A housing property of INR 50 lakh is on sale either through a Full Down Payment (FDP) scheme with an 8% rebate OR a Deferred Payment Plan (DPP) as shown in the table. A customer after converting all the future payments in DPP using 10% annual discount rate, found the DPP scheme to be financially gainful. The customer would be able to save in INR _________ lakh, if DPP is chosen over FDP. (rounded off to two decimal places)
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When evaluating deferred payment plans, always convert future payments into their present value using the appropriate discount rate to assess the financial impact.
In the Full Down Payment (FDP) scheme, the customer pays INR 50 lakh immediately. The rebate is 8%, so the amount paid under FDP is:
\[
\text{Amount paid under FDP} = 50 \, \text{lakh} - 8\% \times 50 \, \text{lakh} = 50 \, \text{lakh} - 4 \, \text{lakh} = 46 \, \text{lakh}
\]
In the Deferred Payment Plan (DPP), the payments are made over 3 years. We will discount these future payments to the present value using the 10% annual discount rate.
Step 1: The payment made at the time of booking is INR 10 lakh, so its present value is:
\[
PV_{\text{Booking}} = 10 \, \text{lakh} \quad (\text{as it's made immediately})
\]
Step 2: The payment made after 1 year is INR 15 lakh. Its present value is:
\[
PV_{\text{Year 1}} = \frac{15 \, \text{lakh}}{(1 + 0.10)^1} = \frac{15}{1.1} = 13.64 \, \text{lakh}
\]
Step 3: The payment made after 2 years is INR 15 lakh. Its present value is:
\[
PV_{\text{Year 2}} = \frac{15 \, \text{lakh}}{(1 + 0.10)^2} = \frac{15}{1.21} = 12.40 \, \text{lakh}
\]
Step 4: The payment made after 3 years is INR 10 lakh. Its present value is:
\[
PV_{\text{Year 3}} = \frac{10 \, \text{lakh}}{(1 + 0.10)^3} = \frac{10}{1.331} = 7.52 \, \text{lakh}
\]
Step 5: The total present value of the DPP scheme is the sum of all the present values:
\[
PV_{\text{DPP}} = 10 + 13.64 + 12.40 + 7.52 = 43.56 \, \text{lakh}
\]
Step 6: The customer would save by choosing the DPP scheme over the FDP scheme:
\[
\text{Savings} = 46 \, \text{lakh} - 43.56 \, \text{lakh} = 2.44 \, \text{lakh}
\]
Conclusion: The customer would save INR 2.44 lakh by choosing the DPP scheme over the FDP scheme.
