Question

3. You have a third project that will cost 1700 to invest in today, will generate cash flows of 50, 100, 200, and 250 at the end of each of the next four years, with cash flows continuing to grow at a constant rate of 3% starting with the fourth cash flow and continuing forever. If the discount rate is 15%, what is the NPV and should you accept the project based on the NPV?

Please show all your work.

Answer 1

Firstly, let's understand the Cash flows-

Year 0 - An investment has been made so the cash flow will be negative= -1700

The investment generates cash flows(so all the cash flows will be positive) of

50 in Year 1

100 in Year 2

200 in Year 3

250 in Year 4

After year 4 the cash flows grows at a constant rate of 3% starting with the fourth cash flow and continuing forever

So we will use constant growth model formula to calculate the PV of cash flows of all the remaining cash flows-

PV of all the cash flows at year 4 = Cash flow in year 4*(1+growth rate) / (Discount rate - Growth rate)

= (250*(1+3%)) / (15% - 3%)

= 2145.833333

So cash flow in year 4 = 250 + 2145.83 = 2395.83

Now, we will calculate the NPV of the cash flows -

NPV = Initial cash outlay + PV of all the cash inflows

PV of cash flow at time n = Cash flow at time n/ ((1+r)^n)

Years	Cash Flows	PV
0	-1700	-1700
1	50	43
2	100	76
3	200	132
4	2395.83	1370
Discount rate	15.00%
NPV	-79.58

The NPV rule says that if the NPV is more than 0, accept the project and if the NPV is less than 0, reject the project.

As we can see that the NPV which we calculated is negative, so we will reject the project.