Sentra Limited is a public company whose headquarters is in Johannesburg, South Africa. It is a manufacturer of automotive products, with a promise to its customers of high quality at affordable prices. It commenced operations on $02$ January $2022$ with authorised share capital of $600000$ ordinary shares of which $400000$ have been issued at R$10$ per share.

At the end of $2022$ the fixed assets $($at carrying value$)$ totalled R$2000000,$ inventories amounted to R$1280000,$ R$2000000$ was owed by trade debtors, cash in the bank amounted to R$320000,$ the accumulated undistributed profits amounted to R$400000$ and R$1200000$ was owed to the trade creditors. The sales of Sentra Limited for $2022$ amounted to R$8000000.$

The following projections and proposals were made for $2023$:

The sales revenue is expected to increase to R$10000000.$ The after$-$tax return on sales is estimated at $20\%.$ The directors are expected to propose dividends of $200$ cents per share at the end of the year $($payable during $2024).$ A vehicle with a cost price of R$300000,$ which was damaged in an accident during December $2022$ and subsequently repaired, is expected to be traded in at a loss of R$20000$ during the last quarter of $2023$ for a new vehicle with a cost price of R$350000.$ The accumulated depreciation of the previously damaged vehicle on the date of the trade$-$in is expected to be R$80000.$ Depreciation for the year is estimated at R$300000.50000$ ordinary shares are expected to be issued during March $2023$ at R$15$ per share. Inventories, accounts receivable and accounts payable are to be calculated using the percentage$-$of$-$sales method. The amount of cash and cash equivalents must be determined $($balancing figure$).$

Sentra Limited has identified a new machine that it is considering for purchase during $2024.$ The machine would cost R$1000000,$ excluding installation costs of R$200000.$ The machine is expected to have a useful life of five years and depreciation per year is estimated at R$220000.$ It is expected that the new machine would generate cash receipts of R$540000$ per year and its annual cash outflows would total R$220000.$ At the end of year $3,$ the machine would require a major overhaul costing R$200000$ cash $($not included in the figures above$).$ A scrap value of R$100000($not included in the figures above$)$ is anticipated. The cost of capital is $15\%.$

Refer to the investment opportunity for $2024($the purchase of a new machine$)$ and calculate the following. $($Ignore taxes.$)$

Question:

Internal Rate of Return $($expressed to two decimal places$)$ if the net cash flows generated by the machine are R$320000$ per year for five years and the scrap value is R$50000.$ Your answer must include two net present value calculations $($using consecutive rates$/$percentages$)$ and interpolation. $($Recommended: Use present value table $2$ for R$320000$ per year and present value table $1$ for R$50000.)5$ mark question

Notes: Two NPV calculations and interpolation are required $($as stated in the question$).$ CONSECUTIVE RATES $($e$.$g$.8\%$ and $9\%)$ must be used $($as stated in the question$).$ The rates must show a positive NPV and a negative NPV