Question

14) b) The British government has consol bonds (perpetuities) outstanding that pay £100 per year, forever. Assume that the current discount rate is 4%. What is the value of the bond today in £, if the last payment was made yesterday? What is the value of the bond today in £, if you will receive the first payment today? Assume an ordinary perpetuity. If this consol trades in the market today at £2,480, what rate of return will an investor earn from this investment? Assume a perpetuity due. If the consol trades in the market today at £2,560, what rate of return will an investor earn from this investment? d)

Answer 1

Part (a):

Present value of a perpetuity (PV)= C/r Where C= periodical cash flow and r= rate of return

Given, yearly cash flow (C )= £100 and r= 4%

PV= £100/4% = £2,500.

Hence value of the bond today, if the last payment was made yesterday= £2,500.

Part (b):

The general formula for PV of perpetuity assumes that the first payment will take place one period ahead.

Since the first payment will take place today, it is a perpetuity due.

Value today = (C/R)+C₀

Hence value today= (£100/4%)+£100= £2,500+£100 = £2,600.

Part (c ):

In an ordinary perpetuity, PV= C/r

Given, PV= £2,480 and C=£100

Substituting the values, £2,480= £100/r.

Therefore, rate of return r= £100/£2,480 = 4.0323%

Part (d):

In a perpetuity due, PV= (C/r)+C

Given, PV= £2,560 and C=£100

Substituting the values, £2,560= (£100/r)+£100

£2,460= £100/r.  

Therefore, rate of return r= £100/£2,460 = 4.06504%