(a) A machine was bought for $80,000 and would be used for the next 20 years, after which it would be scraped with no salvage value. The book value of the machine is calculated using Sum of Years' Digits (SOYD) and Double Declining Balance (DDB) methods. At year 0, the machine's book value is the same for both the methods. After Nth year, the machine's book value calculated using Sum of Years' Digits (SOYD) and Double Declining Balance (DDB) methods are the same. Solve for N. (10 marks) (b) Orange Company has just bought a machine for $50,000 and is able to save $20,000 from its operating cost in the first year. In subsequent years, the savings will be reduced by $3,000 until the 5th year, after which the machine will be scrapped with a residual value of $5,000. Depreciations of the machine will be calculated using the Sum of Years' Digits (SOYD) method. The tax rate for the company is flat at 20%. Present the After Tax Cash Flows (ATCF) from year 0 to year 5 in a table format and determine the IRR for the company. (Hint: Use PWB - PWC = 0, where PWB is the Present Worth of Benefits and PWC is the Present Worth of Costs) (15 marks)