Question

The head of the accounting department at a major software manufacturer has asked you to put together a pro forma statement of the company’s value under several possible growth scenarios and the assumption that the company’s many divisions will remain a single entity forever. The manager is concerned that, despite the fact that the firm’s competitors are comparatively small, collectively their annual revenue growth has exceeded 50 percent over each of the last five years. She has requested that value projection be based on the firm’s current profits of $3.2 billion (which have to be paid out to stockholders) and the average interest rate over the past 20 years (6 percent) in each of the following profit growth scenarios:

a. Profits grow at an annual rate of 9 percent. (this one is tricky.)

b. Profits grow at an annual rate of 2 percent.

c. Profits grow at an annual rate of 0 percent.

d. Profits decline at an annual rate of 4 percent.

Short answer

a. Profit grows at an annual rate of 9% is infinity.

b. Profit grows at an annual rate of 2% is infinity.

c.Profit grows at an annual rate of 0% is infinity.

d.Profit declines at an annual rate of 4% is $33.920,000.

Step-by-step solution

(a) When the annual rate is 9%.

To find the present value of the firm under different profit growth scenarios based on the task, use the following equation:

$P{V}_{firm}={\pi }_0+\frac{{\pi }_0(1+g)}{(1+i)}+\frac{{\pi }_0{(1+g)}^2}{{(1+i)}^2}+\frac{{\pi }_0{(1+g)}^3}{{(1+i)}^3}+\mathrm{...}={\pi }_0\cdot \left(\frac{1+i}{i-g}\right)$

Where PV is present value of the firm, g is the constant annual growth rate and I is the interest rate.

With the constant annual growth rate of 9%, a current profit of $3.2 billion and with an interest rate of 6%,the profit growth rate is greater than the interest rate. So, if it will be calculated,the result will be infinity.

(b) When the annual rate is 2%.

With the annual growth rate of 2%, a current profit of $3.2 billion and with an interest rate of 6%, the profit growth rate is greater than the interest rate. So, if it will be calculated, the result will be infinity.

(c) When the annual rate is 0%.

With an annual growth rate of 0%, a current profit of $3.2 billion and with an interest rate of 6%, the profit growth rate is greater than the interest rate. So, it will be calculated,the result will be infinity.

(d) When the annual rate is 4%.

To find the present value of the firm with a profit growth rate of 4%, use the following equation:

$P{V}_{firm}={\pi }_0.\left(\frac{1+i}{i-g}\right)$

Where ${\pi }_0$ is the current profit, g it’s the constant annual growth rate, I is the interest rate.

With: =$3.2 billion; i=6%=0.06

We substitute all the given numbers in the equation:

$\begin{array}{l}P{V}_{firm}=\$3.2\cdot \left(\frac{1+0.06}{0.06-0.04}\right)\\ =\$3.2\cdot 10.6\\ =\$33.92\end{array}$

Therefore the annual rate is 4%, the profit growth rate is $33.92 billion.