Question

Year	IBM’s yearly stock return	Yearly return on the S&P500
1999	17.02%	21.04%
2000	-21.21%	-9.10%
2001	13.09%	-1.89%
2002	16.22%	-22.10%

The riskless rate for this period is 3.5%, and the covariance between returns on IBM stock and the S&P500 over this period is 0.02276.

1E. What is the variance of the S&P500 over this period?

1F. What is IBM’s CAPM beta according to this data?

1G. What is IBM’s CAPM cost of equity according to this data?

1H. If IBM’s debt to equity ratio is 0.57, what is their unlevered cost of equity according to this model?

Please show work for each.

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

Cell reference -

We can also solve it with manual calculations, as below:

1E. Variance of S&P500

IBM = A

S&P500 = M

Firstly calculated the average return of M with following equation:

where,

Mi = S&P500 return in each period

n = No. of period

We can calculate the variance of S&P500 with following equation:

1F. IBM's CAPM Beta

We can calculate IBM's Beta with following equation:

1G. IBM's CAPM Cost of equity

We can compute Cost of equity under CAPM with following equation:

where,

kA = Cost of equity of IBM

rf = risk free rate

1H. Unlevered Cost of equity of IBM

Firstly we need to calculated the unlevered beta with following equation.

where,

D/E = Debt to equity ratio

Now, We can compute the unlevered cost of equity with following equation: