Question

You are considering two possible marketing campaigns for a new product. The first marketing campaign requires an outlay next year of 2M, and then will pay 0.24M in all subsequent years. The second marketing campaign requires an outlay of 3M next year and then will pay 0.27M in all subsequent years.

What is the IRR for the first marketing campaign?

*Make sure to input all percentage answers as numeric values without symbols, and use four decimal places of precision. For example, if the answer is 6%, then enter 0.0600.

Answer 1

To find the Internal Rate of Return (IRR) for the first marketing campaign, we need to solve the equation where the net present value (NPV) of the cash flows equals zero. The cash flows for the first campaign can be expressed as follows:

- Year 0 (next year, at present time): Cash outflow of 2M (which can be represented as -2,000,000)
- Year 1 and beyond: Cash inflow of 0.24M annually (which can be represented as 240,000)

The IRR is the discount rate \( r \) that satisfies the following equation:

\[
\text{NPV} = -2,000,000 + \sum_{t=1}^{\infty} \frac{240,000}{(1 + r)^t} = 0
\]

The sum of the cash flows from year 1 to infinity can be expressed using the formula for the present value of a perpetuity:

\[
\sum_{t=1}^{\infty} \frac{C}{(1 + r)^t} = \frac{C}{r}
\]

In our case, \( C = 240,000 \). Thus, we can rewrite the NPV equation as:

\[
-2,000,000 + \frac{240,000}{r} = 0
\]

Now we can solve for \( r \):

\[
\frac{240,000}{r} = 2,000,000
\]

Multiplying both sides by \( r \):

\[
240,000 = 2,000,000r
\]

Now, divide both sides by 2,000,000:

\[
r = \frac{240,000}{2,000,000} = 0.12
\]

Thus, the IRR for the first marketing campaign is:

\[
\text{IRR} = 0.12
\]

In decimal form with four decimal places, the answer is:

\[
\text{IRR} = 0.1200
\]