# Should the valuation decision of the following question be undervalued or overvalued?

The official solution to this question is B, but I don't understand that if the recommendation is given by the CAPM model, then the CAPM estimated return should be regarded as "fair" and benchmark for comparison. Then the valuation decision should be undervalued (and hence the answer should be D). Is the official answer wrong?

Patricia Franklin makes buy and sell stock recommendations using the capital asset pricing model. Franklin has derived the following information for the broad market and for the stock of the CostSave Company (CS):

• Expected market risk premium 8%
• Risk-free rate 5%
• Historical beta for CostSave 1.50

Franklin believes that historical betas do not provide good forecasts of future beta, and therefore uses the following formula to forecast beta:

forecasted beta = 0.80 + 0.20 x historical beta

After conducting a thorough examination of market trends and the CS financial statements, Franklin predicts that the CS return will equal 10%. Franklin should derive the following required return for CS along with the following valuation decision (undervalued or overvalued):

A. overvalued 8.3%
B. overvalued 13.8%
C. undervalued 8.3%
D. undervalued 13.8%

## 1 Answer

The price and the discount rate are inversely related. So if the stock is going to earn a lower return than CAPM predicts/requires, one way to look at it is that you are buying it at too high a price today; so as a CAPM believer you shouldn't buy it at this price, it gives you too low a return, wait for a lower price. In other words the stock is overvalued.

If the return is going to be 10%, then the "terminal price" 1 year from now is going to be $P_T=1.1*P_0$ but according to CAPM the price today has to be $\hat{P_0}=\frac{P_T}{1.138}=\frac{1.1*P_0}{1.138}=0.966*P_0$. The equilibrium (or "fair") price is below today's price, it needs to come down by 3.33% to be fair.