7,500.00 is invested at an APR of 4.9% compounded semi annually (twice per year). Write a numerical expression that would comput
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Answer:
NPV with a 14.9% discount rate: 6,329.06
The toy should be produced as the NPV is positive.
IRR = 26.65%
Explanation:
First we calculate for the NPV using the given discount rate of 14.9%
We will calculate the present value of each year cash inflow:
Year 1 cash inflow: 47,500.00
time 1.00
rate 0.149
PV 41,340.30
Year 2 cash inflow: 18,600.00
time 2.00
rate 0.149
PV 14,088.76
Then, we add them and subtract the investment to get NPV
NPV = 14,088.76 + 41,340.3 - 49,100 = 6,329.06
The toy should be produced as the NPV is positive.
Now for the IRR
That is the rate at which NPV equals zero we can solve for this using the quadratic equation as there are only two cash flow:
Year 1 will discount at (1+IRR)
Year 2 will be discount at (1+IRR )^2
So we can express and recreate the quadratic formula:
18,600 X^2 + 47,500 X - 49,500 = 0
A = 18,600
B = 47,500
C = -49,100
We can solve and get:
x1 = 0.78957
x2 = -3.3433
We take the positive value.
and now solve for IRR
IRR = 0,2665121 = 26.65%
This will be the IRR for the project.