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.