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

nism-series-xb-education-sinking-fund-two-year-payout[ INVESTMENT ADVISER (LEVEL 2) ]

If Mr. Y decides to set apart a dedicated fund at the end of Year 5 in an instrument yielding 6% p.a. to fully cover the Year 5 expense (Rs. 30,17,036) and Year 6 expense (Rs. 34,69,591), how much total capital must he set apart at the end of Year 5?

[ A ]Rs. 59,34,184

[ B ]Rs. 64,12,209

[ C ]Rs. 62,90,235[ CORRECT ]

[ D ]Rs. 60,35,259

Takeaway

Setting aside the Year 5 cost plus the present value of the Year 6 cost discounted at 6% for one year requires a total of Rs. 62,90,235 at the end of Year 5, so option C is correct.

Derivation

Fund required at end of Year 5 = Year 5 cost + PV of Year 6 cost discounted at 6% for one year = Rs. 30,17,035.78 + (Rs. 34,69,591.15 / 1.06) = Rs. 30,17,035.78 + Rs. 32,73,199.20 = Rs. 62,90,234.98, rounding to Rs. 62,90,235. The key test here is recognising that the Year 6 outflow is one year away from the Year 5 valuation date and must be discounted at the fund's 6% yield — not simply added at face value — since the sinking fund itself earns interest while waiting to pay out the second instalment.

Why the others fail

A — Rs. 59,34,184

Obtained if the Year 6 cost is discounted using the 15% education inflation rate instead of the fund's actual 6% investment yield, understating the required capital.

B — Rs. 64,12,209

Obtained by adding the two undiscounted future cashflows (30.17L + 34.70L = 64.87L) with an arithmetic slip, ignoring that Year 6 needs to be discounted back one year.

D — Rs. 60,35,259

Reflects discounting both the Year 5 and Year 6 costs back one additional year to Year 4, which is not what the question asks for — the valuation date is the end of Year 5.