IPetro$-$U$.$K$.$ is a British energy firm that needs to raise $150$ million to finance expansion projects. Suppose that Petro$-$U$.$K$.$ is seeking a capital

structure comprising $30\%$ debt and $70\%$ equity. The corporate tax rate in the U$.$K$.$ is $21\%.$ Petro$-$U$.$K$.$ finds that it can raise finance in the domestic

ILondon stock market as follows: both debt and equity would have to be sold in multiples of $50$ million $(30\%$ debt and $70\%$ equity$).$ For equity

and debt respectively, the financing costs are $8\%$ and $6\%$ on the U$.$K$.$ market and $10\%$ and $8\%$ on the Latin American market.

A consultancy firm advises Petro$-$U$.$K$.$ that incremental finance could be raised in multiples of $50$ million $($maintaining the $\frac{30}{70}$ capital structure$).$

Each increment of cost would be influenced by the total amount of capital raised.

For equity and debt respectively, the first increment or $50$ million $(30\%$ debt and $70\%$ equity$)$ would

cost $10\%$ and $8\%$ on the U$.$K$.$ market and $12\%$ and $10\%$ on the Latin American market. The second increment of $50$ million would cost $12\%$ and

$10\%$ on the U$.$K$.$ market and $16\%$ and $14\%$ on the Latin American market.

a$.$ Calculate the lowest average cost of capital for each increment of $150$ million of new capital, where Petro$-$U$.$K$.$ raises $45$ million in the equity

imarket and an additional $105$ million in the debt market at the same time.

b$.$ If Petro$-$U$.$K$.$ plans an expansion of only $75$ million, how should that expansion be financed? What will be the weighted average cost of capital

Ifor the expansion?