When comparing benchmarking alternatives, it is often necessary to take into consideration the fact that cash is received and/or disbursed in different time periods for each of the alternatives. Cash received in the future is not as valuable as cash received today because cash received today can be reinvested and earn a return. In order to compare the current value of cash received or disbursed in different periods, it is necessary to convert a future dollar value to its present value.
For example, the present value of $1100 received a year from now is $1000 if money can be invested at 10%. The alternative way to view this is to note that the future value of $1000 invested for one year at 10% is equal to 1000 times 1.10 or $1100.
The following table can be used to determine the present value of a future cash flow depending upon the discount rate and the number of years from the present that the investment is made. To relate to the discussion above, note that the Present Value Factor for one year at 10% is .9091. Therefore, the present value of $1100 received a year from now is $1000, i.e., $1100 times .9091.
A typical capital project of benchmark alternative evaluation is discussed in the following pages. The projected net income after tax as well as a summary of the investments made in the project, the after-tax salvage value, and the cash flow associated with the project are indicated.
The assumptions used to generate the net income are indicated below the projection. Note the separation of fixed and variable cost and the relationship between specific assumptions and the level of capacity utilization. In this case, the investment is assumed to occur at the end of the first year. Also, there is no increase in working capital associated with the construction of the plant.
The cash flow can be determined in one of two ways: (a) it is equal to the net income after tax plus depreciation or (b) it is equal to revenue minus operating expenses minus taxes. The net present value is indicated for several discount rates (10 to 40%). The net present value at 10% is determined, for example, as in Table 3.2.
End of Year | Cash Flow | Present Value Factor | Present Value |
---|---|---|---|
1 | -1,000,000 | 0.9091 | -909,091 |
2 | 246,680 | 0.8264 | 203,868 |
3 | 597,764 | 0.7513 | 449,109 |
4 | 1,008,814 | 0.6830 | 689,034 |
Total Net Present Value | 432,919 |
Present Value Factors | ||||
---|---|---|---|---|
Discount Rate | ||||
Year | 10% | 20% | 30% | 40% |
1 | 0.9091 | 0.8333 | 0.7692 | 0.7143 |
2 | 0.8264 | 0.6944 | 0.5917 | 0.5102 |
3 | 0.7513 | 0.5787 | 0.4552 | 0.3644 |
4 | 0.6830 | 0.4823 | 0.3501 | 0.2603 |
5 | 0.6209 | 0.4019 | 0.2693 | 0.1859 |
6 | 0.5645 | 0.3349 | 0.2072 | 0.1328 |
7 | 0.5132 | 0.2791 | 0.1594 | 0.0949 |
8 | 0.4665 | 0.2326 | 0.1226 | 0.0678 |
9 | 0.4241 | 0.1938 | 0.0943 | 0.0484 |
10 | 0.3822 | 0.1615 | 0.0725 | 0.0346 |
If the company cost of capital is 15%, then this project would be acceptable because the net present value is positive at that discount rate. A similar analysis can be used to determine a breakeven product price ” see Table 3.3.
2001 | 2002 | 2003 | 2004 | |
---|---|---|---|---|
Sales (units) | 21,000 | 49,000 | 66,500 | |
Unit price | 38.00 | 40.66 | 45.54 | |
Revenue | 798,000 | 1,992,340 | 3,028,357 | |
Operating expense | 420,200 | 1,029,400 | 1,397,000 | |
Depreciation | 50,000 | 50,000 | 50,000 | |
Net income before tax | 327,800 | 912,940 | 1,581,357 | |
Tax | 131,120 | 365,176 | 632,543 | |
Net income after tax | 196,680 | 547,764 | 948,814 | |
Investment | 1,000,000 | |||
Salvage value | 10,000 | |||
Cash flow | -1,000,000 | 246,680 | 597,764 | 1,008,814 |
Interest rate (%) | 10 | 20 | 30 | 40 |
Net present value | 432,919 | 170,404 | 2,030 | -107,982 |
Assumptions | ||||
Plant capacity (units) | 70,000 | |||
Unit price ” start | 38.00 | |||
Tax rate (%) | 40 | |||
Depreciation (%) | 5 | |||
Capacity utilization (%) | 30 | 70 | 95 | |
Price increase (%) | 7 | 7 | 12 |
Operating Expense | ||
---|---|---|
Units | Fixed | Variable |
10,000 | 200 | 20.00 |
20,000 | 200 | 20.00 |
30,000 | 200 | 20.00 |
40,000 | 400 | 21.00 |
50,000 | 400 | 21.00 |
60,000 | 500 | 21.00 |
70,000 | 500 | 21.00 |