We have to pay [tex]\$400000[/tex] for the property if you believe its market risk is the same as the market portfolio’s.
Explanation:
CAPM(Capital Asset Pricing Model) Formula:
[tex]\text {Expected returm }=\text {risk free rate}+\text { beta } \times \text { (market return-risk free rate) }[/tex]
We know the risk-free price, return on the market, so beta (as risk on the market is the same as risk in the portfolio, beta is one) so we are trying to plug all the values in order to achieve the expected return of this investment.
[tex]0.05+1 \times(0.125-0.05)=0.125 \text { or } 12.5 \% \text { Return }[/tex]
We already know that we will get [tex]\$ 50,000[/tex] annually, so use the perpetuity formula:
[tex]Present value = \frac{payment}{rate of return}[/tex]
[tex]\Rightarrow\frac{50,000}{0.125}= \$400000[/tex]
