Archive / Investment Adviser (Level 2) / Miscellaneous Aspects of Retirement Planning

nism-series-xb-present-value-retirement-shortfall-mr-smart[ INVESTMENT ADVISER (LEVEL 2) ]

In Case 4, Mr. Smart (age 60) has living expenses of Rs. 4,80,000 p.a. and social/leisure expenses of Rs. 1,00,000 p.a., both growing at 6% inflation. His pension starts at Rs. 4,80,000 p.a. but adjusts for inflation at only 50% (3% annual growth). If the annual net cashflow shortfall stream over his 28-year horizon is discounted at 5% p.a. in advance, what is the total present value of this shortfall?

[ A ]Rs. 76,36,867

[ B ]Rs. 92,45,000

[ C ]Rs. 80,18,710[ CORRECT ]

[ D ]Rs. 1,91,39,462

Takeaway

The present value of Mr. Smart's 28-year shortfall stream, discounted at 5% p.a., is Rs. 80,18,710, so option C is correct.

Derivation

Each year's shortfall (inflation-escalated expenses at 6% minus the partially-indexed pension at 3%) is projected across the 28-year horizon and discounted back to today at 5% p.a., typically using an NPV of the ordinary shortfall stream plus the immediate Year-0 shortfall since it is already due. Excel's NPV function applied to this cashflow series returns Rs. 80,18,710. The test here is whether a candidate correctly handles a growing, non-constant cashflow stream (not a level annuity) and remembers to include the Year-0 outflow separately, since NPV in Excel discounts the first cashflow by one full period by default.

Why the others fail

A — Rs. 76,36,867

Obtained if the Year 0 initial shortfall of Rs. 1,00,000 is left out of the present value sum, understating the true total.

B — Rs. 92,45,000

Assumes the pension is completely frozen with zero inflation indexation at all, rather than the stated 50%/3% partial indexation, which materially changes every year's shortfall.

D — Rs. 1,91,39,462

This is the undiscounted nominal sum of all 28 years of projected shortfalls, ignoring the time value of money entirely rather than discounting at 5%.