Chapter 6 Chapter 6

5
• Present value of Rs.1,000 to be received after 10 years = Rs.190
• PV of Re.1 to be received after 10 years = 0.19.
• Consulting the PVF table, we find that the rate of interest in this case is in the
range of 18% to 19%.
• NPV at 18 % = -190 +(1000 x 0.191) = + 1
• As NPV (at 18%) is positive, this shows that the return is greater than 18%.
Let calculate NPV at 19%.
• NPV at 19 % = -190 +(1000 x 0.176) = - 14
• As NPV (at 19%) is negative, this shows that the return is less than 19%.
We can find the exact return (called YTM, also called 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)
1
= 18 + --------- x 1 = 18.066%
1 – (-14)
Yield to Call : Sometimes, the terms of issue of bonds contain a provision for call
option, i.e. issuer has the option of calling (buying) the bonds for redemption before
the date of maturity of the bonds. Yield to Call refers to the annualized rate of return
on the investment that the investor expects ( on the date of investment ) to earn
from the date of the investment to the date of call.
Q. No. 7 : A Bond is currently traded at Rs.950. Its face value is Rs.1000. Coupon
rate is 10%. It is redeemable at par after 5 years from today. However the company
has an option of calling it after 3 years from today at 5% premium. Find Yield To
Call.
Answer
Average return per year per Bond (till call): [(400)/(3)] = 133.33
Approximate annual yield = [133.33 / 950]x100 = 14.04 %
• NPV at 14 % = -950 +(100 x 2.322) +(1050 x 0.675) = - 9.05
• As NPV ( at 14%) is negative, this shows that the return is less than 14%.
Let calculate NPV at 13%.
• NPV at 13 % = -950 +(100 x 2.361) +(1050 x 0.693) = +13.75
• As NPV (at 13%) is positive, this shows that the return is greater than 13%.