Question 2.S2.14: Suppose a particular debenture pays interest at 8 per cent p......
Suppose a particular debenture pays interest at 8 per cent per annum. The debenture is to be paid after 10 years at a premium of 5 per cent. The face value of the debenture is Rs 1,000. Interest is paid after every six months. What is the current worth of the debenture, assuming the appropriate market discount rate on debentures of similar risk and maturity is equal to the debenture’s coupon rate, that is, 8 per cent?
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 (4 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 for the interest cash flows of Rs 543.60. The present value of a maturity value of Rs 1,050 (as the debenture is to be redeemed at 5 per cent premium) will be found by multiplying Rs 1,050 by the factor for the present value of Re 1 to be received 20 years from now at 4 per cent. The relevant present value factor from Table A-3 is 0.456. Multiplied by Rs 1,050 maturity value, it gives us a present sum of Rs 478.8. The total value of the debentures would be equal to the total of these two values, that is, Rs 543.60+ Rs 478.8= Rs 1,022.4.