Question

What is the present value of a perpetuity that pays you annual, end-of-year payments of $950? Use a nominal rate (monthly compounding) of 7.50%.

Answer 1

Answer:

PV= $12,242.27

Explanation:

Giving the following information:

Cf= 950

Nominal interest= 0.0750 monthly compounded

First, we need to determine the real interest rate:

Monthly interest rate= 0.075/12= 0.0625

Real annual rate= (1.00625^12) - 1= 0.0776

Now, we can calculate the present value using the following formula:

PV= Cf/ i

PV= 950/0.0776

PV= $12,242.27

Answer 2

Answer:

The present value of the perpetuity is $12,242.27.

Explanation:

A perpetuity is an annuity that provide cash flow for an infinite period .Examples are Non -redeemable Preference Share.

Present Value (perpetuity) = Payments ÷ Required Rate

But, first change the 7.50 % nominal rate to Annual Effective Rate to match the period of Cash flow.

Effective Rate = (1 + r / m)^m - 1

                       = ( 1 + 0.0750 / 12) ^12 -1

                       = 7.76%

Therefore, Present Value (perpetuity) = $950 ÷  7.76%

                                                              = $12,242.27