Question

Recall British Consols first issued in 1700s are considered perpetuities. If a British Consol will pay 100 GBP annually starting one year from now and interest rate is 5%.

Required:
a. What is this asset worth today?
b. If interest rate is always 5%, what is the asset worth 3 year from now?
c. Does the asset appreciate or depreciate in value?
d. Do you have any return if you are holding an asset that does not change in value? What is your rate of return?

Answer 1

a. Present value of perpetuity today = Perpetuity amount / Interest rate = 100 / 0.05 = 2,000GBP. Thus, this asset worth 2,000GBP today

b. Value of perpetuity 3 years from now = Perpetuity amount / Rate = 100/.05 = 2000GBP. The asset worth 3 year from now is 2,000GBP.

c. Since this is a perpetuity; it neither appreciate nor depreciate in value provided the interest rate is constant.

d. There will be a return since we are getting cash-flows in a yearly basis; rate of return will be the interest rate = 5%