Question

Now suppose the project has no cash flows in years 1 to 5, has a cash flow of $44,000 in year 6 that then grows at a rate of 2% forever. The discount rate is 10%. What is the value of this project?

1) Less than $375,657.4
2) Equal to $375,657.4
3) More than $375,657.4
4) Unanswered

Answer 1

The value of the project is more than $375,657.4.

Step-by-step explanation:

The value of the project can be calculated by finding the present value of all the cash flows. In this case, there are no cash flows in years 1 to 5, so we only need to consider the cash flow in year 6 and beyond.

To calculate the present value, we use the formula:

PV = CF / (1+r)^n

where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

For this project, the cash flow in year 6 is $44,000 and it grows at a rate of 2% forever. The discount rate is 10%.

Using the formula, the present value of the cash flow in year 6 is:

PV = $44,000 / (1+0.1)^6 = $26,434.02

Since the cash flow grows at 2% forever, we can calculate the present value using the perpetuity formula:

PV = CF / r

where CF is the cash flow and r is the discount rate.

Using the perpetuity formula, the present value of the cash flow starting from year 7 onwards is:

PV = $44,000 / 0.1 = $440,000

Finally, we sum up the present values of the cash flows in year 6 and beyond:

PV = $26,434.02 + $440,000 = $466,434.02

So, the value of this project is more than $375,657.4 (Option 3).