Sonny's BBQ Company recently issued $85 par value preferred stock that pays an annual dividend of $9. Analysts estimate that the stock has a beta of 1.01. The current T-bill rate is 2.4%. The S&P 500's expected return is 12.1%. Assuming that CAPM holds, what is the intrinsic value of this preferred stock?

Intrinsic value=$73.77

Explanation:

The Dividend Valuation Model(DVM) is a technique used to value the worth of an asset.

According to this model, the value of an asset is the sum of the present values of the future cash flows would that arise from the asset discounted at the required rate of return.

Price = D/Kp

D- Dividend payable

Kp- cost of preferred stock

So will need to work out the cost of equity using CAPM

The capital asset pricing model (CAPM): relates the price of a share to the market risk or systematic risk. The systematic risk is that which affects all the all the economic agents, e.g inflation, interest rate e.t.c  

This model is considered superior to DVM. Hence, we will use the CAPM

Using the CAPM , the expected return on a asset is given as follows:  

E(r)= Rf +β(Rm-Rf)  

E(r) =? , Rf- 2.4%, Rm- 12.1% β- 1.01

E(r) = 2.4% + 1.23×(12.1- 2.4)%  = 12.20 %

Cost of preferred stock= 12.20 %

Using the dividend valuation model

Intrinsic value = 9/0.1220=73.77

Intrinsic value=$73.77