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.
Under the Full Down Payment (FDP) scheme, an immediate payment of INR 50 lakh is required. With an 8% rebate, the net FDP amount is calculated as:
\[
\text{Amount paid under FDP} = 50 \, \text{lakh} - 8\% \times 50 \, \text{lakh} = 50 \, \text{lakh} - 4 \, \text{lakh} = 46 \, \text{lakh}
\]
The Deferred Payment Plan (DPP) involves payments spread over 3 years. These future payments will be discounted to their present value using a 10% annual discount rate.
Step 1: The booking payment of INR 10 lakh, made immediately, has a present value of:
\[
PV_{\text{Booking}} = 10 \, \text{lakh}
\]
Step 2: The payment of INR 15 lakh due after 1 year has a present value of:
\[
PV_{\text{Year 1}} = \frac{15 \, \text{lakh}}{(1 + 0.10)^1} = \frac{15}{1.1} = 13.64 \, \text{lakh}
\]
Step 3: The payment of INR 15 lakh due after 2 years has a present value of:
\[
PV_{\text{Year 2}} = \frac{15 \, \text{lakh}}{(1 + 0.10)^2} = \frac{15}{1.21} = 12.40 \, \text{lakh}
\]
Step 4: The payment of INR 10 lakh due after 3 years has a present value of:
\[
PV_{\text{Year 3}} = \frac{10 \, \text{lakh}}{(1 + 0.10)^3} = \frac{10}{1.331} = 7.52 \, \text{lakh}
\]
Step 5: The total present value of the DPP scheme is the sum of all individual present values:
\[
PV_{\text{DPP}} = 10 + 13.64 + 12.40 + 7.52 = 43.56 \, \text{lakh}
\]
Step 6: The customer's savings by choosing the DPP scheme over the FDP scheme are:
\[
\text{Savings} = 46 \, \text{lakh} - 43.56 \, \text{lakh} = 2.44 \, \text{lakh}
\]
Conclusion: Opting for the DPP scheme over the FDP scheme results in a customer saving of INR 2.44 lakh.
