Question

Ferrari, the famous​ high-performance automotive​ group, launched its initial public offering​ (IPO) on October​ 20, 2015. Although the share price had initially risen to over euros ​ per​ share, by the end of the year it had settled to euros ​. Ferrari had been owned by Fiat​ (Italy), and had never calculated its own cost of capital​ before, one independent of Fiat. It now needed​ to, and one of its first challenges was estimating its beta. With only two months of trading to base it​ on, the corporate treasury group had started with what were considered​ comparable firms, which for​ Ferrari, meant firms in the luxury goods​ industry, not automotive. Luxury goods were historically less volatile than the​ market, so the initial guess on​ Ferrari's beta was .

Italian​ risk-free cost of debt in euros 4.12%
​Ferrari's cost of debt in euros ​ 4.11%
Italian corporate income tax rate 31%
​Ferrari's prospective beta 0.84
Italian equity market risk premium​ (equity return over​ risk-free rate) 5.6%
​Ferrari's shares outstanding 214,000,000
​Ferrari's share price in euros 41
​Ferrari's debt outstanding in euros 517,000,000
a. What is​ Ferrari's cost of​ debt, after-tax, in​ euros?
b. What is​ Ferrari's cost of equity in​ euros?
c. What is​ Ferrari's market​ capitalization?
d. What is​ Ferrari's total value of equity​ outstanding?

Answer 1

Ferrari's cost of debt after-tax in euros is approximately 2.8339%, while the cost of equity is approximately 8.624%. The market capitalization of Ferrari is 8,774,000,000 euros, and the total value of equity outstanding is 8,257,000,000 euros.

Step-by-step explanation:

a. Ferrari's cost of debt, after-tax, in euros can be calculated using the formula:

Cost of debt after-tax = Cost of debt x (1 - Tax rate)

Using the given information, we can calculate:

Cost of debt after-tax = 4.11% x (1 - 31%) = 2.8339%

Therefore, Ferrari's cost of debt, after-tax, in euros is approximately 2.8339%.

b. Ferrari's cost of equity can be calculated using the formula:

Cost of equity = Risk-free rate + Beta x Equity risk premium

Using the given information, we can calculate:

Cost of equity = 4.12% + 0.84 x 5.6% = 8.624%

Therefore, Ferrari's cost of equity in euros is approximately 8.624%.

c. Market capitalization can be calculated by multiplying the number of outstanding shares by the share price:

Market capitalization = Shares outstanding x Share price = 214,000,000 x 41 = 8,774,000,000 euros.

Therefore, Ferrari's market capitalization is 8,774,000,000 euros.

d. The total value of equity outstanding can be calculated by subtracting the debt outstanding from the market capitalization:

Total value of equity outstanding = Market capitalization - Debt outstanding = 8,774,000,000 - 517,000,000 = 8,257,000,000 euros.

Therefore, Ferrari's total value of equity outstanding is 8,257,000,000 euros.