Answer:
[tex]r=-60.8\%[/tex]
Explanation:
Rate of Return
The rate of return RoR is the net gain or loss on an investment over a time period, expressed as a percentage of the investment's initial cost.
If C1, C2, ..., Cn are the net cash flows at each period of investment, then the actual value of each one of them is
[tex]A_i=C_i(1+r)^{-i}[/tex]
where r is the rate of interest assumed for the investment.
The total value of the cash flows is
[tex]A=\sum C_i(1+r)^{-i}[/tex]
We have the final value of the investment at the present time
[tex]A=800,000\ ;\ C_1=250,000\ ;\ C_2=25,000[/tex]
We can find the r as the RoR of the investment by setting the equation
[tex]800,000=250,000(1+r)^{-1}+25,000(1+r)^{-2}[/tex]
Simplifying by 25,000 and rearranging
[tex](1+r)^{-2}+10(1+r)^{-1}-32=0[/tex]
This is a second-degree equation for [tex](1+r)^{-1}[/tex]. Solving the equation we get only one positive value:
[tex](1+r)^{-1}=2.5498[/tex]
Or, equivalently
[tex]r=-0.608[/tex]
[tex]r=-60.8\%[/tex]
We get a negative RoR
