Question

Problem 1 Great Britain issued perpetual bonds for the first time in 1751. The bonds were used to consolidate debt that Britain had accumulated through various empire building efforts. These bonds are known as consols, shortened from consolidation annuities, and they pay perpetual interest and have no maturity date. The British government has restructured these perpetual bonds over the centuries and they are now known as ‘consolidate stock’ and they pay 2.5% of par to the holder . What is the value of £10,000 face value of consols assuming a required return of 4%? What is the value of £10,000 face value of consols assuming a required return of 4%?

Problem 2:

1. How much will you have to contribute every year in order to accumulate $250,000 prior to retirement? Assume an interest rate of 6% and retiring after 30 years

2. How much will you be able to withdraw annually from this account for the 20 year period? Assume an interest rate of 6%.

Answer 1

QUESTION 1

Consol bond is a perpetual bond issued by the government.

For the consol stock in question, it pays 2.5% of £10,000 forever. This is equal to £250.

For a perpetual issue, its value = Annual payment/Required rate of return

In our question, annual payment = £250, Req. rate of return = 4% (given in question).

Hence, present value of this consol = 250/.04 = £6,250

QUESTION 2

This is an example of annuity, where every year you would contribute amount P, which accumulates to $250,000 for 30 years at 6% interest rate.

Now, future value of an annuity is mathematically represented as:

Substituting the values in our mathematical relation, we get

P = $3,162.23

So, this amount needs to be saved and accumulated each year.

QUESTION 3

Now you want to know the annual withdrawable amount from the accumulated $250,000 assuming withdrawal for 20 years at 6% per annum rate.

We need to use the present value of annuity function for this, which is:

Substituting the values in Equation, we get:

P = $21,796.14

This is the amount that is withdrawable over 20 years of retirement.