Question

A security pays $800 every 9 years forever. The appropriate discount rate is 6% (EAR).

WARNING: This problem can't be solved just by plugging numbers into your calculator. The cash flows aren't annual, and the first one doesn't necessarily occur one period from now! You have to map it out!

What is the value of the security if the first payment occurs 5 years from now?

Answer 1

Given that,

A security pays $800 every 9 years forever.

The appropriate discount rate is 6% (EAR).

first payment occurs 5 years from now

Value of a perpetuity = Annual payment/annual rate

Since payment are once in 9 years, we need to calculate 9 year interest rate

So, 9 year interest rate = (1+EAR)^9 - 1 = 1.06^9 - 1 = 68.95%

Value of security just after the first payment using perpetuity formula is

V5 = payment/interest rate = 800/0.6895 = $1160.30

Value of security today is sum of PV of VAlue at 5 and payment at year 5

=> Value today = Payment/(1+EAR)^5 + V5/(1+EAR)^5

=> Value today = 800/1.06^5 + 1160.30/1.06^5 = $1464.85

value of the security = $1464.85