Question

Genie Corp is an online commerce company with a target debt-equity ratio of 1. Genie’s current capital structure matches its target leverage, and its equity beta is 0.9. Genie has three divisions: Its main e-commerce division (50% of Genie’s total asset value), a banking division (35% of total asset value), and a logistics division (15% of total asset value). Genie aims to apply the same firm-level target debt-equity ratio across all of its divisions, and believes it will be able to borrow at 7% for all divisions. To further estimate costs of capital for its divisions, Genie has collected the following information on the average debt-equity ratios and equity betas of pure-play companies in each of the e-commerce, banking, and logistics industries.

Industry	Average debt-equity ratio	Average equity beta
E-commerce	0.5	0.4
Banking	2.0	1.2
Logistics	No pure-play firms available

The risk-free rate is 3%, and the market risk premium is 6%. Given this information, what would be a good estimate of the cost of capital for Genie’s logistics division? (Assume no taxes and zero debt beta)

Group of answer choices

7.7%

8.40%

12.06%

12.73%

Answer 1

The correct answer is the third option showing 12.06%.

Equity beta is a levered beta. We need to calculate the unlevered beta.

Unlevered beta = Levered beta / [1 + (1 - T) x D/E]

since we have to assume no taxes, Tax rate, T = 0

Hence, the formula takes the form of:

Unlevered beta = Levered beta / (1 + D/E)

For Genie corp overall firm level:

Levered beta = 0.9; D/E = 1; Hence unlevered beta = 0.9 / (1 + 1) = 0.45

For e-commerce industry:

Levered beta = 0.4; D/E = 0.5; Hence unlevered beta = 0.4 / (1 + 0.5) = 0.2667

For banking industry:

Levered beta = 1.2; D/E = 2; Hence unlevered beta = 1.2 / (1 + 2) = 0.4

Unlevered beta for Genie Cor overall = Unlevered beta for e-commerce division x proportion of Genies assets towards e-commerce + Unlevered beta for banking division x proportion of Genies assets towards banking division + Unlevered beta for logistics division x proportion of Genies assets towards logistics.

Hence, 0.45 = 0.2667 x 50% + 0.4 x 35% + Unlevered beta for logistics division x 15%

Hence, 0.45 = 0.2733 + Unlevered beta for logistics division x 15%

Hence, Unlevered beta for logistics division = (0.45 - 0.2733) / 15% = 1.17778

Hence, the levered beta for Logistics division = Unlevered beta x (1 + D/E) = 1.17778 x (1 + 1) =  2.3556

Hence, cost of equity for levered division, Ke = Risk free rate + levered beta for Logistics division x the market risk premium = 3% + 2.3556 x 6% = 17.1333%

Cost of debt, Kd = 7%

D/E = 1; Hence Wd = D / (D + E) = 1 / (1 + 1) = 0.5; We = 1 - Wd = 1 - 0.5 = 0.5

Hence, a good estimate of the cost of capital for Genie’s logistics division = Wd x Kd x (1 - T) + We x Ke = 0.5 x 7% x (1 - 0%) + 0.5 x 17.1333% = 12.06%

Hence, the correct answer is the third option showing 12.06%.