}\) = ₹ 33.33

(iii) K_{d} = \(\frac{\mathrm{I}(1-\mathrm{t})+\left(\frac{\mathrm{RV}-\mathrm{NP}}{\mathrm{n}}\right)}{\frac{\mathrm{RV}+\mathrm{NP}}{2}}\) × 100

= \(\frac{10(1-0.50)+\left(\frac{112-96}{12}\right)}{\frac{112+96}{2}}\) × 100

= 6.089%

**Weighted Average Cost of Capital**

Question 6.

Beeta Ltd. has furnished the following information:

Earning per share (EPS) : ₹ 4.00

Dividend payout ratio : 25%

Market price per share : ₹ 40.00

Rate of tax : 30%

Growth rate of dividend : 8%

The company wants to raise additional capital of ₹ 10 lakhs including debt of ₹ 4 lakhs. The cost of debt (before tax) is 10% upto ₹ 2 lakhs and 15% beyond that.

Compute the after tax cost equity and debt and the weighted average cost of capital. (4 Marks Nov. 2011)

Answer:

K_{0} = K_{e} W_{e} + K_{d1} W_{d1} + K_{d2} W_{d2}

= 10.7% × \(\frac{6}{10}\) + 7% × \(\frac{2}{10}\) + 10.50% × \(\frac{2}{10}\) = 9.92%

K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{4.00 \times 25 \% \times 108 \%}{40}\) + 0.08 = 10.70%

K_{d1} = I (1 – t) = 10% (1 – 0.30) = 7%

K_{d2} = I (1 – t) = 15% (1 – 0.30) = 10.50%

Assumption: DPS ₹ 1.00 is treated at D_{0}.

Question 7.

The following details are provided by GPS Limited:

Equity Share capital : ₹ 65,00,000

12% Preference Share Capital : ₹ 12,00,000

15% Redeemable Debentures : ₹ 20,00,000

10% Convertible Debentures : ₹ 8,00,000

The cost of equity capital for the company is 16.30% and Income Tax Rate for the company is 30%.

You are required to calculate the Weighted Average Cost of Capital (WACC) of the company. (5 Marks May 2014)

Answer:

WACC = K_{e} W_{e} + K_{p} W_{p} + K_{rd} W_{rd} + K_{cd} W_{cd}

Working Notes:

(i) Calculation of cost of Preference Share capital (K_{p}) :

K_{p} = Rate of Preference Dividend = 12%

(ii) Calculation of cost of Redeemable Debentures (K_{rd}):

K_{rd} = I (1 – t) = 15% (1 – 0.30) = 10.50%

(iii) Calculation of cost Convertible Debentures (K_{cd}):

K_{cd} = I (1 – t) = 10% (1 – 0.30) = 7%

Question 8.

A Ltd. wishes to raise additional finance of ₹ 30 lakhs for meeting its investment plans. The company has ₹ 6,00,000 in the form of retained earnings available for investment purposes. The following are the further details:

Debt equity ratio : 30:70

Cost of debt:

Upto ₹ 3,00,000 : 11% (before tax) and

Beyond ₹ 3,00,000 : 14% (before tax)

Earning per share : ₹ 15 per share

Dividend payout : 70% of earnings

Expected growth rate : 10%

Current market price : ₹ 90 per share

Company’s tax rate : 30%

Shareholder’s personal tax rate : 20%

You are required to:

1. Calculate the post tax average cost of additional debt.

2. Calculate the cost of retained earnings and cost of equity.

3. Calculate the overall weighted average (after tax) cost of additional (8 Marks May 2015)

Answer:

Total capital required is ₹ 30 lakhs. With a debt-equity ratio of 30 : 70. It means ₹ 9 lakhs is to be raised through debt and ₹ 21 lakhs through equity. Out of ₹ 21 lakhs, ₹ 6 lakhs are available in the form of retained earnings hence ₹ 15 lakhs will have to raise by issuing equity shares.

1. Post tax average cost of additional debt:

K_{d1} = I (1 – t) = 11% (1 – 0.30) = 7.70%

K_{d2} = I (1 – t) = 14% (1 – 0.30) = 9.80%

Average K_{d} = K_{d1}W_{d1} + K_{d2}W_{d2} = 7.7% × \(\frac{3}{9}\) + 9.8% × \(\frac{6}{9}\) = 9.10%

2. Cost of retained earning & cost of equity:

K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{10.50+10 \%}{90}\) + 0.10 = 22.83%

K_{r} = K_{e} (1 – PT) = 22.83% (1 – .20) = 18.27%

D_{0} = ₹ 15 × 70% = ₹ 10.50

3. Overall cost of additional finance:

K_{0} = K_{e} W_{e} + K_{r} W_{r} + K_{d} W_{d}

= 22.83% × \(\frac{15}{30}\) + 18.27% × \(\frac{6}{30}\) + 9.10% × \(\frac{9}{30}\)

= 17.80%

Assumption: DPS ₹ 10.50 is treated at D_{0}.

Question 9.

The X Company has following capital structure at 31st March, 20015, which is considered to be optimum:

14% debenture : ₹ 3,00,000

11% preference share capital : ₹ 1,00,000

Equity share capital (1,00,000 shares) : ₹ 16,00,000

The company’s share has a current market price of ₹ 23.60 per share. The expected dividend per share in next year is 50 per cent of the 2015 EPS. The EPS of last 10 years is as follows. The past trends are expected to continue:

The company issued new debentures carrying 16% rate of interest and the current market price of debenture is ₹ 96. Preference shares ₹ 9.20 (with dividend of ₹ 1.1 per share) were also issued. The company is in 50% tax bracket.

(i) Calculate the after tax cost of (a) New Debts, (b) New Preference Share, and (c) New Equity Share (assuming new equity from retained earnings).

(ii) Calculate the marginal cost of capital when no new share was issued.

(iii) How much can be spent for capital investment before new ordinary shares must be sold? Assuming that retained earnings for next year’s investment are 50% of 2015.

(iv) What will be marginal cost of capital when the fund exceeds the amount calculated in (iii), assuming new equity is issued at ₹ 20 per share? (8 Marks May 2016)

Answer:

Assumption: The present capital structure is optimum. Hence, it will be followed in future.

Existing Capital Structure Analysis

Name of source | Amount(₹) | Proportion |

14% debentures | 3,00,000 | 0.15 |

11% Preference | 1,00,000 | 0.05 |

Equity share capital | 16,00,000 | 0.80 |

Total | 20,00,000 | 1.00 |

(i) (a) After tax cost of new debt

(ii) MCC(K_{0}) when no new equity share was issued:

K_{d}W_{d} + K_{p} W_{p} + K_{r} W_{r} = 8.33% × .15 + 11.96% × .05 + 15% × .80 = 13.85%

(iii) The company can pay the following amount before issue of new shares:

Equity (retained earnings in this case) = 80% of the total capital

Therefore, investment before new issue = \(\frac{1,18,000}{80 \%}\) = ₹ 1,47,500

Retained earnings = ₹ 2.36 × 50% × 1,00,000 = ₹ 1,18,000

(iv) MCC (K_{0}) when funds exceeds ₹ 1,47,500

K_{d}W_{d} + K_{p}W_{p} + K_{e}W_{e} = 8.33% × .15 + 11.96% × .05 + 15.90% × .80 = 14.57%

If the company pay more than ₹ 1,47,500, it will have to issue new shares. The cost of new issue of ordinary share is:

K_{e} = \(\frac{D_1}{P_0(\text { new })}\) + g = \(\frac{1.18}{20}\) + 20 = 15.90%

WN: Calculation of growth:

Growth from year 2006 to 2007 = (1.10 – 1.00) ÷ 1.00 = 10%

[Same rate of growth is found in future years]

Question 10.

Following is the capital structure of RBT Ltd. As on 31st March, 2016:

Sources of Fund | Book Value | Market Value |

Equity Share of ₹ 10 each
Retained Earnings 11% Preference Share of ₹ 100 each 14% Debentures of ₹ 100 each |
₹ 50,00,000
₹ 13,00,000 ₹ 7,00,000 ₹ 30,00,000 |
₹ 1,05,00,000
Nil ₹ 9,00,000 ₹ 36,00,000 |

Market price of equity shares is ₹ 40 per share and it is expected that a dividend of ₹ 4 per share would be declared. The dividend per share is expected to grow at the rate of 8% every year. Income tax rate applicable to the company is 40% and shareholder’s personal income tax rate is 20%.

