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?
The company will undertake the training program if NPV is positive and reject the project if NPV is negative.
When the cost of capital is 15% , the NPV can be calculated as :
($8,214.41)
NPV is negative , So the company will not accept the training program.
Here no need to consider the marginal tax rate ( which is given as 40%) as all the cash flows are given as after tax basis .
The company will undertake the training program if NPV is positive and reject the project if NPV is negative.
When the cost of capital is 15% , the NPV can be calculated as :
($8,214.41)
NPV is negative , So the company will not accept the training program.
Here no need to consider the marginal tax rate ( which is given as 40%) as all the cash flows are given as after tax basis .
Calculation based on an after-tax basis. We will subtract the taxes from the initial outlay: 75,000-75,000*0.40 = 45,000.
Calculate the Net Present Value:
End of the Year Actual Dollar Benefit PV interest (15%) Present Value(PV)
0 -45,000 1 -45,000
1 7,500 .86957 6521.775
2 7,500 .75614 5671.05
3 7,500 .65752 4931.40
4 7,500 .57175 4288.125
5 7,500 .49718 3728.85
6 7,500 .43233 3242.475
7 7,500 .37594 2819.55
8 7,500 .3269 2451.75
9 7,500 .28426 2131.95
10 7,500 .24718 1853.85
11 7,500 .21494 4836.15
12. 7,500 .18691 4205.475
13 7,500 .16253 3656.925
14 7,500 .14133 3179.925
15 7,500 .12289 2765.025
16 7,500 .10686 2404.35
17 7,500 .09293 2090.925
18 7,500 .0808 1818
19 7,500 .07026 1580.85
20 7,500 .0611 1374.75
NPV= 20553.15
PV= Actual dollar benefit times INF.
Since NPV is positive, so the project should be accepted
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.
Here's how you can calculate the NPV of the training program:
Step 1: Calculate the present value of cash inflows
- For Years 1-10: Calculate the present value of $7,500 per year using the formula 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.
- PV1-10 = $7,500 / (1 + 0.15)^1 + $7,500 / (1 + 0.15)^2 + ... + $7,500 / (1 + 0.15)^10
- For Years 11-20: Calculate the present value of $22,500 per year using the same formula.
- PV11-20 = $22,500 / (1 + 0.15)^11 + $22,500 / (1 + 0.15)^12 + ... + $22,500 / (1 + 0.15)^20
Step 2: Calculate the present value of the initial investment
- Since the entire $75,000 is paid at time zero, there is no discounting needed.
- PV0 = $75,000
Step 3: Calculate the net present value (NPV)
- NPV is the difference between the present value of cash inflows and the present value of the initial investment.
- NPV = PV1-10 + PV11-20 - PV0
Step 4: Consider the tax impact
- The returns from the training program mentioned are on an after-tax basis, so we need to adjust for taxes.
- Multiply the cash flows by (1 - tax rate) to calculate the after-tax cash flows.
- After-tax cash flows for Years 1-10: $7,500 * (1 - 0.40) = $4,500 per year
- After-tax cash flows for Years 11-20: $22,500 * (1 - 0.40) = $13,500 per year
Step 5: Recalculate the present value of cash inflows using the adjusted after-tax cash flows and repeat Step 3 and Step 4.
Once you have calculated the NPV, if the NPV is positive, it means that the present value of cash inflows is greater than the initial investment, indicating that the firm should undertake the training program. If the NPV is negative, it means that the present value of cash inflows is less than the initial investment, indicating that the firm should not undertake the training program.