BKM_Sol_Ch_20 - Chapter 20 Taxes Inflation and Investment...

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Chapter 20 - Taxes, Inflation, and Investment Strategy Chapter 20 Taxes, Inflation, and Investment Strategy 1. With a savings rate of 16%, the retirement annuity would be $205,060 (compared to $192,244 with the 15% savings rate). Spreadsheet 20.1: Adjusted for Change in Savings Rate 2. With a savings rate of 16%, the retirement annuity will be $52,979 (vs. $49,668). The growth in the real retirement annuity (6.67%) is the same as with the case of no inflation. Spreadsheet 20.2: Adjusted for Change in Savings Rate 3. The objective is to obtain a real retirement annuity of $49,668, as in Spreadsheet 20.2. In Spreadsheet 20.3: Backloading the Real Savings Plan, add cell F42 for the desired annuity and cell F43 for the difference between the annuity with savings from real income and the desired annuity in cell F42. Select Tools/Goal Seek from the menu bar. Set up the following parameters: Set Cell: F43 To Value: 0 By Changing Cell: D2 20-1
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Chapter 20 - Taxes, Inflation, and Investment Strategy Spreadsheet 20.3: With Target Cell for Desired Real Annuity We find that a savings rate of 8.3% (C2) from real income yields the desired real retirement annuity, as the modified spreadsheet on the next page shows: 20-2
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Chapter 20 - Taxes, Inflation, and Investment Strategy 4. Because of the exemption from taxable income, only part of income is subject to tax, while a change in ROR affects all savings. Because of the exemption from taxable income, only part of income is subject to tax, while ROR affects all savings. As a result, we find from Spreadsheet 20.4 that the increase in tax rate reduces the real annuity by a relatively small amount, while the increase in ROR increases the annuity substantially. A 1% increase in the tax rate, from 25% to 26% (all else equal), reduces the real annuity from $37,882 to $37,426. A 1% increase in ROR, from 6% to 7%, increases the real annuity from $37,882 to $49,107. Making both changes simultaneously yields a real annuity of $48,505. 20-3
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5. In the original Spreadsheet 20.5, real consumption during retirement is $60,789. A 1% increase in the rate of inflation will reduce real consumption during retirement to $15,780. A 1% increase in the flat-tax rate reduces real consumption during retirement to $58,983. The root of the difference is similar to that of the case of ROR compared to tax rates (see problem 4). While the tax rate affects only part of the income, an increase in the rate of inflation affects all savings, and the reduction in real savings compound over time. Note that, in this example, real consumption during the saving period is fixed, set to equal consumption in Spreadsheet 20.4. To sustain this level of real consumption with a 4% inflation rate, investors must withdraw funds from the saving account as of age 60. In reality, however, households reduce consumption in the face of deteriorating circumstances in order to protect the retirement annuity. [See Spreadsheet 20.5 on next page.]
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This note was uploaded on 08/25/2009 for the course FNCE 4330 taught by Professor Jianyang during the Spring '09 term at University of Colorado Denver.

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BKM_Sol_Ch_20 - Chapter 20 Taxes Inflation and Investment...

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