Calculate the present value of a perpetuity that pays $10,000 annually (at the startof each year) forever. The interest rate is 8%

1. Break Down the Problem

To calculate the present value of a perpetuity that pays $10,000 annually at the beginning of each year, we will:

1. Identify the formula for the present value of a perpetuity.
2. Apply it to the given values.

2. Relevant Concepts

The formula for the present value of a perpetuity that pays at the beginning of each year is given by:

$PV = \frac{C}{r} \cdot (1 + r)$

Where:

• $PV$ = Present Value
• $C$ = Cash payment per period ($10,000)
• $r$ = Interest rate (8% or 0.08)

3. Analysis and Detail

Substituting the given values into the formula:

$PV = \frac{10,000}{0.08} \cdot (1 + 0.08)$

Calculating the components step by step:

1. Calculate the denominator: $0.08 = 8\%$

2. Calculate $\frac{10,000}{0.08}$: $\frac{10,000}{0.08} = 125,000$

3. Calculate $(1 + r)$: $1 + 0.08 = 1.08$

4. Now, substitute to find $PV$: $PV = 125,000 \times 1.08$

5. Perform the multiplication: $PV = 135,000$

4. Verify and Summarize

We have calculated the present value of the perpetuity and verified all steps. The present value accounts for receiving $10,000 at the start of each year, discounted at an 8% interest rate.

Final Answer

The present value of the perpetuity is $135,000.