Question

The Treasury bill rate is 2%, and the expected return on the market portfolio is 12%. Using the Capital Asset Pricing Model (hereafter, CAPM) by William Sharpe (1964) with the given assumptions regarding the risk free rate and market rate to answer the following questions:

A. Draw a graph showing how the expected return varies with beta.

B. What is the risk premium on the market?

C. What is the required return on an investment with a beta of 2.0? Is the beta above or below the Market beta?

D. If an investment has a return (In this case similar to going Market Price) of 7.2% (and a Beta of .7), would this project be considered to have an acceptable NPV, when compared to the required (or expected) “fair or intrinsic” return calculated by using the CAPM formula? Why?

E. If the internal rate of return was calculated to be 10.0%, would we accept the project given the expected return calculated in part D, in other words, given the CAPM calculated in part D?

F. If the market expects a return of 13.5% from stock X, what is its beta (Here we solve for Beta, using all given components of CAPM, except beta which is not given)?

Answer 1

a)The above graph gives the variatiion of expectd return with beta. As beta increases, the expected return also increases

b) Risk premium= Rf-Rm, where Rf=Risk free rate which is the treasury rate, Rm=Return on the market

So Risk premium=12%-2%=10%

c)Using CAPM, Rf+beta*(Rm-Rf)=Required return

Required return=2%+2*(12%-2%)=22.00%

The beta of market is 1 thus the beta of 2 is above the market beta

d) Investment return=7.2%

Required return using CAPM=2%+0.7*(12%-2%)=9%

As the investment return is lower than CAPM required return, this investment will not be having an acceptable NPV

NPV will only be positive when investment return is higher than the required return on that investment. THis is because NPV relies on discounting cash flows at the required retrn rate, and if investment returns are lower than the discounting rate, the NPV will be negetive.

e) For an invetment to be acceptable, the IRR return should be higher than the CAPM returns

f) Pluggin in values in the CAPM formula above =(0.135-0.02)/(12%-2%)=1.15

Thus beta is 1.15

Please reach out for any clarifications