You are required to calculate:

(i) Cost of capital for each source of capital,

(ii) Weighted average cost of capital on the basis of book value weights,

(iii) Weighted average cost of capital on the basis of market value weights. (8 Marks Nov. 2016)

Answer:

(i) Calculation of cost of capital for each source of capital:

K_{e} = \(\frac{D_1}{P_0(\text { new })}\) + g = \(\frac{4}{40}\) + 0.08 = 18%

K_{r} = K_{e} (1 – PT) = 18%(1 – 0.20) = 14.40%

K_{d} = I (1 – t) = 14% (1 – 0.40) = 8.40%

K_{p} = Rate of PD = 11%

(ii) Calculation of WAC.C (K_{0}) using book value proportions

Name of Source | Amount | Proportion | K | K_{0} |

Equity Share Capital | 50,00,000 | 0.50 | 18% | 9.00% |

Retained Earnings | 13,00,000 | 0.13 | 14.40% | 1.87% |

Preference Share Capital | 7,00,000 | 0.07 | 11% | 0.77% |

Debentures | 30,00,000 | 0.30 | 8.40% | 2.52% |

Total | 1,00,00,000 | 1.00 | WACC | 14.16% |

(iii) Calculation of WACC(K_{0}) using market value proportions

Name of Source | Amount | Proportion | K | K_{0} |

Equity Share Capital | 83,33,333 | 0.555 | 18% | 9.99% |

Retained Earnings | 21,66,667 | 0.145 | 14.40% | 2.09% |

Preference Share Capital | 9,00,000 | 0.060 | 11% | 0.66% |

Debentures | 36,00,000 | 0.240 | 8.40% | 2.02% |

Total | 1,50,00,000 | 1.000 | WACC | 14.76% |

Market value of Equity Share Capital = ₹ 1,05,00,000 × 50/63 = ₹ 83,33,333

Market value of Retained Earnings = ₹ 1,05,00,000 × 13/63 = ₹ 21,66,667

‘Market Value of equity has been apportioned in the ratio of Book Value of equity and retained earnings.

Question 11.

Alpha Ltd. has furnished the following information:

Earning per share (EPS) : ₹ 4.00

Dividend payout ratio : 25%

Market price per share : ₹ 50

Rate of tax : 30%

Growth rate of dividend : 10%

The company wants to raise additional capital of ₹ 10 lakhs including debt of ₹ 4 lakhs. The cost of debt (before tax) is 10% upto ₹ 2 lakhs and 15% beyond that.

Compute the after tax cost equity and debt and the weighted average cost of capital. (5 Marks May 2019)

Answer:

K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{4.00 \times 25 \% \times 110 \%}{50}\) + 0.10 = 12.20%

K_{d1} = I (1 – t) = 10% (1 – 0.30) = 7%

K_{d2} = I (1 – t) = 15% (1 – 0.30) = 10.50%

K_{0} = K_{e} W_{e} + K_{d1} W_{d1} + K_{d2} W_{d2}

= 12.20% × \(\frac{6}{10}\) + 7% × \(\frac{2}{10}\) + 10.50% × \(\frac{2}{10}\) = 10.82%

Question 12.

A company wants to raise additional finance of ₹ 5 crores in next year. The company expected to retain ₹ 1 crore in next year. Further details are as follows:

(i) The amount will be raised by equity and debt in the ratio of 3 : 1.

(ii) The additional issue of equity shares will result in price per share being fixed at ₹ 25.

(iii) The debt capital raised by way of term loan will cost 10% for the first ₹ 75 lakhs and 12 % for the next ₹ 50 lakhs.

(iv) The net expected dividend on equity shares is ₹ 2.00 per share. The dividend is expected to grow at the rate of 5%.

(v) Income tax rate of 25%.

You are required:

(a) To determine the amount of equity and debt for raising additional finance.

