Waltech, a firm that specializes in using marine renewable energy to generate electricity, is considering a project to construct a system of wave energy conversion devices called the $`$Sapient$\text{'}.$ The life of the project will be five years. A survey by Waltech, which cost $$5$ million, has shown that the efficiency of the Sapient may be high $($probability $40\%)$ or low $($probability $60\%).$ If the efficiency is high, the sales revenue from operating the Sapient will be $$415$ million in the first year and then grow at $6\%$ each year. If it is low, the sales revenue will be $$350$ million in the first year and then grow at $6\%$ each year.

Variable costs will be $35\%$ of sales revenue. The fixed costs of operating the Sapient are estimated to be $$16\mathrm{.}5$ million each year, excluding depreciation. The Sapient will cost $$750$ million and depreciation allowances for tax purposes will be $20\%$ each year on a reducing$-$balance basis. The Sapient will be scrapped at the end of the project and the scrap proceeds are estimated to be $$25$ million. Any unused depreciation allowance will be immediately applicable when the machine is sold.

Working capital of $$20$ million will be required at the start of the project and after one year this requirement will increase to $$25$ million. All working capital will be recovered at the end of the project. If the Sapient project is undertaken, Waltech plans to pay an additional $$12$ million in dividends to its shareholders in each year of the project's life.

The corporation tax rate is $17\%$ and tax is payable in the same year as taxable profit arises.

The CFO determines the risk$-$free rate to be $5\%$ and the market return to be $12\%.$ Based on the movement of the company$$s stock prices, beta is calculated to be $2\mathrm{.}0.$ The company has a pre$-$tax cost of debt of $10\%.$ Market value of equity comprises $70\%$ while market value of debt comprises $30\%$ of capital employed.

$($a$)$ Calculate the cost of capital that should be used to discount the project cash flows assuming that neither business nor financial risks of the company changes.

$($b$)$ Use the WACC calculated above to calculate the net present value $($NPV$)$ of the $`$best case' and $`$worst case' outcomes for the Sapient project, assuming investment would occur immediately. What is the expected net present value of the project?

$($c$)$ Assume that Waltech could make a payment now for a further study which will find out for certain how efficient the Sapient will be$.$ The project start would be delayed for one year. What is the maximum amount Waltech should pay for the study? If the study costs $$10$ million, what is the net present value of the project? Should the project be undertaken? Explain.