just got a question regarding PV perpetuity… in schewser notes, theres an example where pv perpetuity is $56.25 when the rate ie 8% and pmt is 4.5, when pv perpetuity becomes $75, the rate of return becomes 6%…i dont understand this…if an investor is willing to pay more for a preferred stock for example ($75 compared to $56), wouldnt that mean the rate of return would be greater since they are willing to spend more for the stock? thus should reflect a higher return rate?
The required rate of return on the stock represents the opportunity cost to the investor. The higher the opportunity cost, the less the PV of the cashflows from the investment and thus lower market value for the stock. if the required rate of return falls, the investment cashflows have higher PV than before and thus the investment is worth more.
Pefectly correct, chelseace!
Also you can think in this way, when the investor cannot find better investment opportunity (meaning no other investment gives return rate > 6%), he will be willing to buy the stock at $75. If there is another opportunity (e.g. return rate = 8%), now the investor is only willing to buy the stock at $56.25. So you can see the required rate of return is related to other investment opportunities the investor has.
Think of the relation between PV and interest rate as follows: The PV (at some rate) is the amount you’d have to deposit in an account to EXACTLY duplicate the future cash flows. If you wanted a perpetuity of (for example), $10 per year and could earn 10% on your money, you’d have to deposit exactly $100. So, the pv of a $10 perpetuity at 10% is $100. In other words, saying "the present value of a $10 perpetuity is 100 at 10% equivalent to saying “if we paid $100 to receive a $10 perpetuity, we’d be earning 10%”. So, if we paid $200 for the right to receive $10 annually, we’d be earning 5% (i.e. the pv of the perpetuity at 5% is $200).