(b) To determine the post tax average cost of additional debt.

(c) To determine the cost of retained earning and cost of equity.

(d) To compute the overall weighted average cost of additional finance after tax. (10 Marks Nov, 2019)

Answer:

(a) Total capital required is ₹ 5 crores. With a debt-equity ratio of 1:3. It means ₹ 1.25 crores is to be raised through debt and ₹ 3.75 crores through equity. Out of ₹ 3.75 crores, ₹ 1 crore are available in the form of retained earnings hence ₹ 2.75 crore will have to raise by issuing equity shares.

(b) Post tax average cost of additional debt:

K_{d1} = I (1 – t) = 10% (1 – 0.25) = 7.5%

K_{d2} = I (1 – t) = 12% (1 -0.25) = 9%

Average K_{d} = K_{d2} W_{d2} + K_{d2} W_{d2}

= 7.5% × \(\frac{75}{125}\) + 9% × \(\frac{50}{125}\) = 8.10%

(c) Cost of retained earning & cost of equity:

K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{2}{25}\) + 0.05 = 13%

K_{r} = K_{e} = 13%

(d) Overall cost of additional finance:

K_{0} = K_{e} W_{e} + K_{r} W_{r} + K_{d} W_{d}

= 13% × \(\frac{275}{500}\) + 13% × \(\frac{100}{500}\) + 8.10% × \(\frac{125}{500}\) = 11.78%

Question 13.

The capital structure of PQR Ltd. is as follows:

10% Debentures : ₹ 3,00,000

12% Preference shares : ₹ 2,50,000

Equity shares (face value ₹ 10 per share) : ₹ 5,00,000

Additional information:

- ₹ 100 per debenture redeemable at par has 2% floatation cost & 10 years of maturity. The market price per debenture is ₹ 110.
- ₹ 100 per preference share redeemable at par has 3% floatation cost & 10 years of maturity. The market price per preference share is ₹ 108.
- Equity share has ₹ 4 floatation cost and market price per share of ₹ 25. The next year expected dividend is ₹ 2 per share with annual growth of 5%. The firm has a practice of paying all earnings in the form of dividends.
- Corporate Income tax rate is 30%.

Required:

Calculate Weighted Average Cost of Capital (WACC) using market value weights. (10 Marks Jan. 2021)

Answer:

Calculation of Weighted Average Cost of Capital by Using Market Value Weight

Particular | Market value | Weight | Cost | Weighted cost |

10% Debenture | 3,30,000 | 0.178 | 7.27% | 1.294% |

12% Preference share | 2,70,000 | 0.146 | 12.49% | 1.823% |

Equity Share Capital | 12,50,000 | 0.676 | 14.52% | 9.816% |

Total | 18,50,000 | 1.000 | WACC | 12.933% |

Working notes:

1. Calculation of specific cost of various sources of funds:

2. Calculation of market value of various sources of funds:

Debentures = 3,00,000 × 110/100 = 3,30,000

Preference shares = 2,50,000 × 108/100 = 2,70,000

Equity shares = 5,00,000 × 25/10 = 12,50,000

**Important Questions**

Question 1.

A company issued 10,000,15% Convertible debentures of ₹ 100 each with a maturity period of 5 years. At maturity the debenture holders will have the option to convert the debentures into equity shares of the company in the ratio of 1 : 10 (10 shares for each debenture). The current market price of the equity shares is ₹ 12 each and historically the growth rate of the shares are 5% per annum.

Compute the cost of debentures assuming 35% tax rate.

Answer:

Determination of Redemption value:

Higher of

(i) The cash value of debentures = ₹ 100

(ii) Value of equity shares = 10 shares × ₹ 12(1 + 0.05)^{5}

= 10 shares × 15.312 = ₹ 153.12

₹ 153.12 will be taken as redemption value as it is higher than the cash option and attractive to the investors.

Calculation of Cost of Convertible debenture:

Alternative 1: Using approximation method:

K_{d} = \(\frac{\mathrm{I}(1-\mathrm{t})+\left(\frac{\mathrm{RV}-\mathrm{NP}}{\mathrm{n}}\right)}{\frac{\mathrm{RV}+\mathrm{NP}}{2}}\) × 100 = \(\frac{15(1-0.35)+\frac{153.12-100}{5}}{\frac{153.12+100}{2}}\) × 100 = 16.09%

Alternative 2: Using present value method:

Calculation of NPV at two discount rates:

Question 2.

