Fudge factors $($S$9\mathrm{.}3)$ Mario Barleycorn estimates his firm$$s company cost of capital at only

$8\%.$ Nevertheless, he sets a $15\%$ companywide discount rate to offset the optimistic biases of

project sponsors and to impose $$discipline$$ on the capital budgeting process. Suppose Mr$.$

Barleycorn is correct about the project sponsors, who are, in fact, optimistic by $7\%$ on average.

Explain why the increase in the discount rate from $8\%$ to $15\%$ will not offset the bias.

$($Note: The firm is entirely equity financed.$)$