$51.$ You are planning to buy a petrol station, which costs $$500,000.$ The station will be in operation for $10$ years. If purchased, the business is expected to generate a first cash flow of $$90,000$ this year which is expected to grow at $6\mathrm{.}5\%$ p$.$a$.$ If the similar business offers $14\mathrm{.}5\%$ p$.$a$.$ rate of return, use IRR and NPV approach to identify if it is worth buying.