Question

1. Your company is considering purchasing a new system that costs $200,500. This cost will be depreciated straight-line to zero over the project's five-year life, at the end of which the system is expected to be sold for $35,000 cash. The system will save the firm $110,400 per year in pretax operating costs. What is the after-tax cost saving per year associated with the new system? The tax rate is 21%.

A. $40,100

B. $23,184

C. $87,216

D. $110,400

2. Use the information from the previous question, what is the annual depreciation tax shield?

A. $31,679

B. $40,100

C. $42,105

D. $8,421

3. Use the information from the previous question, what is the net present value of this project if the discount rate is 12 percent?

A. $164,110

B. $119,200

C. $144,249

D. $159,939

4. Use the information from the previous question, what is the internal rate of return for this project?

A. 38.26 percent

B. 39.79 percent

C. 40.18 percent

D. 36.25 percent

Answer 1

(1)- After-tax cost saving per year associated with the new system

After-tax cost saving per year = Pre-tax cost savings x (1 – Tax Rate)

= $110,400 x (1 – 0.21)

= $110,400 x 0.79

= $87,216

(2)-Annual depreciation tax shield

Annual depreciation tax shield = Annual Depreciation x Tax Rate

= [$200,500 / 5 Years] x 0.21

= $40,100 x 0.21

= $8,421

(3)-Net present value of this project

Annual cash flow = After-tax cost savings per year + Depreciation tax shield

= $87,216 + $8,421

= $95,637 per year

Year 1 – 4 Cash Flow = $95,637

Year 5 cash flow = Annual cash flow + Salvage Value after-tax

= $95,637 + [$35,000 x (1 – 0.21)]

= $95,637 + $27,650

= $123,287

Year	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	95,637	0.89286	85,390
2	95,637	0.79719	76,241
3	95,637	0.71178	68,073
4	95,637	0.63552	60,779
5	1,23,287	0.56743	69,956
TOTAL			3,60,439

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $3,60,439 - $200,500

= $159,939

“Net Present Value (NPV) = $159,939”

(4)-Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 39% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 39%	Present Value of Cash Flow ($)
1	95,637	0.71942	68,804
2	95,637	0.51757	49,499
3	95,637	0.37235	35,611
4	95,637	0.26788	25,619
5	1,23,287	0.19272	23,760
TOTAL			2,03,292

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $2,03,292 - $200,500

= $2,792

Step – 2, NPV at 39% is positive, Calculate the NPV again at a higher discount rate, Say 40% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 40%	Present Value of Cash Flow ($)
1	95,637	0.71429	68,312
2	95,637	0.51020	48,794
3	95,637	0.36443	34,853
4	95,637	0.26031	24,895
5	1,23,287	0.18593	22,923
TOTAL			1,99,778

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $1,99,778 - $200,500

= -$722 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.39 + [$2,792 x (0.40 – 0.39)]

              $2,792 – (-$722)

= 0.39 + [$27.92 / $3,514.41]

= 0.39 + 0.0079

= 0.3979 or

= 39.79%

“Internal Rate of Return (IRR) for the Project = B. 39.79 percent”

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.