RBML is proposing to sell a 5-year bond of ₹ 5,000 at 8 percent rate of interest per annum. The bond amount will be amortised equally over its life.

What is the bond’s present value for an investor if he expects a minimum rate of return of 6 percent?

Answer:

The amount of interest will go on declining as the outstanding amount of bond will be reducing due to amortisation. The amount of interest for five years will be:

First year : ₹ 5,000 × 0.08 = ₹ 400

Second year : ₹ (5,000 – ₹ 1,000) × 0.08 = ₹ 320

Third year : ₹ (4,000 – ₹ 1,000) × 0.08 = ₹ 240

Fourth year : ₹ (3,000 – ₹ 1,000) × 0.08 = ₹ 160; and

Fifth year : ₹ (2,000 – ₹ 1,000) × 0.08 = ₹ 80.

The outstanding amount of bond will be zero at the end of fifth year. Since RBML will have to return ₹ 1,000 every year, the outflows every year will consist of interest payment and repayment of principal:

First year : ₹ 1,000 + ₹ 400 = ₹ 1,400

Second year : ₹ l1,000 + ₹ 320 = ₹ 1,320

Third year : ₹ 1,000 + ₹ 240 = ₹ 1,240

Fourth year : ₹ 1,000 + ₹ 160 = ₹ 1,160; and

Fifth year : ₹ 1,000 + ₹ 80 = ₹ 1,080.

The above cash flows of all five years will be discounted with the cost of capital. Here the expected rate i.e. 6% will be used. Value of the bond is calculated as follows:

V_{B} = \(\frac{1,400}{(1.06)^1}+\frac{1,320}{(1.06)^2}+\frac{1,240}{(1.06)^3}+\frac{1,160}{(1.06)^4}+\frac{1,080}{(1.06)^5}\)

= ₹ 1,320.75 + ₹ 1,174.80 + ₹ 1,041.14 + ₹ 918.88 + ₹ 807.05 = ₹ 5,262.62

Question 3.

Mr. Mehra had purchased a share of Alpha Limited for ₹ 1,000. He received dividend for a period of five years at the rate of 10 per cent. At the end of the fifth year, he sold the share of Alpha Limited for ₹ 1,128.

You are required to compute the cost of equity as per realised yield approach.

Answer:

Calculation of IRR/K_{e}

K_{e} = LR + \(\frac{\mathrm{NPV}_{\mathrm{L}}}{\mathrm{NPV}_{\mathrm{L}}-\mathrm{NPV}_{\mathrm{H}}}\) × (H – L) = 11% + \(\frac{38.50}{38.50-(-35.80)}\) × (13% – 11%) = 12.04%

Calculation of NPV at two discount rates:

Question 4.

Calculate the cost of equity from the following data using realized yield approach:

Answer:

In this questions we will first calculate yield for last 4 years and then calculate it geometric mean as follows:

Geometric mean:

K_{e} = [(1 + Y_{1}) × (1 + Y_{2}) × (1 + Y_{n})]^{1/n} – 1

K_{e} = [1.1944 × 1.2821 × 1.0609 × 1.0772]^{1/4} – 1 = 0.15 or 15%

Question 5.

The following is the capital structure of Simons Company Ltd. as on 31.12.1998:

The market price of the company’s share is ₹ 110 and it is expected that a dividend of ₹ 10 per share would be declared for the year 1998. The dividend growth rate is 6%.

(i) If the company is in the 50% tax bracket, compute the WACC.

(ii) Assuming that in order to finance an expansion plan, the company intends to borrow a fund of ₹ 10,00,000 bearing 14% rate of interest, What will be the company’s revised weighted average cost of Capital? This financing decision is expected to increase dividends from ₹ 10 to ₹ 12 per share. However, the market price of equity share is expected to decline from ₹ 110 to ₹ 105 per share.

