Umbrella Company is evaluating a short$-$term project that requires a $$675,000$ investment. The anticipated cash flows are $$112,000$ in first year, no cash flows for the next $2$ years, $$250,000$ in the fourth year and $$352,000$ in fifth year. There is no salvage value for this project. Umbrella Company currently has a $30\%$ debt and $70\%$ equity structure. Their most recent $$1000$ face value bond is selling for $$1050.$ This bond has a coupon rate of $10\%$ which are paid yearly and $8$ years to maturity. Umbrella uses CAPM model to calculate its cost of equity. It has a beta of $2\mathrm{.}5.$ The current $8$ year Treasury Bond has a $2\%$ yield. For the corresponding period, S&P $500$ index has a return of $13\%.$ The applicable corporate tax rate for Umbrella is $18\%.$

a$)$ What is the approximate cost of debt for this company after tax?

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b$)$ What is the cost of equity for this company?

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c$)$ What is the WACC for this company?

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d$)$ What is the approximate NPV of this project for Umbrella Company?

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e$)$ Is this a good project? What is IRR?