Question

You are buying an investment product that costs $50,000 today. The annual interest rate is 5% and the investment period is 3 years. The investment will repay you $10,000 at the end of year 1 and $15,000 at the end of year 2. Based on economic equivalent value of the investment, how much should you receive at the end of year 3? Round the answer to the nearest integer. (e.g. round 10.25 to 10, round 10.78 to 11)

Answer 1

cash flow third year: 23,212

Step-by-step 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.

`50,000 = PV_(year1)+PV_(year2)+PV_(year3)`

We will calculate each PV:

First year:

`(Nominal)/((1 + rate)^(time) ) = PV`

Nominal: 10,000.00

time 1 year

rate 5% = 0.05

`(10000)/((1 + 0.05)^(1) ) = PV`

PV 9,523.81

Second Year:

Nominal: 15,000.00

time 2 years

rate 0.05

`(15000)/((1 + 0.05)^(2) ) = PV`

PV 13,605.44

Now, we go back to our previous formula:

`50,000 = PV_(year1)+PV_(year2)+PV_(year3)`

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

`(N)/((1 + 0.05)^(3) ) = 26,870.75`

N = 23211.96415

The third year cash inflow should be for this amount to made the project economic equivalent