Question

You are hired as a manager for AT&T. You are asked to make a presentation as to whether they should undertake the following project. For the purpose of this question, assume AT&T is all equity financed.

a) First, you calculate that AT&T has a covariance with the market of .02, and that the standard deviation of the market’s returns is .3. What is AT&T’s Beta?

b) Treasury bills are currently yielding 1%. If you believe the market has a risk premium of 7%, what is the expected return to AT&T?

c) AT&T is looking into constructing a new wireless network around San Antonio. The risk inherent in this project is similar to the overall risk of AT&T. Once built, you believe this project will provide cash flows of $10 million/year for the next 20 years. What is the most AT&T should be willing to pay to build this network?

Answer 1

a) Beta of the stock = covariance between the stock and market / variance of market

= 0.02 / 0.3^2 = 0.22

( variance = standard deviation ^2)

b)

As per CAPM ,

Expected return = Risk free rate + Market risk premium * beta

= 1+ ( 7 - 1 ) *0.22

= 2.33%

c)

most AT&T should be willing to pay to build this network is the present value of the cash flows recieved in the future for the next 20 years. The discount rate to be used is 2.33% is the expected return on equity

The present value of cash flows = presnet value of annuity

= regular cash inflows * [ 1 - ( 1 + return )^ - no of years ] / return

= 10 * [ 1 - 1.0233^ -20 ] / 0.0233

= 10-15.8425

= 158.42

most AT&T should be willing to pay to build this network = $ 158.42 million