Answer:

In this questions we will first calculate yield for last 4 years and then calculate it geometric mean as follows:

WACC(K_{0}) = K_{e} W_{e} + K_{p} W_{p} + K_{d} W_{d}

= 15.09% × \(\frac{10}{20}\) + 10% × \(\frac{4}{20}\) + 6% × \(\frac{6}{20}\) = 11.35%

K_{e} = \(\frac{D_1}{P_0}\) + g = \(\frac{10}{110}\) + 0.6 = 15.09%

K_{p} = Rate of preferential dividend [FV = NP] = 10%

K_{d} = I (1 – t) = 12% (1 – 0.50) = 6%

(ii) Calculation of Revised WACC

Revised WACC (K_{0})

= K_{e} W_{e} + K_{p} W_{p} + K_{d} W_{d} + K_{TL} W_{TL}

= 17.43% × \(\frac{10}{30}\) + 10% × \(\frac{4}{30}\) + 6% × \(\frac{6}{30}\) + 7% × \(\frac{10}{30}\) = 10.68%

Revised K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{12}{105}\) + .06 = 17.43%

K_{TL} = I (1 – t) = 14%(1 – 0.50) = 7%

Question 6.

XYZ Ltd. has the following book value capital structure:

Equity Share Capital (₹ 10 each, fully paid up at par) : ₹ 15 crores

11% Preference Share Capital (₹ 100 each, fully paid up at par) : ₹ 1 crores

Retained Earnings : ₹ 20 crores

13.5% Debentures (of ₹ 100 each) : ₹ 1o crores

15% Terms Loans : ₹ 12.5 crores

The next expected dividend on equity shares per share is ₹ 3.60; the dividend per share Is expected to grow at the rate of 7%. The market price per share is ₹ 40. Preference stock, redeemable after 10 years, is currently selling at ₹ 75 per share. Debentures, redeemable after six years, are selling at ₹ 80 per debenture. The income – tax rate for the company is 40%.

Required:

(i) Calculate the weighted average cost of capital (K_{0}) using:

a. Book value proportions; and

b. Market value proportions.

(ii) Define the weighted marginal cost of capital schedule for the company, if it raises ₹ 10 crores next year, given the following information:

a. The amount will be raised by equity and debt in equal proportions;

b. The company expects to retain ₹ 1.5 crores earnings next year;

c. The additional Issue of equity shares will result In the net price per share being fixed at ₹ 32;

d. The debt capital raised by way of term loans will cost 15% for the first ₹ 2.5 crores and 16% for the next ₹ 2.5 crores.

Answer:

(i) Calculation of WACC(K_{0})

(a) By Using Book Value Proportions

*K_{c} & K_{r} are same, so calculated together.

(ii) Weighted Marginal Cost of Capital Schedule and Marginal WACC:

Marginal Cost of Capital Schedule:

Finance through Equity:

Retained earnings = ₹ 1.5 crores

New issue = ₹ 3.5 crores

Finance through Debt:

15% Debt = ₹ 2.5 crores

16% Debt = ₹ 2.5 crores

Marginal Cost of Capital

Working Notes:

Calculation of existing K_{e}, K_{r}, K_{d}, K_{p} and K_{TL}:

K_{TL} = I (1 – t) = 15% (1 – 0.40) = 9%

Calculation of revised K_{e}, K_{r}, K_{d1} and K_{d2}

K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{3.60}{32}\) + 0.07 = 18.25%

K_{r} = K_{e} (existing) = 16%

K_{d1} = I (1 – t) = 15% (1 – 0.40) = 9%

K_{d2} = I (1 – t) = 16% (1 – 0.40) = 9.60%

Question 7.

Calculate the WACC using the following data by using:

(a) Book value weights

(b) Market value weights

The capital structure of the company is as under:

Debentures (₹ 100 per debenture) : ₹ 5,00,000

Preference shares (₹100 per share) : ₹ 5,00,000

Equity shares (₹10 per share) : ₹ 10,00,000

The market prices of these securities are:

Debentures : ₹ 105 per debenture

Preference shares : ₹ 110 per share

Equity shares : ₹ 24 each

Additional information:

- ₹100 per debenture redeemable at par, 10% coupon rate, 4% floatation cost, 10 years of maturity. The market price per debenture is ₹ 105.
- ₹ 100 per preference share redeemable at par, 5% coupon rate, 2% floatatlon cost, 10 years of maturity.
- Equity share has ₹ 4 floatation cost and market price per share of ₹ 24, The next year expected dividend is ₹ 1 per share with annual growth of 5%. The firm has a practice of paying all earnings in the form of dividends. Corporate Income-tax rate is 50%.

