Question

How much are you willing to pay for an investment that promises to pay $10,000 a year in perpetuity if your required rate of return on this investment is 10 percent and the first $10,000 payment starts in 10 years? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

Answer 1

Present Value= 38,554.33

Step-by-step explanation:

Giving the following information:

The investment promises to pay $10,000 a year in perpetuity. The required rate of return is 10 percent and the first $10,000 payment starts in 10 years.

We will separate the calculation in two different steps. First, we calculate the value ten years from now of the annuity. Then we calculate the present value.

The present value of the annuity (10 years from now):

PV= Cf/i

Cf= cash flow

PV= 10,000/0.10= 100,000

Now, we calculate the value today:

PV= FV/ (1+i)^n

PV= 100,000/ 1.10^10= 38,554.33