Oliver, an insurance agent, meets with Roman and Julie. They are a married couple with a five-year- old son William. After performing a needs…

The income replacement approach calculates the capital required to generate a specific after-tax income stream indefinitely. The net annual shortfall is $30,000. Since the investment return is taxed at 40%, we must calculate the pre-tax income needed to yield $30,000 net. Pre-tax income = Net Income / (1 - Tax Rate) = $30,000 / (1 - 0.40) = $50,000. Next, we calculate the capital required to generate this $50,000 pre-tax income at a 4% rate of return. Capital Required = Pre-tax Income / Rate of Return = $50,000 / 0.04 = $1,250,000. This lump sum will generate enough income to cover the shortfall after taxes are paid.

A. $390,000 is the result of an erroneous calculation and does not align with the standard formula for income replacement adjusted for taxes.
B. $750,000 is calculated by incorrectly dividing the net shortfall by the pre-tax rate of return ($30,000 / 0.04), failing to account for taxes on the investment income.
D. $1,875,000 is the result of an illogical calculation, likely dividing the unadjusted capital amount from option B by the tax rate ($750,000 / 0.40).

1. IFSE Institute, Life Insurance (LLQP) Course, Module 4: Needs Analysis, Section 3.2: Capital Needs Analysis. The official curriculum details the capital retention (or income replacement) approach, emphasizing the need to adjust for factors like inflation and taxes to determine the required capital sum. The calculation requires using either an after-tax rate of return or grossing up the net income requirement.

2. Zastawniak, F. (2016). Actuarial Mathematics for Life Contingent Risks. Cambridge University Press. Chapter 2: Survival Models. This text provides the foundational mathematical principles for life insurance calculations, including the concept of present value of future income streams, which underpins the income replacement method. Adjustments for variables like taxes are critical for accurate calculations.

3. Kapoor, J. R., Dlabay, L. R., Hughes, R. J., & Ahmad, A. (2020). Personal Finance (7th Canadian ed.). McGraw-Hill Ryerson. Chapter 11: Life Insurance. This university-level textbook explains the "needs approach" for determining life insurance amounts, which includes calculating the lump sum required to produce a desired stream of income, explicitly noting the need to account for investment returns and taxes.