Question

a. What is the time 0 value of a $500 perpetuity at an interest rate of 4.5 percent?

b.What is the value of the above assuming that it is a perpetuity due? That is, the first payment occurs at time 0 and continues forever.

c.What is the time 0 value of a $500 deferred perpetuity that makes its first payment 6 years from now? Assume a 4.5 percent interest rate.

d. Given an interest rate of 4.5 percent per year, what is the value 3 years from now of a perpetual stream of $500 payments that begins 8 years from now?

( pls show how you solved for it)

Answer 1

A. Present value (PV) at time 0 for a $ 500 perpetuity at an interest rate of 4.5% = PMT / R = 500 / 4.5% = $ 11,111.11

B. Present value (PV) of a perpetuity due = PMT + PMT/R = $ 500 + $ 11,111.11 = $ 11,611.11

C. Since the payment starts from 6 years from now.

So, Value of perpetuity payment on 6th year = PMT / R = 500 / 0.045 = $ 11,111.11

Hence the present value of value of the perpetuity = Value of perpetuity paid on 6th year / (1+R/100)^5

= 11,111.11 / (1.045)^5

= 11,111.11 / 1.246182 = $ 8,916.122

D. Referring to the above question,

Value of perpetuity payment on 8th year = PMT / R = 500 / 0.045 = $ 11,111.11

The present value of value of the perpetuity = Value of perpetuity paid on 8th year / (1+R/100)^7

=  11,111.11 / (1.045)^7

= 11,111.11 / 1.360862 = $ 8,164.76

Hence, Future value of the perpetuity 3 years from now = PV (1+R/100) ^ 3

= 8,164.76 * (1.045) ^ 3 = $ 9,317.347

Hope this resolves the query.