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# 1. Case analysis of Gemini: Deciding the best capital structure

## 1.1 Weighted average cost of capital calculation

Weighted average cost of capital (WACC) is the return that the providers of a company’s capital require. Calculating it requires knowing the rates of return required focr each source of capital. The cost of capital will be different for each source of capital and class of securities a company has, reflecting the different risks. The WACC is the weighted average of the costs of each of the different types of capital. The weights are proportion of the company’s capital that comes from each source (Moneyterms.co.uk 2011). As mentioned in the previous session, in a Standard Cost of Capital Approach, there factors need to be identified and computed: cost of equity, after tax cost of debts and the overall weighted cost of capital. The data that has been given includes:

Percentage of the debt | Cost of debt before tax (per cent) | Credit rating |

10 per cent | 6.5 per cent | AAA |

20 per cent | 7.1 per cent | AA |

30 per cent | 7.8 per cent | A |

40 per cent | 8.5 per cent | BBB |

50 per cent | 10.0 per cent | BB |

60 per cent | 12.0 per cent | B |

70 per cent | 15.0 per cent | C |

The company’s ungeared equity Beta, B (unlevered) is 0.85, risk free rate 6per cent, expected return on a market portfolio is 14per cent, and the corporate taxation rate is at 30per cent.

Assume that the company has a profit which is more than the debt in order to enjoy the tax deduction. Because Cost of debt = Pre-tax cost of debt (firm’s bonds or short-term) X (1 – marginal tax rate), and the marginal tax rate refers to the corporate taxation rate which is 0.3 in this case, as a result, the cost of debt could be computed like this:

Cost of debt = | Pre-tax cost of debt (per cent) X | (1 – marginal tax rate) |

4.55 per cent | 6.5 per cent | 70 per cent |

4.97 per cent | 7.1 per cent | 70 per cent |

5.46 per cent | 7.8 per cent | 70 per cent |

5.95 per cent | 8.5 per cent | 70 per cent |

7s per cent | 10 per cent | 70 per cent |

8.4 per cent | 12 per cent | 70 per cent |

10.5 per cent | 15 per cent | 70 per cent |

Another item needs to be calculated is the cost of equity, it is formula is:

Cost of equity = Risk free rate of return + Beta (levered) X (market rate of return- risk free rate of return)

In order to calculate this formula, we need to calculate the Beta (levered), since the Beta (levered) is flexible and moving based on the debt to equity ratio, its calculation formula is: Beta (levered) = Beta (unlevered) X [1+ (1-t) X (D/E)], so the results are:

Percentage of the debt | Beta (levered) = | Beta (unlevered) X | [1 + | (1-t) X | (D/E)] |

10 per cent | 0.91611111111111 | 0.85 | [1 + | 0.7 X | (0.11111111111111)] |

20 per cent | 0.99875 | 0.85 | [1 + | 0.7 X | (0.25)] |

30 per cent | 1.105 | 0.85 | [1 + | 0.7 X | (0.42857142857143)] |

40 per cent | 1.24666666666667 | 0.85 | [1 + | 0.7 X | (0.66666666666667)] |

50 per cent | 1.445 | 0.85 | [1 + | 0.7 X | 1] |

60 per cent | 1.7425 | 0.85 | [1 + | 0.7 X | 1.5] |

70 per cent | 2.23833333333333 | 0.85 | [1 + | 0.7 X | 2.33333333333333] |

With the calculated Beta (levered) we can apply the formula that Cost of equity = Risk free rate of return + Beta (levered) X (market rate of return- risk free rate of return) to calculate the cost of equity in this case. Since Market Risk Premium is the difference between the expected return on a market portfolio and the risk-free rate, Market Risk Premium = market portfolio – the risk-free rate = 14 per cent – 6 per cent = 8 per cent. Calculation is demonstrated below:

Percentage of the debt | Cost of equity = | Risk free rate of return + | Beta (levered) X | (market rate of return- | risk free rate of return) |

10 per cent | 13.33 per cent | 6 per cent | 0.91611111111111 | 14 per cent | 6 per cent |

20 per cent | 13.99 per cent | 6 per cent | 0.99875 | 14 per cent | 6 per cent |

30 per cent | 14.84 per cent | 6 per cent | 1.105 | 14 per cent | 6 per cent |

40 per cent | 15.97 per cent | 6 per cent | 1.24666666666667 | 14 per cent | 6 per cent |

