Archive / Investment Adviser (Level 2) / Life Insurance Products

nism-series-xb-hlv-when-income-growth-equals-investment-return[ INVESTMENT ADVISER (LEVEL 2) ]

When calculating Human Life Value (HLV) using the income replacement method, what is the resulting HLV if the assumed annual rate of income increase exactly EQUALS the assumed post-tax investment return?

[ A ]HLV becomes zero because discounting cancels out compounding

[ B ]HLV is halved due to capital gains taxation

[ C ]HLV equals the Current Annual Income multiplied by the exact Number of Years remaining until retirement[ CORRECT ]

[ D ]HLV approaches infinity

Takeaway

When income growth exactly equals the investment return, the real discount rate becomes 0%, so HLV simply equals current annual income multiplied by the number of years to retirement, making option C correct.

Derivation

Real rate = ((1 + growth)/(1 + return)) - 1. If growth equals return, this expression equals ((1+r)/(1+r)) - 1 = 0%. At a 0% discount rate, the present value of a level annuity collapses to PV = PMT x Nper, since there is no time-value adjustment to apply. This is a conceptual thumb rule tested in Chapter 2.2.1: it isolates the boundary case of the HLV formula and checks whether candidates understand what the discount rate mechanically does to a PV calculation, rather than just plugging numbers into a formula without understanding why.

Why the others fail

A — HLV becomes zero because discounting cancels out compounding

The discount rate becomes 0%, meaning future cash flows are summed at full face value without any discount applied — it does not make HLV zero.

B — HLV is halved due to capital gains taxation

HLV represents gross economic earnings replacement and is never arbitrarily halved for capital gains tax in this formula.

D — HLV approaches infinity

HLV is bounded by the finite number of remaining working years to retirement (Nper); it cannot approach infinity even at a 0% discount rate.