Answer:

(a) Calculation of Weighted Average Cost of Capital by Using Book Value Weight

(b) Calculation of Weighted Average Cost of Capital by Using Market Value Weight

Question 8.

ABC Ltd. wishes to raise additional finance of ₹ 20 lakhs for meeting its Investment purpose. The company has ₹ 4,00,000 in the form of retained earnings available for Investment purposes. The following are the further details:

Debt equity ratio : 25 : 75

Cost of debt:

Upto ₹ 2,00000 : 10% (before tax) and

Beyond ₹ 200000 : 13% (before tax)

Earning per share : ₹ 12 per share

Dividend payout : 50% of earnings

Expected growth rate : 10%

Current market price : ₹ 60 per share

Company’s tax rate : 30%

Shareholder’s personal tax rate : 20%.

Required:

(i) Calculate the post tax average cost of additional debt.

(ii) Calculate the cost of retained earnings and cost of equity.

(iii) Calculate the overall weighted average (after tax) cost of additional

Answer:

Total capital required is ₹ 20 lakhs. With a debt-equity ratio of 1 : 3. It means ₹ 5 lakhs is to be raised through debt and ₹ 15 lakhs through equity. Out of ₹ 15 lakhs, ₹ 4 lakhs are available in the form of retained earnings hence ₹ 11 lakhs will have to raise by issuing equity shares.

(i) Post tax average cost of additional debt:

K_{d1} = I (1 – t) = 10% (1 – 0.30) = 7%

K_{d2} = I(1 – t) = 13%(1 0.30) = 9.10%

Average K_{d} = K_{d1} W_{d1}+ K_{d2} W_{d2}

= 7% × \(\frac{2}{5}\) + 9.10% × \(\frac{3}{5}\) = 8.26%

(ii) Cost of retained earning & cost of equity:

K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0}\) + g = \(\frac{6+10 \%}{60}\) + 0.10 = 21%

K_{r} = K_{e}(1 – PT) = 21% (1 – .20) = 16.80%

D_{0} = ₹ 12 × 5096 = ₹ 6

(iii) Overall cost of additional finance:

K_{0} = K_{e} W_{e} + K_{r} W_{r} + K_{d} w_{d}

= 21% × \(\frac{11}{20}\)+ 16.80% × \(\frac{4}{20}\) + 8.26% × \(\frac{5}{20}\) = 16.98%

Assumption: DPS is treated at D_{0}.

Question 9.

The R & G Company has following capital structure at 31st March, 2004, which is considered to be optimum:

13% debenture : ₹ 3,60,000

11% preference share capital : ₹ 1,20,000

Equity share capital (2,00,000 shares) : ₹ 9,20,000

The company’s share has a current market price of ₹ 27.75 per share. The expected dividend per share in next year is 50 per cent of the 2004 EPS. The EPS of last 10 years is as follows. The past trends are expected to continue:

The company can issue 14 per cent new debenture. The company’s debenture is currently selling at ₹ 98. The new preference issue can be sold at a net price of ₹ 9.80, paying a dividend of ₹ 1.20 per share. The company’s marginal tax rate is 50%.

(i) Calculate the after tax cost (a) of a new debts and new preference share capital, (b) of ordinary equity, assuming new equity comes from retained earnings.

(ii) Calculate the marginal cost of capital.

(iii) How much can be spent for capital investment before new ordinary share must be sold? Assuming that retained earning available for next year’s investment are 50% of 2004 earnings.

(iv) What will be marginal cost of capital [cost of fund raised in excess of the amount calculated in part (iii)] if the company can sell new ordi-nary shares to net ₹ 20 per share? The cost of debt and of preference capital is constant.

