The risk free rate in a given economy is 5% and the expected return on the market is 10%. I am buying a firm with a perpetual annual cash flow of $2000. If I think the beta of the firm is 0.8 when the beta in fact is 1.6, how much more will I offer for the firm that it is really worth?
WARNING! I'm no expert in this type of investment, but I will give it a go and you decide!!.
The risk free rate in a given economy is 5% and the expected return on the market is 10%. I am buying a firm with a perpetual annual cash flow of $2000. If I think the beta of the firm is 0.8 when the beta in fact is 1.6, how much more will I offer for the firm that it is really worth?
The expected return at your assumption of beta of 0.8 would be:
5% + 0.8[10% - 5%] = 9%. Therefore, the current value of perpetual annuity would be:
$2,000 / 0.09 =$22,222.22 at your assumption
The expected return at the actual beta of 1.6 would be:
5% + 1.6[10% - 5%] =13%. Therefore, the current value of the perpetual annuity would be:
$2,000 / .13 =$15,384.62 at actual beta of 1.6. Therefore, you would be paying:
$22,222.22 - $15,384.62 =$6,837.60 extra at your assumption of beta of 0.8.
