A consulting project will generate revenue of $20,250.00 next quarter. Revenues will increase by 1.00% per quarter for a 5.00 year period. If the consulting firm wants a 10.60% APR (with quarterly compounding) return on their projects, what is the value of the project to the firm today?



To determine the present value of the project to the consulting firm, we can use the **Present Value (PV)** formula for a stream of growing cash flows, taking into account the 10.60% APR with quarterly compounding.

### Given information:

- Initial revenue (cash flow) in the first quarter: $ C_1 = 20,250 $
- Growth rate per quarter: $ g = 1.00\% = 0.01 $ per quarter
- Annual percentage rate (APR) with quarterly compounding: $ r_{APR} = 10.60\% $
- Period of the project: 5 years, or $ N = 5 \times 4 = 20 $ quarters

### Step 1: Convert APR to quarterly effective interest rate
The quarterly interest rate is given by:

\[
r = \frac{10.60\%}{4} = 0.0265 \text{ (or 2.65% per quarter)}
\]

### Step 2: Use the Present Value formula for a growing annuity

The present value of a growing annuity can be calculated using the formula:

\[
PV = \frac{C_1}{r - g} \left( 1 - \left( \frac{1+g}{1+r} \right)^N \right)
\]

Where:
- $ C_1 $ is the first quarter's cash flow
- $ r $ is the quarterly interest rate
- $ g $ is the quarterly growth rate
- $ N $ is the total number of quarters

Let me calculate the present value using this formula.The present value of the project to the consulting firm today is approximately **$339,729.56**.

Would you like more details on the steps, or do you have any further questions?

Here are 5 related questions to expand on this concept:
1. How would the present value change if the APR was 12%?
2. What if the growth rate increased to 1.5% per quarter?
3. How would the value differ with monthly compounding instead of quarterly?
4. What is the effect of extending the project period to 6 years instead of 5?
5. How do you calculate the present value of a constant (non-growing) cash flow?

**Tip:** The difference between the interest rate and growth rate significantly impacts the present value of growing cash flows.

A consulting project will generate revenue of $20,250.00 next quarter. Revenues will increase by 1.00% per quarter for a 5.00 year period. If the consulting firm wants a 10.60% APR (with quarterly compounding) return on their projects, what is the value of the project to the firm today?

Calculate the present value of a consulting project with initial revenue of $20,250.00, a 1.00% quarterly revenue growth over 5 years, and a 10.60% APR with quarterly compounding. Learn how to apply the present value formula for a growing annuity and key financial concepts, such as compounding interest and revenue growth.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation