## Cost of Retained Earning

Retained earnings are profit reserves held by companies that are not distributed as dividends. These are preserved to fund a firm’s longterm and short-term activities. It is claimed that the organisation incurs no costs as a result of the retained earnings. It is debatable if there is any legal or inferred requirement to make a profit by investing retained earnings.

Investors expect the organisation to invest the retained earnings in attractive initiatives if it does not distribute dividends and keeps a portion of profit as reserves. Furthermore, investors anticipate that the company would disperse the profits generated by investing retained earnings as dividends.

Table of Content

The cost of retained earnings can be computed using a variety of methods, including the following:

- K
_{E}= K_{R }Approach

This approach implies that if an organisation’s profit is not retained but instead it is dispersed as dividend, the stakeholders will reinvestthe pay out in other ventures to generate more profit. If a company keeps its dividend, it prevents its investors from gaining more money.

As a result, to keep the dividend, the company must make a profit, which the stakeholders would have made if the dividend had been invested in other projects. The cost of retained earnings is the amount of profit anticipated from the organisation on retained earnings. - Soloman Erza Approach

The Soloman Erza Approach entails an organisation’s choice between keeping revenue to meet potential risk or investing in its own or other organisations’ projects.

Cost of preference capital is the amount of dividend payable on them and expenses incurred for raising preference shares. The dividend paid on preference shares is not tax deductible as dividends are appropriated from profits and not considered as an expense.

Cost of preference share can be calculated by using the following formulae:

- Cost of redeemable preference shares:

K_{P}= [{D + F/N (1– T) RP / N] × 100 {P + NP/2}

Where,

K_{P}= Cost of preference share

D = Annual preference dividend

F = Expenses including underwriting commission, brokerage, and discount

N = Number of years to maturity

RP = Redemption premium

P = Redeemable value of preference share

NP = Net proceeds of preference shares - Cost of irredeemable preference shares:

K_{P}= (D/NP) × 100

**Example: **Zen Ltd. issues 10% preference shares of ₹100 each, redeemable at par after 20 years. Calculate the cost of preference share assuming 4% floatation cost and 50% corporate tax in the following conditions:

- When preference shares are issued at par
- When preference shares are issued at 10% discount
- When preference shares are issued at 10% premium

**Solution:**

Cost of redeemable preference shares

= [{D + F/N (1 – T) + RP/N}] ×100

{P + NP/2}

- When preference shares are issued at par:

K_{P}= [{(10 + 4)/20(1 – 0.50) + 0/20}] × 100

{( 100 + 96) /2 }

= 10.30% - When preference shares are issued at 10% discount:

K_{P}= [{(10 4) / 20 (1– 0.50) 0/20}] × 100

{( 100 + 86) /2 }

= 10.86% - When preference shares are issued at 10% premium:

K_{P}= [{(10 4) / 20 (1– 0.50) 0/20}] × 100

{( 100 + 106) /2 }

= 9.80%

## Cost of Debt

Companies may raise debt capital through issue of debentures or loan from financial institutions or deposits from public. All these resources involve a specific rate of interest. The interest paid on these sources of funds is a charge on the profit & loss account of the company. In other words, interest payments made by the firm on debt issue qualify tax deduction in determining net taxable income. Computation of cost of debenture or debt is relatively easy, because the interest rate that is payable on debt is fixed by the agreement between the firm and the creditors.

Computation of cost of debenture or debt capital depends on their nature. The debt/debentures can be perpetual or irredeemable and redeemable cost of debt capital is equal to the interest paid on that debt, but from company’s point of view it will be less than the interest payable, when the debt is issued at par, since the interest is tax deductible.

Hence, computation of debt is always after-tax cost. The entire cost or rate of interest paid by an organisation when raising debt capital is referred to as cost of debt capital. In practise, however, total interest paid for loan capital is not considered cost of debt because entire interest is handled as an expense and taxed separately.

A firm’s tax liability is reduced due to debt. As a result, the company will need to make some modifications to assess the cost of debt. Let us look at an example to assist us comprehend how to calculate the cost of debt. Assuming a company secured ₹10,000 in loan capital and paid a 10% interest rate on it. The company is subject to a 50% corporate tax rate. The complete 10% interest rate would not be subtracted from tax in this case and the reduction would be 50% of 10%.

As a result, the cost of debt would be merely 5%. Discount permitted, underwriting commission and cost of publicity are all factors in determining the cost of borrowed financing. When these costs are added to the amount of interest paid, the overall cost of loan capital is calculated. When a firm’s debt capital percentage exceeds the appropriate amount, the risk factor rises. As a result, investors become uneasy and their anticipation for EPS rises, which is the hidden cost of loan financing.

