**EXAMPLE 2.11**

Company XYZ is establishing a sinking fund 10 retire Rs 5.00,000, 8 per cent debentures, 10 years from today. The company plans to put a fixed amount into the fund each year for 10 years. The first payment will be made at the end of the current year. The company anticipates that the funds will earn 6 per cent a year. What equal annual contributions must be made to accumulate Rs 5,00:000, 10 years from now?

**Solution **The solution to this problem is closely related to the process of finding the compounded sum of an annuity. Table A-2 indicates that the annuity factor for 10 years at 6 per cent is 13.181. That is. one rupee invested at the end of each year for 10 years will accumulate to Rs 13.181 at the end of the 10th year. In order 10 have Rs 5.00,000 the required amount would be Rs 5,00,000 + 13.181 z Rs 37,933.39. If Rs 37,933.39 is deposited at the end of each year for ten years, there Will be Rs 5,00,000 in the account

**2.** When the amount of loan taken from financial institutions or commercial banks is to be repaid in a specified number of equal annual installments, the financial manager will be interested in determining the amount of the annual installment. Consider Example 2.12.

**EXAMPLE 2.12**

A limited company borrows from a commercial bank Rs 10,00,000 at 12 per cent rare of interest to he paid in equal annual end-of-year installments. What would the size of the instrumental be? Assume the repayment period is 5 years:

**Solution**. The problem relates to loan amortization. The loan amortization process involves finding out the future payments over the term of the loan whose present value at the interest just equals the initial principal borrowed. In this 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). P(ADF) in which P is the amount of loan, that is Rs 10,00,(00), 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

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).

**Example (2.13)**

Mr X wishes to determine the rate of growth of the following Stream of dividends he has received from a company:

**Solution **Growth has been experienced for four years. In order to determine this rate of growth, the amount of dividend received in year 5 has been divided by the amount of dividend received in the first year. This gives us a compound factor which is 1.216 (Rs 3.0-4 + Rs 2.50). Now, we have to look at Table A-1 which gives the compounded values of Re 1 at various rates of interest (for our purpose the growth rate) and number of years. We have to look to the compound factor 1.216. against fourth year in the row side. looking across year 4 of Table A-1 shows that the factor for 5 per cent is exactly 1.216; therefore, the rate of growth associated with the dividend stream is 5 percent.

**4. ** To determine the Current values of debentures, the present value Tables A·3 and A-4 can be of immense use. The cash flow from a debenture consists of two parts first, interest inflows at periodic intervals say, semi-annually or annually and second the repayment of the principal on maturity. Since the interest payments on a debenture are made periodically throughout its life, it is easy to calculate the present value of this annuity type interest inflow by consulting A-4 and the present value of value of the debentures can ascertained by discounting it at the market rate of interest by consulting Table A-3. The sum of the values so obtained will be current worth of a debenture. If the interest is paid after six months, the factors an: obtained for one-half of the discount rate and the number of years double Consider Example 2.14

**EXAMPLE 2.14**

Suppose a particular debenture pays interest at 8 percent per Annam. The debenture is to be paid after 10 years at a premium of 5 percent. What is the current worth of the debenture, assuming the appropriate market discount rate on debenture of similar risk and money is equal to the debenture's coupon rate, that is, 8 percent?

**Solution**

Since the interest is compounded semi-annually over 10 years, the relevant compounding period equals to 20 and the discount rate will be one-half (4 per cent) of the yearly interest of 8 per cent. In other words, the investor will have an annuity of Rs 40 per cent of Rs 1,000 for a compounding period of 20 years. The present value factor for 20 years and 4 per cent from Table A-4 is 13.59 which, when multiplied by Rs 40. gives us a present value fur the interest cash flows of Rs;4.60. The present value of malarial value is the debenture is 10 be redeemed at 5 per cent premium) will he found by multiplying Rs 1.000 by the factor for the present value of received 20 years from now at 4 per cent. The relevant present value factor from Table A-3 is 0.456. Multiplied that maturity value, will gives us a present sum of Rs 1.078. The total value of the debentures would be equal of these two values, that is, Rs 543.60 + Rs 478.8 = Rs 1.022.4.