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

Answer:

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

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:

= $3+ 1.6\times (15-3)$

= $3+ 1.6\times 12$

= $22.2 \ percent$

The actual worth of the firm will be:

= $\frac{cash \ flow}{rate \ of \ return}$

= $\frac{2000}{22.2 \ percent}$

= $\frac{2000}{0.222}$

= $9,009$

With 0.8 beta, the stock return will be:

= $3+ 0.8\times (15-3)$

= $3+ 0.8\times 12$

= $12.6 \ percent$

So that I'm paying for the firm,

= $\frac{2000}{12.6 \ percent}$

= $\frac{2000}{0.126}$

= $15,573.01$ ($)

Hence,

I'm paying,

= $15,573.01-9,009$

= $6,564.01$ ($)