# The book value of the machine is the gross investment

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of the machine during its life. The book value of the machine is the gross investment minus the accumulated depreciation. Average book value = (Book value0+ Book value1+ Book value2+ Book value3+ Book value4+ Book value5) / (Economic life)Average book value = (\$28,000 + 21,000 + 14,000 + 7,000 + 0) / (5 years)Average book value = \$14,000Average project earnings = \$4,300
To find the average accounting return, we divide the average project earnings by the average book value of the machine to calculate the average accounting return. Doing so, we find: Average accounting return = Average project earnings / Average book valueAverage accounting return = \$4,300 / \$14,000Average accounting return = 0.3071 or 30.71%b.The three flaws of the AAR are: 1) The AAR does not work with the right raw materials. It uses net income and book value of the investment, both of which come from the accounting books. Accounting numbers are somewhat arbitrary. 2) AAR takes no account of timing. The AAR would be the same if the net income in the first year occurs in the last year. 3) The AAR uses an arbitrary interest rate as the cutoff rate and offers no guidance on what the right targeted rate of return should be.6.First, we need to determine the average book value of the project. The book value is the gross investment minus accumulated depreciation. Purchase DateYear 1Year 2Year 3Gross Investment\$12,000\$12,000\$12,000\$12,000Less: Accumulated depreciation04,0009,50012,000Net Investment\$12,000\$8,000\$2,500\$0Now, we can calculate the average book value as:Average book value = (\$12,000 + 8,000 + 2,500 + 0) / 4Average book value = \$5,625To calculate the average accounting return, we must remember to use the aftertax average net income when calculating the average accounting return. So, the average aftertax net income is: Average aftertax net income = (1 – tc) Annual pretax net incomeAverage aftertax net income = (1 – 0.25) \$2,450Average aftertax net income = \$1,838The average accounting return is the average after-tax net income divided by the average book value, which is: Average accounting return = \$1,838 / \$5,625Average accounting return = 0.3267 or 32.67%7.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:0 = C0+ C1/ (1 + IRR) + C2/ (1 + IRR)2+ C3/ (1 + IRR)30 = –\$9,000 + \$5,300/(1 + IRR) + \$3,600/(1 + IRR)2+ \$1,900/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 11.65% Since the IRR is greater than the required return we would accept the project.8.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this Project A is:0 = C0+ C1/ (1 + IRR) + C2/ (1 + IRR)2+ C3/ (1 + IRR)30 = – \$4,500 + \$1,600/(1 + IRR) + \$1,900/(1 + IRR)2+ \$2,400/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 13.82% And the IRR for Project B is:0 = C0+ C1/ (1 + IRR) + C2/ (1 + IRR)2+ C3/ (1 + IRR)30 = – \$2,900 + \$800/(1 + IRR) + \$1,500/(1 + IRR)2+ \$1,900/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 18.22%