Calculation of cost of debt is done using the following formulae:

- When the debt is issued at par

K_{D}= [(1-T) × R] × 100

Where,

K_{D}= Cost of debt

T = Tax rate

R = Rate of interest on debt capital

K_{D}= Cost of debt capital - Debt issued at premium or discount when debt is irredeemable:

K_{D }= [1/NP × (1-T) × 100]

Where,

NP = Net proceeds of debt - Cost of redeemable debt:

K_{D}= [{I (1-T) -H (P-NP/N) × (1- T)}/ (P -H NP/2)] × 100

Where,

N = Numbers of years of maturity

P = Redeemable value of debt

**Example:** Fox Co. issued 10% debentures of the face value of ₹100 redeemable at par after 20 years.

Assuming 50% tax rate and 5% floatation cost, calculate cost of debt in the following conditions:

- When debentures are issued at par
- When debentures are issued at 10% discount
- When debentures are issued at 10% premium

**Solution:**

Cost of redeemable debt = [{I (1 − T) + (P − NP / N (1 − T)}] × 100

(P + NP/2)

- When debentures are issued at par

K_{D}= [{10 (1– 0.50) +(100 – 95 / 20) (1– 0.50)}] × 100 = 5.25%

(100 + 95/2) - When debentures are issued at 10% discount

K_{D}= [{10 (1– 0.50) +(100 – 85 / 20) (1– 0.50)}] × 100 = 5.81%

(100 + 85/2) - When debenture is issued at 10% premium

K_{D}= [{10 (1– 0.50) +(100 – 110 / 20) (1– 0.50)}] × 100 = 4.52%

(100 + 110/2)

## Weighted Average Cost of Capital (WACC)

The Weighted Average Cost of Capital (WACC) refers to an organisation’s overall cost of capital in which each category of capital weighted in different proportions. In the calculation of WACC, all the sources of capital such as common stock, preferred stock, bonds and other long-term debt are included. To arrive at the Weighted Average Cost of Capital (WACC), the cost of each source of capital is multiplied by its proportion in the total capital.

Let us now consider an example to understand the concept of WACC. Assume that a company generates funds by issuing debentures and equity shares. On loan capital, it pays interest, and on equity capital, it pays a dividend. The WACC is calculated by adding the total interest paid on debt capital to the total dividend paid on equity capital.

The WACC is calculated using the following formula:

Weighted Average Cost of Capital = (K_{E }× E) + (K_{P} × P) + (K_{D} × D) × (1-T) + (K_{R} × R)

Where,

E = Proportion of equity capital in the capital structure

P = Preference capital proportion in capital structure

D = Debt capital proportion in capital structure

R = Retained earnings proportion in capital structure

K_{E} = Cost of equity

K_{P} = Cost of preference shares

K_{D} = Cost of debt

K_{R} = Cost of retained earnings

**Example:** Barco Ltd. has the following capital structure on 31s^{t} March 2010:

Equity shares (20,000 shares issued) = ₹20,00,000

10% preference shares = ₹4,00,000

10% debentures = ₹12,00,000

Barco’s shares are sold at ₹200 each and Barco projects to pay dividend of ₹20 per share and will rise at 10% every year indefinitely. Calculate the WACC on the capital structure given using a 50% corporate tax rate.

**Solution:**

Cost of debt after tax = [(1 – T) × R] × 100

K_{D} = [(1 – 0.50) × 10%] × 100 = 5%

Cost of equity capital when growth rate is given = [(D/MP) + g] × 100

K_{E }= [(10/100) + 10%] × 100 = 10%

Weighted Average Cost of Capital is calculated by using the below formula:

Source of Capital | Amount ₹ | Weight (W) | Specific cost of capital | W*CC |
---|---|---|---|---|

Equity Shares | 20,00,000 | 1.10 | 0.20 | 0.1100 |

10% Preference Share | 4,00,000 | 0.22 | 0.20 | 0.0220 |

10% Debentures | 12,00,000 | 0.66 | 0.10 | 0.0230 |

Total | 36,00,000 | 0.1550 |

Therefore, weighted average cost of capital = 0.1550 = 15.5%

**Example:** Acorpus Ltd., a tube light manufacturing company is in the process of analysing its capital budgeting projects and wants to calculate weighted average cost of capital. You are given the following information:

Liabilities | Amount ₹ | Assets | Amount ₹ |
---|---|---|---|

Equity Shares | 20,00,000 | Fixed Assets | 30,00,000 |

Preference Share | 10,00,000 | Current Assets | 28,00,000 |

Retained Earnings | 4,00,000 | ||

Debentures | 16,00,000 | ||

Current Liabilities | 8,00,000 | ||

58,00,000 | 58,00,000 |

- 10% debentures of 2000 face value for 10 years redeemable at 10% premium is sold at par, 5% floatation costs.
- 10% preference shares of selling prices ₹2,000 per share and 5% floatation costs
- Equity shares of selling price ₹200 per share with ₹10 floatation cost per share.

