Question

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)

 

Hint:

When evaluating deferred payment plans, always convert future payments into their present value using the appropriate discount rate to assess the financial impact.

Answer 1

Correct Answer: 2.3

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: \[ {Amount paid under FDP} = 50 \, {lakh} - 8% \times 50 \, {lakh} = 50 \, {lakh} - 4 \, {lakh} = 46 \, {lakh} \] 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: \[ PV_{{Booking}} = 10 \, {lakh} \quad ({as it's made immediately}) \] Step 2: The payment made after 1 year is INR 15 lakh. Its present value is: \[ PV_{{Year 1}} = \frac{15 \, {lakh}}{(1 + 0.10)^1} = \frac{15}{1.1} = 13.64 \, {lakh} \] Step 3: The payment made after 2 years is INR 15 lakh. Its present value is: \[ PV_{{Year 2}} = \frac{15 \, {lakh}}{(1 + 0.10)^2} = \frac{15}{1.21} = 12.40 \, {lakh} \] Step 4: The payment made after 3 years is INR 10 lakh. Its present value is: \[ PV_{{Year 3}} = \frac{10 \, {lakh}}{(1 + 0.10)^3} = \frac{10}{1.331} = 7.52 \, {lakh} \] Step 5: The total present value of the DPP scheme is the sum of all the present values: \[ PV_{{DPP}} = 10 + 13.64 + 12.40 + 7.52 = 43.56 \, {lakh} \] Step 6: The customer would save by choosing the DPP scheme over the FDP scheme: \[ {Savings} = 46 \, {lakh} - 43.56 \, {lakh} = 2.44 \, {lakh} \] Conclusion: The customer would save INR 2.44 lakh by choosing the DPP scheme over the FDP scheme.