Question

The risk-free rate in a given economy is 5%, and the expected rate of return on the market is 10%. I am buying a firm with a perpetual annual cash flow of Rs. 2,000. If I think the beta of the firm is 0.8, when the beta is in fact 1.6, how much more will I offer for the firm than it is really worth

Answer 1

According to the CAPM,

Required Return = Risk-free Rate + [Beta * (Expected Market Return - Risk-free Rate)]

If the beta is 0.8;

= 5% + [0.8* (10% - 5%)]

= 5% + 4% = 9%

PV = Perpetual Cash Flow / Required Return

= Rs. 2,000 / 0.09 = Rs. 22,222.22

If the beta is 1.6;

= 5% + [1.6* (10% - 5%)]

= 5% + 8% = 13%

PV = Perpetual Cash Flow / Required Return

= Rs. 2,000 / 0.13 = Rs. 15,384.62

Therefore, you would be paying:

Rs. 22,222.22 - Rs. 15,384.62 = Rs. 6,837.60 extra at your assumption of beta of 0.8.