The expected growth in equity dividend is 20% per year and the corporate tax is 50%. In the current financial year, the expected dividend is 20% per share.

Calculate the weighted average cost of capital.

**Solution:**

Cost of Debt Capital = [{I (1-T) + (P – NP/N) (1-T)}/ (P + NP/2)] × 100

K_{D} = [ 1 (200 (1– 0.50) + (2,200 – 1,900 / 10) (1– 0.50)] × 100

(2,200 + 1,900 / 2)

= 11.2%

Cost of preference share = (D/NP) × 100

K_{P} = {10/ (2000 – 100)} × 100

= 2.10%

Cost of equity capital = [(D/MP) + G] × 100

K_{E} = 1(10/200) + 0.20) × 100 = 60%

Source of Capital | Amount ₹ | Weight (W) | Specific cost of capital | W*CC |
---|---|---|---|---|

Equity Shares | 20,00,000 | 0.86 | 0.6000 | 0.1290 |

10% Preference Share | 10,00,000 | 0.42 | 0.0210 | 0.0022 |

10% Debentures | 16,00,000 | 0.68 | 0.112 | 0.01900 |

Total | 46,00,000 | 0.30048 |

The weighted average cost of capital therefore is 30.048%.

**Example: **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 |

20,00,000 |

The market prices of these securities are:

Debentures ₹105 per debenture

Preference shares ₹110 per preference share

Equity shares ₹24 each

Additional information:

- ₹100 per debenture redeemable at par, 10% coupon rate, 4% floatation costs, 10-year maturity.
- ₹100 per preference share redeemable at par, 5% coupon rate, 2% floatation cost and 10-year maturity.
- Equity shares has ₹4 floatation cost and market price ₹24 per share.

The next year expected dividend is ₹1 with annual growth of 5%. The firm has practice of paying all earnings in the form of dividend.

Corporate tax rate is 30%. Use Yield to maturity (YTM) method to calculate cost of debentures and preference shares.

You are required to calculate the WACC using the above information by using:

- Book value weights
- Market value weights

**Solution:**

- Cost of Equity (K
_{e})

D_{1}+ g P_{0}− F

1 + 0.05 24 − 4

= .01 or 10% - Cost of Debt (K
_{d})

Current market price (P0) – floatation cost = I(1-t) × PVAF(r,10) + RV × PVIF(r,10)

₹105 – 4% of ₹105 = ₹10(1-0.3) × PVAF (r,10) + ₹100 × PVIF (r,10)

Calculation of NPV at discount rate of 5% and 7%:

Year | Cash flows (₹) | Discount factor @ 5% | Present Value | Discount factor @ 7% | Present Value (₹) |
---|---|---|---|---|---|

0 | 100.8 | 1.000 | (100.8) | 1.000 | (100.8) |

1 to 10 | 7 | 7.722 | 54.05 | 7.024 | 49.17 |

10 | 100 | 0.614 | 61.40 | 0.508 | 50.80 |

NPV | +14.65 | -0.83 |

Calculation of IRR:

**IRR** = 5 % + 14.65 (7% – 5%)

14.65 − (−0.83)

5 % + 14.65 (7% – 5%)

15.48

Cost of Debt (Kd) = 6.89%

Cost of Preference shares (Kp)

Current market price (P0) – floatation cost = PD×PVAF(r,10) + RV×PVIF(r,10)

₹110 – 2% of ₹110 = ₹5×PVAF (r,10) + ₹00×PVIF (r,10)

Calculation of NPV at discount rate of 3% and 5%:

Year | Cash flows (₹) | Discount factor @ 3% | Present Value | Discount factor @ 5% | Present Value (₹) |
---|---|---|---|---|---|

0 | 107.8 | 1.000 | (107.8) | 1.000 | (107.8) |

1 to 10 | 5 | 8.530 | 42.65 | 7.722 | 38.61 |

10 | 100 | 0.744 | 74.40 | 0.614 | 61.40 |

NPV | +9.25 | -7.79 |

Calculation of IRR:

**IRR = **3% + 9.25 (5% – 3%)

9.25 − (− 7.79)

3 % + 9.25 (5% – 3%)

17.04

= 4.08%

Calculation of WACC using book value weights:

Source of capital | Book Value | Weights | After tax cost of capital | WACC (Ko) |
---|---|---|---|---|

(₹) | (a) | (b) | (c) = (a)×(b) | |

10% Debentures | 5,00,000 | 0.25 | 0.0689 | 0.01723 |

5% Preference shares Equity shares | 5,00,000 10,00,000 | 0.25 0.50 | 0.0408 0.10 | 0.01020 0.05000 |

