Question

Assume that the risk-free rate of interest is 3% and the expected rate of return on the market is 15%. I am buying a firm with an expected perpetual cash flow of $2,000 but am unsure of its risk. If I think the beta of the firm is 0.8, when in fact the beta is really 1.6, how much more will I offer for the firm than it is truly worth

Answer 1

The correct solution is "$6,564.01". A further solution is given below.

Step-by-step explanation:

The given values are:

beta,

= 1.6

market return,

= 15%

cash flow,

= $2,000

risk free rate of interest,

= 3%

Now,

The stock return will be:

=
`3+ 1.6* (15-3)`

=
`3+ 1.6* 12`

=
`22.2 \ percent`

The actual worth of the firm will be:

=
`(cash \ flow)/(rate \ of \ return)`

=
`(2000)/(22.2 \ percent)`

=
`(2000)/(0.222)`

=
`9,009`

With 0.8 beta, the stock return will be:

=
`3+ 0.8* (15-3)`

=
`3+ 0.8* 12`

=
`12.6 \ percent`

So that I'm paying for the firm,

=
`(2000)/(12.6 \ percent)`

=
`(2000)/(0.126)`

=
`15,573.01` ($)

Hence,

I'm paying,

=
`15,573.01-9,009`

=
`6,564.01` ($)