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You're considering starting a software company with an initial (t=0) cost of $465.The first positive cash flow will be $30 in one year (t=1), and will grow by 7% pa for 3 years. So the next cash flows will be:$30 at t=1;$32.1 (=30*(1+0.07)^1) at t=2;$34.347 (=30*(1+0.07)^2) at t=3.From t=3 onwards, these positive cash flows will grow at the lower rate 2% pa in perpetuity. So the subsequent cash fows will be:$35.0339 (=30*(1+0.07)^2*(1+0.02)^1) at t=4;$35.7346 (=30*(1+0.07)^2*(1+0.02)^2) at t=5;$36.4493 (=30*(1+0.07)^2*(1+0.02)^3) at t=6, and so on forever.The required return is 12% pa. What is the net present value (NPV) of starting this company? All results above and below are rounded to 4 decimal points. The NPV of starting this company is:Question 3Select one:a.-$172.021b.-$144.0277c.-$138.8122d.$292.979e.$321.2983

Question

You're considering starting a software company with an initial (t=0) cost of 465.Thefirstpositivecashflowwillbe465.The first positive cash flow will be 30 in one year (t=1), and will grow by 7% pa for 3 years. So the next cash flows will be:30att=1;30 at t=1;32.1 (=30*(1+0.07)^1) at t=2;34.347(=30(1+0.07)2)att=3.Fromt=3onwards,thesepositivecashflowswillgrowatthelowerrate234.347 (=30*(1+0.07)^2) at t=3.From t=3 onwards, these positive cash flows will grow at the lower rate 2% pa in perpetuity. So the subsequent cash fows will be:35.0339 (=30*(1+0.07)^2*(1+0.02)^1) at t=4;35.7346(=30(1+0.07)2(1+0.02)2)att=5;35.7346 (=30*(1+0.07)^2*(1+0.02)^2) at t=5;36.4493 (=30*(1+0.07)^2*(1+0.02)^3) at t=6, and so on forever.The required return is 12% pa. What is the net present value (NPV) of starting this company? All results above and below are rounded to 4 decimal points. The NPV of starting this company is:Question 3Select one:a.-172.021b.172.021b.-144.0277c.-138.8122d.138.8122d.292.979e.$321.2983

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Solution

To calculate the Net Present Value (NPV), we need to discount all future cash flows back to the present value and then subtract the initial investment.

First, we calculate the present value of the cash flows for the first 3 years:

PV1 = 30/(1+0.12)1=30 / (1+0.12)^1 = 26.7857 PV2 = 32.1/(1+0.12)2=32.1 / (1+0.12)^2 = 25.5102 PV3 = 34.347/(1+0.12)3=34.347 / (1+0.12)^3 = 24.3301

Next, we calculate the present value of the perpetuity cash flows starting from year 4. The formula for the present value of a growing perpetuity is:

PV = C / (r - g)

where C is the cash flow in the first period, r is the discount rate, and g is the growth rate.

So, the present value of the perpetuity cash flows is:

PV_perpetuity = 35.0339/(0.120.02)=35.0339 / (0.12 - 0.02) = 350.339

However, this value is as of year 3, so we need to discount it back to the present:

PV_perpetuity_discounted = 350.339/(1+0.12)3=350.339 / (1+0.12)^3 = 247.619

Finally, we calculate the NPV by adding up all the present values and subtracting the initial investment:

NPV = PV1 + PV2 + PV3 + PV_perpetuity_discounted - 465=465 = 26.7857 + 25.5102+25.5102 + 24.3301 + 247.619247.619 - 465 = -$140.754

The closest answer to this is option c.-$138.8122.

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