Question

This year Finance Corp has a free cash flow of $17 million. The total market value of their outstanding shares is $140 million. Finance Corp is 100% financed through equity and has $30 million in cash. From next year, the free cash flows are expected to increase by 5% in perpetuity. Assume that all cash flows occur at the end of the years. Finance Corp has a Beta of 2. The expected return on the market portfolio is 8% and that the risk-free interest rate is 1%.

A) Calculate the expected rate of return for Finance Corp.
B) Calculate the present value of the free cash flows.
C) Is the current valuation of Finance Corp, i.e. $140 million too high?

Answer 1

The expected rate of return for Finance Corp is 15%. The present value of the free cash flows is $195 million. The current valuation of Finance Corp, i.e. $140 million, is too low.

Step-by-step explanation:

To calculate the expected rate of return for Finance Corp, we will use the capital asset pricing model (CAPM).

The CAPM formula is: Expected rate of return = Risk-free rate + Beta x (Market return - Risk-free rate).

In this case, the risk-free rate is 1%, the Beta is 2, and the expected return on the market portfolio is 8%. Plugging these values into the formula, we get: Expected rate of return = 1% + 2 x (8% - 1%) = 1% + 2 x 7% = 1% + 14% = 15%.

Therefore, the expected rate of return for Finance Corp is 15%.

To calculate the present value of the free cash flows, we will use the formula: Present value = (Cash flow / (1 + Discount rate))^Years.

In this case, the cash flow is $17 million and the discount rate is 15%. The cash flow is expected to increase by 5% in perpetuity. Plugging these values into the formula, we get:

Present value = ($17 million / (1 + 15%))^1 + ($17 million x 1.05 / (1 + 15%))^2 + ($17 million x 1.05^2 / (1 + 15%))^3 + ...

To calculate the present value, we need to sum up an infinite geometric series. The formula for the sum of an infinite geometric series is: Sum = First term / (1 - Common ratio).

In this case, the first term is $17 million and the common ratio is 1.05 / (1 + 15%). Plugging these values into the formula, we get:

Sum = $17 million / (1 - 1.05 / (1 + 15%)) = $17 million / (1 - 1.05 / 1.15) = $17 million / (1 - 0.913) = $17 million / 0.087 = $195 million.

Therefore, the present value of the free cash flows is $195 million.

To determine if the current valuation of Finance Corp, i.e. $140 million, is too high, we need to compare it to the present value of the free cash flows.

If the present value of the free cash flows is greater than the total market value of the outstanding shares, then the current valuation is too low. If the present value is less than the total market value, then the current valuation is too high.

In this case, the present value of the free cash flows is $195 million and the total market value of the outstanding shares is $140 million. Since $195 million is greater than $140 million, the current valuation of Finance Corp is too low.