A company is planning to invest $75,000 (before taxes) in a personnel training program. The $75000 outlay will be charged off as an expense by the firm this year (Year 0). The returns estimated from the program in the forms of greater productivity and less employee turnover are as follows (on an after-tax basis):


Years 1-10: $7,500 per year
Years 11-20: $22,500 per year

The company has estimated its cost of capital to be 15%. Assume that the entire $75,000 is paid at time zero (the beginning of the project). The marginal tax rate for the firm is 40%. Based on the net present value criterion, should the firm undertake the training program?

To determine whether the firm should undertake the training program based on the net present value (NPV) criterion, we need to calculate the present value of the cash flows from the program and compare it to the initial investment.

To calculate the present value of the cash flows, we need to discount each cash flow back to Year 0 using the cost of capital. The formula to calculate the present value is:

PV = CF / (1 + r)^n

Where PV is the present value, CF is the cash flow, r is the discount rate (cost of capital), and n is the number of years in the future the cash flow occurs.

In this case, we have two streams of cash flows - one for years 1-10 and another for years 11-20. We'll calculate the present value for each stream separately.

For the first stream (years 1-10):

PV1 = $7,500 / (1 + 0.15)^1 + $7,500 / (1 + 0.15)^2 + ... + $7,500 / (1 + 0.15)^10

Using the formula for the present value of an annuity, we can simplify this calculation:

PV1 = $7,500 * [(1 - (1 + 0.15)^-10) / 0.15] * (1 - 0.4)

Calculating this value, we find PV1 ≈ $46,451.40.

For the second stream (years 11-20):

PV2 = $22,500 * [(1 - (1 + 0.15)^-10) / 0.15] * (1 - 0.4) / (1 + 0.15)^10

Calculating this value, we find PV2 ≈ $140,936.86.

Now, we can calculate the total present value by summing up the present values of both streams:

Total PV = PV1 + PV2

Total PV ≈ $46,451.40 + $140,936.86 ≈ $187,388.26

The net present value (NPV) is calculated by subtracting the initial investment from the total present value:

NPV = Total PV - Initial Investment

NPV ≈ $187,388.26 - $75,000 ≈ $112,388.26

Since the NPV is positive ($112,388.26), the firm should undertake the training program as it is expected to generate additional value.