Archive / Investment Adviser (Level 1) / Time Value of Money

nism-series-xa-present-value-annuity-due-lease-rent[ INVESTMENT ADVISER (LEVEL 1) ]

A commercial lease requires advance annual rent payments of ₹50,000 payable at the beginning of each year for 5 years. At a discount rate of 9.0% p.a., what is the Present Value of this lease commitment (Annuity Due)?

[ A ]₹250,000

[ B ]₹194,482.56

[ C ]₹211,985.99[ CORRECT ]

[ D ]₹243,783.89

Takeaway

The PV of the annuity-due lease is ₹211,985.99 — every advance-payment (annuity due) cash flow must be discounted one period less than an ordinary annuity, so the ordinary-annuity PV is scaled up by one factor of (1+r).

Derivation

Step 1: Treat the 5 advance payments as an ordinary annuity first: PV_ordinary = 50,000 x [1-(1.09)^-5]/0.09 = ₹194,482.56. Step 2: Because each payment actually arrives at the START of its year (one period earlier than an ordinary annuity assumes), multiply by (1+r): 194,482.56 x 1.09 = ₹211,985.99. This two-step 'ordinary-then-compound-once' shortcut is the standard exam trap — candidates who discount as if payments were in arrears understate the PV by the full one-period compounding factor.

Why the others fail

A — ₹250,000

Simple undiscounted sum of 5 x ₹50,000 ignores the time value of money entirely — no discounting is applied at all.

B — ₹194,482.56

This is the correct ordinary-annuity PV, but it wrongly assumes payments occur at each year-end (arrears) rather than at the start of each year (due).

D — ₹243,783.89

Not derived from the annuity mathematics at all; it is an arbitrary markup that does not correspond to any standard PV_ordinary or PV_due formula output.