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

nism-series-xb-present-value-year-6-education-cost-discounted[ INVESTMENT ADVISER (LEVEL 2) ]

In Case 2, the Year 6 education cost is Rs. 34,69,591.15. If this sum is funded from an instrument earning 6% interest during Year 6, what is its present value at the end of Year 5?

[ A ]Rs. 30,17,036

[ B ]Rs. 34,69,591

[ C ]Rs. 32,73,199[ CORRECT ]

[ D ]Rs. 36,77,766

Takeaway

Discounting the Year 6 education cost of Rs. 34,69,591.15 back one year at the 6% fund yield gives a present value at the end of Year 5 of Rs. 32,73,199, so option C is correct.

Derivation

PV at Year 5 = Year 6 cashflow / (1 + 0.06)^1 = Rs. 34,69,591.15 / 1.06 = Rs. 32,73,199.20, rounding to Rs. 32,73,199. This tests the discounting direction and rate: candidates must divide (not multiply) by 1.06 to bring a future cashflow back to an earlier valuation date, using the fund's own 6% investment yield as the discount rate rather than the 15% education inflation rate that generated the cashflow in the first place.

Why the others fail

A — Rs. 30,17,036

This is the Year 5 immediate education expense itself, not the discounted present value of the separate Year 6 cashflow.

B — Rs. 34,69,591

This is the undiscounted, nominal Year 6 cost, ignoring the one-year discounting adjustment back to the Year 5 valuation date.

D — Rs. 36,77,766

Results from multiplying by 1.06 instead of dividing, which compounds the cashflow forward rather than discounting it backward to Year 5.