Question

Cost of​ equity: SML.  Stan is expanding his business and will sell common stock for the needed funds. If the current​ risk-free rate is

4.7​%

and the expected market return is

12.4​%,

the cost of equity for Stan is a.10.24​%

if the beta of the stock is 0.72.

b.  11.86​%

if the beta of the stock is 0.93.

c.  12.32​%

if the beta of the stock is 0.99.

d.  13.40​%

if the beta of the stock is 1.13.

Suppose Stan had to delay the sale of the common stock for six months. When he finally did sell the​ stock, the​ risk-free rate had fallen to

3.7​%,

but the expected return on the market had risen to

13.4​%.

What was the effect on the cost of equity by waiting six​ months, using the four different​ betas? What do you notice about the increases in the cost of equity as beta​ increases?

a.  What is the new cost of equity if the beta of the stock is 0.72​?

b. What is the new cost of equity if the beta of the stock is 0.93​?

c. What is the new cost of equity if the beta of the stock is 0.99​?

d. What is the new cost of equity if the beta of the stock is 1.13​?

Answer 1

First lets calculate the cost of equity under both scenarios:

BETA	RFR	Rm	Cost of equity
0.72	4.70%	12.40%	10.24%
0.93	4.70%	12.40%	11.86%
0.99	4.70%	12.40%	12.32%
1.13	4.70%	12.40%	13.40%
BETA	RFR	Rm	Cost of equity
0.72	3.70%	13.40%	10.68%
0.93	3.70%	13.40%	12.72%
0.99	3.70%	13.40%	13.30%
1.13	3.70%	13.40%	14.66%

Change in cost of equity can be seen in the below graph:

When RFR falls and Rm increases, the cost of equity rises for each level of beta as shown in the above graph. As beta rises, cost of equity rises which is logical because, beta signifies riskiness of the portfolio relative to the market, higher beta says higher risk and therefore higher required return to bear that risk in the form of cost of equity.