Question 11.I.18: The Hypothetical Consumer Finance Ltd (HFCL) has structured ......
The Hypothetical Consumer Finance Ltd (HFCL) has structured the following types of consumer credit schemes to finance some specified assets for Rs 30,000:
(A) Zero Deposit Scheme: (1) Repayment period, 36 months, (2) equated monthly instalment, Rs 1,110, (3) bullet instalment/payment at the end of Rs 2,700.
(B) 25% Deposit Scheme: (1) Repayment period, 36 months, (2) equated monthly instalment, Rs 1,068, (3) accumulated interest on deposit after 36 months, Rs 3,833.
(C) Prompt Payment Bonus Scheme: Bonus of Rs 10 per Rs 1,000 per month on the expiry of the repayment period in respect of both the above schemes—A and B.
The HFCL levies a front-ended (advance) documentation and service = fee of Rs 600 in both the schemes.
The EMI is payable at the end of every month.
Required:
(a) Calculate the effective rate of interest for all the schemes.
(b) Assume an early settlement after 24 months under the second (B) scheme. The HFCL would levy a 2 per cent service charge on the principal amount outstanding on the date of settlement. It also gives a prompt payment bonus in respect of the instalment paid. Further, interest rebate would also be due according to rule of 78 method. What would the effective rate of interest be on the completed transaction?
(a) (i) Effective rate of interest implicit in the 25% deposit scheme:
The effective rate of interest, i, is given by the equation:
Loan amount–Present value of instalment paid–Service fee + Present value of accumulated value of deposit + Present value of prompt payment bonus = 0
Accumulated value of deposit after 36 months = Rs 7,500 (deposit) + Rs 3,833 (accumulated interest) = Rs 11,333
or Rs 7,500 × PVIF (i,_3) = Rs 11,333
Simplifying the equation, i_1 = 14.75 per cent per annum or 14 per cent per annum, compounded quarterly.
(a)(ii) Effective rate of interest on zero deposit scheme, with prompt bonus:
Prompt payment bonus = \frac{\mathrm{Rs \>1,110}}{\mathrm{Rs\> 3,000}} × 0.10 × 36 = Rs 39.96
Effective rate of interest (i_1) is given by the equation:
Rs 30,000 – Rs 600 – [Rs 1,110 × 12 × PVIFA_\mathrm{m} (i_1, 3)] – Rs 2,700 × PVIF (i_1,3) + Rs 39.96 × PVIF (i_1,3) = 0
By trial and error and interpolation, i_1 = 27.41 per cent
(a)(iii) Effective rate of interest, i_2, on 25% deposit scheme with prompt payment bonus:
Prompt payment bonus = \frac{\mathrm{Rs \>1.068}}{\mathrm{Rs\> 3,000}} × 0.10 × 36 = Rs 38.45
Effective rate of interest (i_2) can be obtained from the equation:
Rs 22,500 – Rs 600 – {Rs 1,068 × 12 × PVIFA_\mathrm{m} (i_2,3) + Rs 11,333 × PVIF (i_2,3) + [Rs 38.45 × PVIF (i_2,3) = 0
By trial and error and interpolation, i_2 = 25.3 per cent
(b) Effective rate of interest (i_3) on the completed transaction:
The i_3 is given by the equation:
Rs 22,500 – Rs 600 – Rs 1,068 × 12 × PVIFA_\mathrm{m} (i_3,2) + Rs 12,037 × PVIF (i_3,2) + Rs 9,876 × PVIF (i_3,2) = 0
By trial and error and interpolation, i_3 = 24.85 per cent
Thus, the effective rate of interest on the completed transaction is higher than the effective rate of interest implicit in the original transaction.
Working Notes
1. Total charge for credit = (Rs 1,068 × 12 × 3) – Rs 30,000 = Rs 8,448
2. Interest rebate according to the rule of 78 method = \frac{12×13}{36×37} × Rs 8,448 = Rs 989.4
3. Capital content of the instalment outstanding on payment of the 24^\mathrm{th} instalment:
\, (Rs 12,816** – Rs 989.4) = Rs 11,827
\, **Total payment liability (Rs 30,000 + 8,448 = Rs 38,498) – Payment made upto 24 months
\, (EMI × 24 = Rs 25,632) = Rs 12,816
4. Service charge on the amount of principal outstanding = (Rs 11,827 × 0.02) = Rs 236.54
5. Rebate for prompt payment = \frac{\mathrm{Rs\> 1, 068}}{\mathrm{Rs\> 3, 000}} × 0.10 × 24 = Rs 25.5
6. Amount payable on early settlement = (Rs 12,816 + Rs 236.4 – Rs 989.4 – Rs 25.5) = Rs 12,037.5
7. Accumulated value of deposits after 2 years
= Rs 7,500 \left[1+\frac{0.14}{4} \right] = Rs 7,500 × (1.035)^8 = Rs 9,876