At the beginning of 2020,market analysts expect Atlantis Company,holder of a valuable patent,to earn the following stream of economic profits over the next five years.At the end of five years,Atlantis will lose its patent protection,and analysts expect economic profit to be zero after five years. $$\begin{array}{l}
\text { Axpected Aconomic }\
\begin{array} { l l l }
\text { Yaar } & \text { Frofit } \
\hline 2020 & \$ 225,000 \
2021 & \$ 325,000 \
2022 & \$ 425,000 \
2023 & \$ 200,000 \
2024 & \$ 100,000
\end{array}
\end{array}$$ If investors apply an annual risk-adjusted discount rate of 15%,the value of Atlantis Company in 2020 is $______________________,which is also the maximum price investors would be willing to pay for Atlantis Company.

Question

At the beginning of 2020,market analysts expect Atlantis Company,holder of a valuable patent,to earn the following stream of economic profits over the next five years.At the end of five years,Atlantis will lose its patent protection,and analysts expect economic profit to be zero after five years. $$\begin{array}{l}
\text { Axpected Aconomic }\
\begin{array} { l l l } 
\text { Yaar } & \text { Frofit } \
\hline 2020 & \$ 225,000 \
2021 & \$ 325,000 \
2022 & \$ 425,000 \
2023 & \$ 200,000 \
2024 & \$ 100,000
\end{array}
\end{array}$$ If investors apply an annual risk-adjusted discount rate of 15%,the value of Atlantis Company in 2020 is $______________________,which is also the maximum price investors would be willing to pay for Atlantis Company.

Quizplus · Accepted Answer

To calculate the present value of the economic profits, we need to discount each year's profit using the given annual risk-adjusted discount rate of 15%.

PV(2020) = $225,000 / (1+0.15)^1 = $195,652.17 
PV(2021) = $325,000 / (1+0.15)^2 = $241,169.87 
PV(2022) = $425,000 / (1+0.15)^3 = $281,085.75 
PV(2023) = $200,000 / (1+0.15)^4 = $106,395.26 
PV(2024) = $100,000 / (1+0.15)^5 = $46,609.22

The present value of the stream of economic profits is:

PV = $195,652.17 + $241,169.87 + $281,085.75 + $106,395.26 + $46,609.22 
PV = $870,912.27

Therefore, the maximum price investors would be willing to pay for Atlantis Company in 2020 is $870,912.27, which is closest to option B ($884,912).

At the Beginning of 2020,market Analysts Expect Atlantis Company,holder of a Valuable