Question

Assume that the risk-free rate of interest is 5% and the expected rate of return on the market is 13%. I am buying a firm with an expected perpetual cash flow of $2,000 but am unsure of its risk. If I think the beta of the firm is 1.1, when in fact the beta is really 2.2 how much more will offer for the firm than it is truly worth? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Amount offered in excess

Answer 1

Using the Capital Asset Pricing Model with incorrect and correct beta values, the valuation of the firm was calculated, resulting in an excess offer of $5,643.19 when rounded to two decimal places due to a misjudgment of the firm's risk.

Step-by-step explanation:

When evaluating how much more one might offer for a firm than it is truly worth due to a misconception about the firm's risk measured by its beta, we use the Capital Asset Pricing Model (CAPM). The CAPM states that the expected rate of return on a security is equal to the risk-free rate plus the security's beta times the market risk premium (the market rate of return minus the risk-free rate). Given that the risk-free rate is 5%, the market rate of return is 13%, and the incorrect beta is 1.1, the estimated cost of equity using CAPM would be 5% + 1.1 ( 13% - 5% ) = 13.8%. The correct beta should be 2.2, leading to a true expected rate of return of 5% + 2.2 ( 13% - 5% ) = 22.6%.

Using the formula for the valuation of a perpetual cash flow (the Gordon Growth Model when the growth rate is zero), which is Cash Flow / Required Rate of Return, the valuation with incorrect beta would be $2,000 / 0.138 = $14,492.75, and the true valuation with the correct beta would be $2,000 / 0.226 = $8,849.56. Therefore, the amount offered in excess is $14,492.75 - $8,849.56 = $5,643.19 when rounded to two decimal places.