The Finance director of Gemini PLC wishes to find the company’s optimal capital structure. The cost of debt varies according to the company’s credit rating, which itself depends, amongst other factors, upon the level of gearing of the company.

Percentage of debt Likely credit rating Pretax Cost

10 AAA 6.5%

20 AA 7.1%

30 A 7.8%

40 BBB 8.5%

50 BB 10%

60 B 12%

70 C 15%

The company’s ungeared equity Beta (asset beta) is 0.85

The risk free rate is 6% per annum and the market return 14% per annum.

Corporate taxation is at 30% per annum.

i) Estimate the company’s optimal weighted average cost of capital. State clearly any assumptions that you make.

Hitchner (2011) defined the weighted average cost of capital (WACC) as the blended cost on the structure of the capital components. The method of WACC is appreciated especially when the purpose is to estimate the capital invested or capital structure of this firm. For Gemini PLC, this method is also optimal for the finance director to get the capital structure of this company with the support of given data.

First, according to Hitchner (2011), WACC= (E / V) x Re + (D / V) x Rd x (1 – Tc). And there are different meanings of each element in this formula as follows.

Re: total cost of equity

Rd: total cost of debt

E: total market value of the equity of the firm

D: the current market value of the firm’s debt

V= E + D

Tc: the corporate tax rate

**Cost of equity **

Based on this formula and the meanings of these elements, we can first start with the calculation of the cost of equity with the given data in Gemini PLC. According to Hitchner (2011), the formula to calculate the cost of equity is as follow.

Cost of Equity = Risk Free Rate + Beta levered (Risk Premium)

As we have the data of risk free rate (6%), and risks premium ( 14%), we only need to get the data of Beta levered. As the Unlevered Beta given as the ungeared equity Beta (asset beta) is 0.85, which has the relationship with the Levered Beta we need in the following formula.

Unlevered Beta = Levered Beta*((1+ (1-t) (D/E))

And then we can get the data of the Unlevered Beta in the following.

Table 2.0 the data of debt / equity

Debt ratio |
Equity Ratio |
D/E |

0.1 |
1-0.1=0.9 |
0.11 |

0.2 |
1-0.2=0.8 |
0.25 |

0.3 |
1-0.3=0.7 |
0.43 |

0.4 |
1-0.4=0.6 |
0.67 |

0.5 |
1-0.5=0.5 |
1.00 |

0.6 |
1-0.6=0.4 |
1.50 |

0.7 |
1-0.7=0.3 |
2.33 |

And then we know t= 30%

So we can get the data of Levered Beta as follow.

Table 3.0 Data for Levered Beta

T |
D/E |
Unlevered Beta |
Levered Beta |

0.3 |
0.11 |
0.85 |
0.915 |

0.3 |
0.25 |
0.85 |
0.9988 |

0.3 |
0.43 |
0.85 |
1.105 |

0.3 |
0.67 |
0.85 |
1.249 |

0.3 |
1.00 |
0.85 |
1.445 |

0.3 |
1.50 |
0.85 |
1.742 |

0.3 |
2.33 |
0.85 |
2.238 |

And according to the formula and data such as Cost of Equity = Risk Free Rate + Beta levered (Risk Premium), risk free rate (6%), and risks premium (market return – risk free rate = 14% – 6% = 8%), we can get the data of Cost of Equity finally in the following.

Table 4.0 the data of total cost of equity

Cost of Equity |
Risk-Free Rate |
Beta levered |
Risk Premium |

0.1332 |
0.06 |
0.915 |
0.08 |

0.1399 |
0.06 |
0.9988 |
0.08 |

0.1484 |
0.06 |
1.105 |
0.08 |

0.1597 |
0.06 |
1.249 |
0.08 |

0.1756 |
0.06 |
1.445 |
0.08 |

0.1994 |
0.06 |
1.742 |
0.08 |

0.2391 |
0.06 |
2.238 |
0.08 |

**Cost of debt **

According to Hitchner (2011), the cost of debt of the firm can give the firm a clear outline of its actual rate of its entity in the business paid on the debt which bears interest. And when some long term debt involved, there may a different rate caused by the changes from market influences, in which the pretax interest rate is important for company to get the cost of the debt following the formula:

Cost of Debt = Pretax Interest Rate (1 – Tax Rate)

According to the above formula and obtained data from Gemini PLC, we can get the cost of debt in the following.

Table 5.0 the data of total cost of debt

Cost of Debt (after tax) |
Pretax Interest Rate |
Tax Rate |
Debt Ratio |

0.0455 | 0.065 |
0.3 |
0.1 |

0.0497 | 0.071 |
0.3 |
0.2 |

0.0546 | 0.078 |
0.3 |
0.3 |

0.0595 | 0.085 |
0.3 |
0.4 |

0.07 | 0.10 |
0.3 |
0.5 |

0.084 | 0.12 |
0.3 |
0.6 |

0.105 | 0.15 |
0.3 |
0.7 |

**Weighted average cost of capital **

According to the formula to calculate the weighted average cost of capital given by Hitchner (2011), we know that WACC= (E / V) x Re + (D / V) x Rd x (1 – Tc). And then we have already calculate the necessary elements in this formula, then with the assistance of these important data we can finally get the data of the WACC for Gemini PLC.

(E / V) x Re + (D / V) x Rd x (1 – Tc)

Table 5.0 the data of WACC

WACC |
Market value of Equity |
Market value of Debt |
Cost of equity |
Cost of debt before tax |
T |

0.1245 | 90% | 10% | 0.1332 | 0.065 |
0.3 |

0.1219 | 80% | 20% | 0.1399 | 0.071 |
0.3 |

0.1203 | 70% | 30% | 0.1484 | 0.078 |
0.3 |

0.1196 | 60% | 40% | 0.1597 | 0.085 |
0.3 |

0.1228 | 50% | 50% | 0.1756 | 0.1 |
0.3 |

0.1302 | 40% | 60% | 0.1994 | 0.12 |
0.3 |

0.1452 | 30% | 70% | 0.2391 | 0.15 |
0.3 |

From the final data calculated by us, we can get that when the debt value equals 40% and the WACC reaches the level of 0.1196, the cost of the capital for the company will be the lowest level.