Question

The Cambro Foundation, a nonprofit organization, is planning to invest $209710 in a project that will last for three years. The project will produce net cash inflows as follows:

Year 1 $ 65000
Year 2 $ 79000
Year 3 ?
Assuming that the project will yield exactly a 7% rate of return, what is the expected net cash inflow for Year 3?

Answer 1

To calculate the expected net cash inflow for Year 3, we need to use the present value formula:

PV = FV / (1 + r)^n

Where PV is the present value, FV is the future value, r is the rate of return, and n is the number of years.

We know that the present value of the investment is $209,710, and we know the net cash inflows for the first two years ($65,000 and $79,000). We can use the present value formula to solve for the future value of the third year's net cash inflow:

$65,000 / (1 + 0.07)^1 = $60,747.66
$79,000 / (1 + 0.07)^2 = $63,063.84

$209,710 = $60,747.66 + $63,063.84 + FV / (1 + 0.07)^3

Solving for FV, we get:

FV = $209,710 - $60,747.66 - $63,063.84 * (1 + 0.07)^3
FV = $209,710 - $60,747.66 - $63,063.84 * 1.225043
FV = $209,710 - $60,747.66 - $77,261.51
FV = $71,700.83

Therefore, the expected net cash inflow for Year 3 is $71,700.83.

Answer 2

solve for the cash inflow in Year 3.

The present value of an investment is the current value of all future cash inflows discounted at the required rate of return. For this problem, we can use a discount rate of 7%.

The present value of the investment can be calculated as follows:

PV = Year 1 cash inflow / (1 + r)^1 + Year 2 cash inflow / (1 + r)^2 + Year 3 cash inflow / (1 + r)^3

where r is the discount rate.

Substituting the given values, we get:

$209710 = $65000 / (1 + 0.07)^1 + $79000 / (1 + 0.07)^2 + Year 3 cash inflow / (1 + 0.07)^3

Simplifying the equation, we get:

Year 3 cash inflow / (1 + 0.07)^3 = $209710 - $65000 / (1 + 0.07)^1 - $79000 / (1 + 0.07)^2

Year 3 cash inflow / (1 + 0.07)^3 = $32825.66

Multiplying both sides by (1 + 0.07)^3, we get:

Year 3 cash inflow = $32825.66 x (1 + 0.07)^3

Year 3 cash inflow = $32825.66 x 1.225

Year 3 cash inflow = $40205.09

Therefore, the expected net cash inflow for Year 3 is $40205.09.