Question 2.S2.12: A limited company borrows from a commercial bank Rs 10,00,00......
A limited company borrows from a commercial bank Rs 10,00,000 at 12 per cent rate of interest to be paid in equal annual end-of-year instalments. What would the size of the instalment be? Assume the repayment period is 5 years.
The problem relates to loan amortisation. The loan amortisation process involves finding out the future payments over the term of the loan whose present value at the interest rate just equals the initial principal borrowed. In this case, the company has borrowed Rs 10,00,000 at 12 per cent. In order to determine the size of the payments, the 5-year annuity discounted at 12 per cent that has a present value of Rs 10,00,000 is to be determined.
Present value, P, of an n year annuity of amount C is found by multiplying the annual amount, C, by the appropriate annuity discount factor (ADF) from Table A-4, that is, P=C (ADF), or C=P / A D F in which P is the amount of loan, that is, (Rs 10,00,000), ADF is the present value of an annuity factor corresponding to 5 years and 12 per cent. This value is 3.605 as seen from Table A-4. Substituting the values, we have
C=\frac{\text { Rs } 10,00,000}{3.605}=\text { Rs } 2,77,393
Thus, Rs 2,77,393 is to be paid at the end of each year for 5 years to repay the principal and interest on Rs 10,00,000 at the rate of 12 per cent.
3. An investor may often be interested in finding the rate of growth in dividend paid by a company over a period of time. It is because growth in dividends has a significant bearing on the price of the shares. In such a situation compound interest tables are used. Let us illustrate it by an Example (2.13).