Answer:

Assumption. The present capital structure is optimum. Hence, it will be followed in future.

Existing Capital Structure Analysis

Name of source | Amount(₹) | Proportion |

13% debentures | 3,60,000 | 0.15 |

11% Preference | 1,20,000 | 0.05 |

Equity share capital | 19,20,000 | 0.80 |

Total | 24,00,000 | 1.00 |

(i) (a) After tax cost of new debt

K_{d} = \(\frac{\mathrm{I}(1-\mathrm{t})}{\mathrm{NP}}\) × 100 = \(\frac{14(1-.50)}{98}\) × 100 = 7.143%

After tax cost of new preference shares

K_{p} = \(\frac{\text { PD }}{\mathrm{NP}}\) × 100 = \(\frac{1.20}{9.80}\) × 100 = 12.25%

(b) Cost of new equity (comes from retained earnings)

K_{e} = \(\frac{D_1}{P_0 \text { (old) }}\) + g = \(\frac{1.3865}{27.75}\) + 0.12 = 17%

(ii) MCC(K_{0}) = K_{d} W_{d} + K_{p} W_{p} + K_{e} W_{e}

= 7.143% × .15 + 12.245% × .05 +17% × .80 = 15.28%

The company can pay the following amount without selling the new shares:

Equity (retained earnings in this case) = 80% of the total capital

Therefore, investment before new issue = \(\frac{2,77,300}{80 \%}\) = ₹ 3,46,625

Retained earnings = ₹ 1.3865 × 2,00,000 = ₹ 2,77,300

(iv) MCC(K_{0}) = K_{d} W_{d} + K_{p} W_{p} + K_{e} W_{e}

= 7.143% × . 15 + 12.245% × .05 + 18.93% × .80 = 16.83%

If the company pay more than ₹ 3,46,625, it will have to issue new shares. The cost of new issue of ordinary share is:

K_{e} = \(\frac{\mathrm{D}_1}{\mathrm{P}_0(\text { new })}\) + g = \(\frac{1.3865}{20}\) + 0.12 = 18.93%

Question 10.

Determine the cost of capital of Best Luck Limited using the book value (BV) and market value (MV) weights from the following information:

Sources of Fund | Book Value | Market Value |

Equity Shares | ₹ 1,20,00,000 | ₹ 2,00,00,000 |

Retained Earnings | ₹ 30,00,000 | Nil |

Preference Shares | ₹ 36,00,000 | ₹ 33,75,000 |

Debentures | ₹ 9,00,000 | ₹ 10,40,000 |

Additional Information:

- Equity: Equity shares are quoted at ₹ 130 per share and a new issue priced at ₹ 125 per share will be fully subscribed; floatation costs will be ₹ 5 per share.
- Dividend: During the previous 5 years, dividends have steadily increased from ₹ 10.60 to ₹ 14.19 per share. Dividend at the end of the current year is expected to be ₹ 15 per share.
- Preference Shares: 15% Preference shares with face value of ₹ 100 would realise ₹ 105 per share.
- Debentures: The company proposes to issue 11 year 15% debentures but the yield on debentures of similar maturity and risk class is 16%; floatation cost is 2%.
- Tax: Corporate tax rate is 35%. Ignore dividend tax.

Answer:

(a) Calculation of Weighted Average Cost of Capital by Using Book Value Weight

(b) Calculation of Weighted Average Cost of Capital by Using Market Value Weight

MV of Debenture = \(\frac{\text { Interest }}{\text { Market rate of Interest }}\) = \(\frac{15 \% \text { of } 100}{16 \%}\) × 100 = ₹ 93.75

NP of Debenture = MV of Debenture – Floatation Cost

= ₹ 93.75 – ₹ 2 (2% of ₹ 100) = ₹ 91.75

Note: Since yield on similar type of debentures is 16 per cent, the company would be required to offer debentures at discount.

Market value of Equity Shares = ₹ 2,00,00,000 × 120/150 = ₹ 1,60,00,000

Market value of Retained Earnings = ₹ 2,00,00,000 × 30/150 = ₹ 40,00,000

Market Value of equity has been apportioned in the ratio of Book Value of equity and retained earnings.