Intercoastal Corporation recently paid a common stock dividend of $2.75. Analysts predict that the firm and its dividends will grow at a rate of 6% per year. Intercoastal has a beta of 1.20. The current risk-free rate of interest is 5.0% and the current return on the market is 13%. What is the intrinsic value of Intercoastal common stock

$33.89.

Explanation:

It is given that the Intercoastal's dividends will grow at a rate of 6% per year. It means that the corporation has achieved a constant growth rate. So, Gordon Dividend Discount Model for Constant Growth will be used to calculate the intrinsic value (Maximum price that an investor is willing to pay) of Intercoastal common stock. The model is given below:

                                 Intrinsic value / Price = D1 / Ke - g

where

D1 = Dividend of year 1. It is calculated as Current Dividend * (1 + g).

Ke = Cost of equity or discount rate. It will be calculate using CAPM.

g = Growth rate.

Workings:

Calculation of Ke using CAPM (Capital Asset Pricing Model)

Ke = Risk-free rate + Beta (Market Return - Risk-free Rate)

⇒ Ke = .05 + 1.20 (.13 - .05) = .146 or 14.6%.

Calculation of D1

D1 = 2.75 * (1 + 6%) = $2.915.

Putting values in the model;

⇒ Intrinsic value = 2.915 / (.146 - .06) = $33.89.

by knowing conditionality

explanation: