11-8 a. Sales = 1,000($138) $138,000 Cost = 1,000($105) 105,000 Net before tax $ 33,000 Taxes (34%) 11,220 Net after tax $ 21,780 Not considering inflation, NPV is -$4,800. This value is calculated as -$150,000 + = -$4,800. Considering inflation, the real cost of capital is calculated as follows: (1 + rr)(1 + i) = 1.15 (1 + rr)(1.06) = 1.15 rr = 0.0849057. Thus, the NPV considering inflation is calculated as -$150,000 + = $106,520. After adjusting for expected inflation, we see that the project has a positive NPV and should be accepted. This demonstrates the bias that inflation can induce into the capital budgeting process: Inflation is already reflected in the denominator (the cost of capital), so it must also be reflected in the numerator. A more straightforward way to calculate the present value without having to calculate a real required rate of return is to use the constant growth formula, instead. Here, the present value of all of the future cash flows is: so the NPV = 256,520 150,000 = 106,520, which is the have – same answer we’d gotten above if in calculating the real required rate of return we had used enough decimal places.
11-8 a. Sales = 1,000($138) $138,000 Cost = 1,000($105) 105,000 Net before tax $ 33,000 Taxes (34%) 11,220 Net after tax $ 21,780 Not considering inflation, NPV is -$4,800. This value is calculated as -$150,000 + = -$4,800. Considering inflation, the real cost of capital is calculated as follows: (1 + rr)(1 + i) = 1.15 (1 + rr)(1.06) = 1.15 rr = 0.0849057. Thus, the NPV considering inflation is calculated as -$150,000 + = $106,520. After adjusting for expected inflation, we see that the project has a positive NPV and should be accepted. This demonstrates the bias that inflation can induce into the capital budgeting process: Inflation is already reflected in the denominator (the cost of capital), so it must also be reflected in the numerator. A more straightforward way to calculate the present value without having to calculate a real required rate of return is to use the constant growth formula, instead. Here, the present value of all of the future cash flows is: so the NPV = 256,520 – 150,000 = 106,520, which is the same answer we’d have gotten above if in calculating the real required rate of return we had used enough decimal places.
FM14e_SM_Ch11.docx