Answer:
cash flow third year: 23,212
Explanation:
the economic equivalent value means the third payment will make the project equal to 50,000 today at 5% discount rate.
It mill make both option equivalent.
So the present value of the three payment will be 50,000.
[tex]50,000 = PV_{year1}+PV_{year2}+PV_{year3}[/tex]
We will calculate each PV:
First year:
[tex]\frac{Nominal}{(1 + rate)^{time} } = PV[/tex]
Nominal: 10,000.00
time 1 year
rate 5% = 0.05
[tex]\frac{10000}{(1 + 0.05)^{1} } = PV[/tex]
PV 9,523.81
Second Year:
Nominal: 15,000.00
time 2 years
rate 0.05
[tex]\frac{15000}{(1 + 0.05)^{2} } = PV[/tex]
PV 13,605.44
Now, we go back to our previous formula:
[tex]50,000 = PV_{year1}+PV_{year2}+PV_{year3}[/tex]
50,000 = 9,523.81 + 13,605.44 + PV3
And solve for PV of third year:
PV3 = 26,870.75
Now we go into the formula for PV and solve for the nominal
Third Year:
Nominal: N
time 3 years
rate 0.05
PV 26,870.75
[tex]\frac{N}{(1 + 0.05)^{3} } = 26,870.75[/tex]
N = 23211.96415
The third year cash inflow should be for this amount to made the project economic equivalent
