Question 11.I-A.2 (Deposit Linked Plan): Under a purchase deal structured by the Hypothetical Finance......
Under a purchase deal structured by the Hypothetical Finance Ltd (HFL) for the Hypothetical Industries Ltd (HIL), the HFL offers to provide 100 per cent finance to the HIL at a flat rate of interest of 13 per cent. The HIL has to invest 20 per cent of the investment cost as fixed deposit with the HFL, during the hire purchase period of three years, at 15 per cent compounded monthly. The repayment has to be made in 36 monthly instalments, in arrears. Compute the ERI/APR on an investment cost of Rs 1,000.
APR/ERI (I) = Rate of interest, which equates the present value of the cash inflows with the present value of the cash outflows. The elements of the monthly cash flows are (1) loan amount (2) initial deposit (3) instalment amount (4) accumulated value of deposit. The monthly net cash flow = Loan amount less initial deposit less instalment amount plus accumulated value of deposit.
Monthly instalment = \frac{\mathrm{Total\>charge\>for\>credit}}{\mathrm{Months}}=\frac{\mathrm{Rs\>1, 390}}{36}= Rs 38.61
\, Total charge for credit = Loan amount + Interest
\, = Rs 1,000 + [(Rs 1,000 × 0.13 × 3)] = Rs 1390
Accumulated value of deposit = Rs 200 \left[1+\frac{0.15}{36} \right] ^{36} = Rs 312.79
ERI, (I) is given by the equation:
\, Rs 38.61 × PVIFA_\mathrm{m} (I,35/12) = Rs 800 + Rs 274.17 × PVIF (I,3)
or Rs 463.32 × \frac{I}{I^{(12)}} × PVIFA (I,2.9167) = Rs 800 + Rs 274.18 × PVIF (I,3)
By trial and error and interpolation: I = 31.39 per cent
| Net\>Monthly\>Cashflow | Month |
| Rs 800 [Rs 1,000 (loan) – Rs 200 deposit] | 0 |
| –38.61 (monthly instalment) | 1–35 |
| 274.18 (accumulated deposit, Rs 312.79 – instalment, Rs 38.61)] | 36 |