50 per cent | 17.56 per cent | 6 per cent | 1.445 | 14 per cent | 6 per cent |

60 per cent | 19.94 per cent | 6 per cent | 1.7425 | 14 per cent | 6 per cent |

70 per cent | 23.91 per cent | 6 per cent | 2.23833333333333 | 14 per cent | 6 per cent |

Calculation of WACC follows this formula:

WACC = RE X (E / E+D) + RD X [D/ (E+D) X (1-t)]

Where

E = Market value of equity

D = Market value of debt

re = Cost of equity

rd = Cost of debt

t = Marginal tax rate (corporate taxation rate)

One assumption is that the capital of the company is consisting of equity and debt without other capital such as the preferred stock that has different cost rate, hence the calculation is like following:

Percentage of the debt | WACC= | RE X | (E / E+D) + | RD X | [D/ (E+D) X | (1-t)] |

10 per cent | 12.45 per cent | 13.33 per cent | 0.9 | 4.55 per cent | 10 per cent | 0.7 |

20 per cent | 12.19 per cent | 13.99 per cent | 0.8 | 4.97 per cent | 20 per cent | 0.7 |

30 per cent | 12.03v | 14.84 per cent | 0.7 | 5.46 per cent | 30 per cent | 0.7 |

40 per cent | 11.96 per cent | 15.97 per cent | 0.6 | 5.95 per cent | 40 per cent | 0.7 |

50 per cent | 12.28 per cent | 17.56 per cent | 0.5 | 7s per cent | 50 per cent | 0.7 |

60 per cent | 13.02 per cent | 19.94 per cent | 0.4 | 8.4 per cent | 60 per cent | 0.7 |

70 per cent | 14.52 per cent | 23.91 per cent | 0.3 | 10.5 per cent | 70 per cent | 0.7 |

Findings: when the Percentage of the debt reaches 40 per cent, the Weighted-Average Cost of Capital is 11.96 per cent, the cost of capital is the least among the seven options and therefore 40 per cent debt and 60 per cent equity would make the optimal capital structure which maximizes the value of the company.

## 1.2 Evaluation of the results and other factors to be accessed

Assume that there are only seven options of capital structure as given by the example in the example, when the debt to capital ratio reaches 40 per cent based on the calculation of the weighted average cost of capital the overall cost of the capital will be minimized and hence it will be recommended that the company adopts this capital structure to maximize the company’s value. Nevertheless there are more elements that should have been checked before the management makes the eventual decision about the capital structure that will have heavy influence over the company future development and operations.

### 1.2.1 Industry standards

Financial analysts, investment bankers, bond rating agencies, common stock investors, and commercial bankers normally compare the financial risk for a firm, as measured by its interest and fixed charge coverage ratios and its long term debt ratio with the industry standards or norm (Moyer, McGuigan & Kretlow 2009, p.483). And because it is common that capital structure of an average firm varies significantly form industry to industry, it is better for a company not only to calculate the WACC using the cost of capital model, but also compare the result with the industry average, if there should be any major significant differences, further consideration and pondering should be taken. In addition, a company also could calculate and monitor the changes of the capital structure of the major competitors to keep a close eye on the major competitors’ major strategic movements. For example, when the main competitor has increased debt to equity ratio significantly, the company needs to figure out the key strategic business decision that the competitor is going to make, whether it would be new product development or will hold a series of promotion activities.

### 1.2.2 Flexibility to borrow

Utilizing the loan capacity to reduce tax expanses is not always a right decision for a company. A firm should be flexible enough to borrow as and when required. As the external policies change, the firms should be able to restructure their borrowings. Like many companies that have change their debt portfolios due to a decreases in interest rates in the market, thereby lowering the cost of debt (Kapil 2011, p.308). The market conditions would not remain the same even for a month, there are changes happening every minute and some of them need to be noticed because of they could change the cost of the equity as well as the cost of debt which means that the company needs react to these changes.

### 1.2.3 Raising capital at the proper time

The formula of the weighted average cost of capital only measures the cost of the capital at a point of time but has not take into consideration of price change of the equity and the debts, the the decision of when the capital should be raised should be made by the senior management or the board of the directors who have the knowledge of the capital market as well as the techniques of investment.