Question

1. a) I a hold a consol that pays coupon C in perpetuity. Current interest rate is i. Avg expectation is that market will not change. Find the price of consol today (1%) b) next period interest rate changes to i'. Find new price of the bond, if the bond is sold at the beginning of the next period what is the yield from the consol. Does the yield increase or decrease if i′ > i? [4%] c) suppose alternatively that the market expectations are that interest rate will change to i′ after the initial period. What is the initial value of the consol, and what is the yield from selling it after one period? [5%

Answer 1

a) Coupon received in perpetuity = C
Current interest rate = i
As per the question, market will not change
So, Price of bond = Coupon (Rs.)/Interest Rate
= C/i

b) In Next period, i changes to i' but bond is sold at the beginning of the next period.
Cash inflow at the end of 1st period = interest amount (C)
Price of bond, at the beginning of next year = Interest amount (C)/ interest rate(i')
= C/i'
Yield of Bond = Interest amount (C)/ Market price of bond at the beginning of new year (M.P)
= C/M.P * 100

There will be no impact on yield from change in interest rate as bond is sold at the beginning of next year.

Note - Bond is considered to be non-reedemable. Coupon rate (C) will remain constant every year.

**If C doesn't remain constant and we get i' (interest rate amount) in next year,
then, Yield of bond = Interest rate amount(i')/M.P. * 100

In this case, if i' > i, then yield will be more and vice versa.

c) if i changes to i' after initial period
Price of bond at the initial period = Coupon/(1+i) + Coupon/i'
= C[1/(1+i) + 1/i']
Yield will remain the same as we calculated in case (b) i.e C(next period)/M.P. * 100