20,00,000 | 1.00 | 0.07743 |

WACC (Ko) = 0.07743 or 7.74%

Calculation of WACC using market value weights:

Source of capital | Market Value | Weights | After tax cost of capital | WACC (Ko) |
---|---|---|---|---|

(₹) | (a) | (b) | (c) = (a)×(b) | |

10% Debentures (₹105× 5,000) | 5,25,000 | 0.151 | 0.0689 | 0.0104 |

5% Preference shares (₹110× 5,000) | 5,50,000 | 0.158 | 0.0408 | 0.0064 |

Equity shares (₹24× 1,00,000) | 24,00,000 | 0.691 | 0.10 | 0.0691 |

34,75,000 | 1.000 | 0.0859 |

WACC (Ko) = 0.0859 or 8.59%

## Marginal Cost of Capital (MCOC)

The cost of additional capital needed by the company to finance investment ideas is known as the marginal cost of capital. It is derived by first calculating the cost of each capital source depending on the capital’s market value. Following that, which type of capital would be the best for financing a project is determined.

The marginal cost of capital is calculated by factoring in the impact of higher capital costs on the overall earnings. To put it another way, the marginal cost of capital is computed in the same way that the weighted average cost of capital is obtained: by simply adding more capital to the total cost of capital.

The following formula can be used to calculate the marginal cost of capital:

Marginal Cost of Capital = E + D+ P+ R = K_{E} + K_{D} + K_{P} + K_{R}

**Example: **Following is the capital structure of Ego Ltd. Find which is considered to be optimum as on 31st March, 2018

Particular | (₹) |
---|---|

14% Debentures | 30,000 |

11% Preference shares | 10,000 |

Equity Shares (10,000 shares) | 1,60,000 |

2,00,000 |

The company share has a market price of ₹23.60. Next year, dividend per share is 50% of year 2017, EPS. The following is the trend of EPS for the preceding 10 years, which is expected to continue in future.

Year | EPS (₹) | Year | EPS (₹) |
---|---|---|---|

2008 | 1.00 | 2013 | 1.61 |

2009 | 1.10 | 2014 | 1.77 |

2010 | 1.21 | 2015 | 1.95 |

2011 | 1.33 | 2016 | 2.15 |

2012 | 1.46 | 2017 | 2.36 |

The company issued new debentures carrying 16% rate of interest and the current market price of debenture is ₹96.

Preference shares ₹9.20 (with annual dividend of ₹1.1 per share) were also issued. The company is in 50% tax bracket.

- Calculate after tax:

- Cost of new debt
- Cost of new preference shares
- New equity share (assuming new equity from retained earnings)

- Calculate marginal cost of capital when no new shares are issued.
- Calculate the amount that can be spent for capital investment before new ordinary shares must be sold. Assuming that retained earnings for next year’s investment is 50 percent of 2017.
- Calculate marginal cost of capital when the fund exceeds the amount calculated in (C), assuming new equity is issued at ₹20 per share.

**Solution:**

- Cost of new debt

K_{d}I(1− t)

P_{0}

= 16 ( 1 − 0.5)

96

= 0.0833 - Cost of new preference shares

K_{p}= PD

P_{0}

= 1.1

9.2

= 0.12 - Cost of new equity shares

= K_{e}= D_{1}+ g

P_{0}

1.18 + 0.10

23.60

= 0.05 + 0.10 = 0.15

Calculation of D1

D1 = 50% of 2017 EPS = 50% of 2.36 = ₹1.18

Calculation of marginal cost of capital:

Type of Capital | Proportion | Specific Cost | Product |
---|---|---|---|

(1) | (2) | (3) | (2) × (3) = (4) |

Debenture | 0.15 | 0.0833 | 0.0125 |

Preference Share | 0.05 | 0.12 | 0.0060 |

Equity Share | 0.80 | 0.15 | 0.1200 |

Marginal cost of capital | 0.1385 |

- The company can spend the following amount without increasing marginal cost of capital and without selling the new shares:

Retained earnings = (0.50) (2.36 × 10,000) = ₹11,800

The ordinary equity (Retained earnings in this case) is 80% of total capital 11,800 = 80% of Total Capital

Capital investment before issuing equity = 11,800

0.80

= ₹14,750 - If the company spends in excess of ₹14,750 it will have to issue new shares.

Capital investment before issuing equity= 1.18 + 0.10

20

= 0.159

The marginal cost of capital will be:

Type of Capital | Proportion | Specific Cost | Product |
---|---|---|---|

(1) | (2) | (3) | (2) × (3) = (4) |

Debenture | 0.15 | 0.0833 | 0.0125 |

Preference Share | 0.05 | 0.1200 | 0.0060 |

Equity Share (New) | 0.80 | 0.1590 | 0.1272 |

Marginal cost of capital | 0.1457 |

**Financial Accounting**

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