Question

Toy Town is considering a new toy that will cost $49,100 in startup costs. The toy is expected to produce cash flows of $47,500 in Year 1 and $18,600 in Year 2. The toy will be discontinued after the second year. The discount rate assigned to the toy is 14.9 percent. Should the toy be produced? What is the IRR?

Answer 1

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:

$\frac{inflow}{(1 + rate)^{time} } = PV$  

Year 1 cash inflow: 47,500.00

time   1.00

rate  0.149

$\frac{47500}{(1 + 0.149)^{1} } = PV$  

PV   41,340.30

Year 2 cash inflow:  18,600.00

time   2.00

rate  0.149

$\frac{18600}{(1 + 0.149)^{2} } = PV$  

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

$x_1 = \frac{-b+\sqrt{b^{2} -4ac}}{2a}\\x_2 = \frac{-b -\sqrt{b^{2} -4ac}}{2a}$

We can solve and get:

x1 =  0.78957

x2 = -3.3433

We take the positive value.

and now solve for IRR

$\frac{1}{1+ IRR} = 0.78957\\IRR = \frac{1}{0.78957} -1$

IRR = 0,2665121 = 26.65%

This will be the IRR for the project.