Divisional Costs of Capital

A firm$$s cost of capital is often a reflection of its activities and funding needs. Consider the case of Wizard Company, and answer the following questions:

Wizard Co$.$ currently has only a real estate division and uses only equity capital; however, it is considering creating consulting and distribution divisions. Its beta is currently $1\mathrm{.}2.$ The risk$-$free rate is $4\mathrm{.}8\%,$ and the market risk premium is $6\mathrm{.}2\%.$

This means that the firm$$s real estate division will have a cost of capital of:

$12\mathrm{.}24\%$

$10\mathrm{.}56\%$

$9\mathrm{.}60\%$

$3\mathrm{.}84\%$

The consulting division is expected to have a beta of $1\mathrm{.}8,$ because it will be riskier than the firm$$s real estate division.

This means that the firm$$s consulting division will have a cost of capital of:

$17\mathrm{.}31\%$

$16\mathrm{.}91\%$

$15\mathrm{.}96\%$

$18\mathrm{.}46\%$

The distribution division will have less risk than the firm$$s real estate division, so its beta is expected to be $0\mathrm{.}7.$

This means that the distribution division$$s cost of capital will be:

$9\mathrm{.}14\%$

$16\mathrm{.}71\%$

$18\mathrm{.}01\%$

$17\mathrm{.}91\%$

Wizard Co$.$ expects $75\%$ of its total value to end up in the real estate division, $10\%$ in the consulting division, and $15\%$ in the distribution division.

Based on this information, what rate of return should its investors require once it opens the new divisions? $($Note: Round your intermediate calculations to two decimal places.$)$

$16\mathrm{.}87\%$

$12\mathrm{.}12\%$

$13\mathrm{.}42\%$

$14\mathrm{.}97\%$