$1.$ Calculate Net Present Value, Internal Rate of Return, Profitability Index, Payback period and the discounted payback period for the below case scenario.

BSeated Limited is a profitable listed company that designs and manufactures furniture. Over the last six months, the company has spent $$250,000$ developing a new chair design for the executive office market. This is not a market in which the company has previously operated and it is considered riskier than their current markets. Due to the upfront investment needed to move forward with the project, the company$$s Investment Review Committee now requires a full financial analysis upon which it can make a decision on the project$$s future.

If the project goes ahead, the chairs will be sold wholesale in line with the company$$s standard business model, rather than direct to end consumers. Based on discussions with key retailers in the executive office furniture market, the selling price per chair in year one will be set at $$1,000.$ Demand at this price is likely to fall over time due to competition, design innovations and changing fashion trends. The project team therefore expects a price decrease of $10\%$ per year will be required from year two in order to maintain estimated annual sales of $8,000$ units $($chairs$).$ Stable sales volume will aid efficiency in production and logistics$.$ The product will be discontinued at the end of five years.

Cost of goods sold related to the project is estimated to be roughly $$400$ per unit in year one and will increase each year after that by $4\%$ in line with expert inflation forecasts over the project period. The company$$s Operations Manager has considered various locations where product manufacturing might take place. Her recommendation to the project team is that the project use company$-$owned factory space that BSeated currently rents for $$400,000$ per year to another business. Other selling, general and administrative costs $($excluding depreciation$)$ are forecast to be $$1$ million per year.

Based on company standards, net working capital needs for the project will begin upfront and be $10\%$ of the next year$$s forecast sales revenue. In the final year of the project, all remaining net working capital investment will be recovered. Quotes on equipment for manufacturing the product are $$3$ million. Depreciation on the equipment will at a prime cost rate of $20\%($based on tax office guidelines$).$ The equipment will be sold at the end of the final year of the project for $$200,000.$

A $30\%$ income tax rate applies to BSeated and, for project analysis purposes, all taxes are assumed to be paid $($credited$)$ in the year of the income to which they relate. The company$$s after$-$tax WACC is $12\%.$

Recently, with the aim of incentivising the reduction of company emissions, the company$$s Board of Directors directed management to implement a centrally$-$collected internal carbon fee. The funds from the fee will be used for energy efficiency initiatives, buying renewable energy, and purchasing carbon offsets. The fee must be considered in all new project proposals. The annual greenhouse gas emissions $($in tonnes of carbon dioxide equivalents, tCO$2$e$.$ of a project are estimated and multiplied by the carbon fee, set at $$50/$tCO$2$e$,$ to value the project$$s carbon footprint and the annual internal fee applicable. Estimates suggest that each unit of the new chair product will result in emissions of $0\mathrm{.}15$ tCO$2$e$.$ The Investment Review Committee has advised that the annual fee is not to be included in calculating taxable income for the project $($i$.$e$.$ assume no income tax applies$)$ but should be included as a cash flow related to the project $($i$.$e$.$ assume funds equivalent to the fee will be spent by the company each year$).$