Chapter 6 Chapter 6

3
Q. No. 3 : A company has outstanding 8 per cent debentures of
Rs.10,00,000 on which interest is payable annually on 31 December. The debentures
are due for redemption at par on 1.1.1993. The market price of debenture at
31.12.1989 was Rs.103 cum-interest. Ignore Tax. What do you estimated to be
current market rate of interest (This is also called yield to Maturity.)
Answer
Average return per year per debenture: [(24+5) / (3)] = 9.67
Approximate annual rate = [9.67 / 95] x100 = 10.18%
NPV at 10 % = -95 +(8 x 0.909) +( 8 x 0.826) +(108 x 0.751) = - 0.012
As NPV (at 10%) is negative, this shows that the return is less than 10%.
Let calculate NPV at 9%.
NPV at 9 % = -95 + (8 x 0.917) + (8 x 0.842) + (108 x 0.772) = + 2.448
As NPV (at 9%) is positive, this shows that the return is greater than 9%. We can
find the exact return (YTM, also called as current interest rate) through
interpolation.
YTM or current interest rate-
Lower rate NPV
= Lower rate+--------------------------- x (difference in rates)
(Lower rate NPV - Higher rate NPV)
2.448
= 9 + ---------------- x 1 = 9.995%
2.448 – (-0.012)
Q. No. 4 : There is a 9% 5-year bond issue in the market, The issue price is Rs.90
and the redemption price is Rs.105. For an investor with marginal tax rate of 30%
and capital gain tax rate of 10% ( assuming no indexation), what is the post tax yield
to maturity (May, 2004)
Answer
Let’s assume that the face value of the bond is Rs.100.
Average return per year per Bond: [(31.50 + 13.50) / (5)] = 9
Approximate post tax annual yield = [9.00 / 90] x 100 = 10 %
NPV at 10 % = -90 +(6.3 x 3.791) +(103.50 x 0.621) = - 1.8432
As NPV ( at 10%) is negative, this shows that the return is less than 10%.
Let calculate NPV at 9%.
NPV at 9 % = -90 +(6.3 x 3.89) +(103.50 x 0.650) = +1.782