Suppose that Caterpillar $($CAT$)$ has a project with the following cash flows:

YEAR $01234$

Cash flow $-$$$40\mathrm{.}00$ $$14\mathrm{.}00$ $$10\mathrm{.}00$ $$12\mathrm{.}00$ $$12\mathrm{.}00$

The company has debt valued at $45\mathrm{.}00$ billion on its balance sheet, while the market value of its common stock is roughly $32\mathrm{.}00$ billion. The yield to maturity on the debt is $5\mathrm{.}50\%,$ and the cost of equity for the firm is $12\mathrm{.}00\%.$ Finally, the marginal tax rate facing the company is $32\mathrm{.}00\%.$

What is the weighted average cost of capital for Caterpillar? What is the NPV for this project?