Considering the time value of money is important when evaluating projects with different costs, different cash flows, and different service lives. Discounted cash flow techniques, such as the net present value method, consider the timing and amount of cash flows. To use the net present value method, you will need to know the cash inflows, the cash outflows, and the company’s required rate of return on its investments. The required rate of return becomes the discount rate used in the net present value calculation. For the following examples, it is assumed that cash flows are received at the end of the period.
Managerial Economics Using data for the Cottage Gang and assuming a required rate of return of 12%, the net
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present value is $80,452. It is calculated by discounting the annual net cash flows and salvage value using the 12% discount factors. The Cottage Gang has equal net cash flows of $50,000 ($250,000 cash receipt minus $200,000 operating costs) so the present value of the net cash flows is computed by using the present value of an annuity of 1 for seven periods. Using a 12% discount rate, the factor is 4.5638 and the present value of the net cash flows is $228,190. The salvage value is received only once, at the end of the seven years (the asset’s life), so its present value of $2,262 is computed using the Present Value of 1 table factor for seven periods and 12% discount rate factor of .4523 times the
$5,000 salvage value. The investment of $150,000 does not need to be discounted because it is already in today’s dollars (a factor value of 1.0000). To calculate the net present value (NPV), the investment is subtracted from the present value of the total cash inflows of
$230,452. See the examples that follow. Because the net present value (NPV) is positive, the required rate of return has been met.
Present Value of 1
Capital Budgeting and Risk and
Project Cost $150,000 Cash from Customers (1) $250,000
Operating Costs (2) 200,000 Salvage Value 5,000
Estimated Useful Life 7 years
Minimum Required Rate of Return 12%
Annual Net Cash Flows ($250,000 - $200,000) $50,000
(1) - (2)
Present Value of Cash Flows
Annual Net Cash Flows ($50,000 × 4.5638) $228,190
Salvage Value ($5,000 × .4523) 2,262
Total Present Value of Net Cash Inflows 230,452
Less: Investment Cost (150,000)
Net Present Value $ 80,452
When net cash flows are not all the same, a separate present value calculation must be made for each period’s cash flow. A financial calculator or a spreadsheet can be used to
Period Estimated Annual Net Cash Flow (1) 12% Discount Factor (2) Present Value (1) × (2)
1 $ 44,000 .8929 $ 39,288
2 55,000 .7972 43,846
3 60,000 .7118 42,708
4 57,000 .6355 36,224
5 51,000 .5674 28,937
6 44,000 .5066 22,290
7 39,000 .4523 17,640
Totals $350,000 $230,933
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calculate the present value. Assume the same project information for the Cottage Gang’s investment except for net cash flows, which are summarized with their present value calculations below
The NPV of the project is $83,195, calculated as follows:
Present Value of Cash Flows
Annual Net Cash Flows $230,933
Salvage Value ($5,000 × .4523) 2,26
Total Present Value of Net Cash Inflows 233,195
Less: Investment Cost (150,000)
Net Present Value $ 83,195
The difference between the NPV under the equal cash flows example ($50,000 per year for seven years or $350,000) and the unequal cash flows ($350,000 spread unevenly over seven years) is the timing of the cash flows.
Most companies’ required rate of return is their cost of capital. Cost of capital is the rate at which the company could obtain capital (funds) from its creditors and investors. If there is risk involved when cash flows are estimated into the future, some companies add a risk factor to their cost of capital to compensate for uncertainty in the project and, therefore, in the cash flows.
Most companies have more project proposals than they do funds available for projects.
They also have projects requiring different amounts of capital and with different NPVs. In comparing projects for possible authorization, companies use a profitability index. The index divides the present value of the cash flows by the required investment. For the
Cottage Gang, the profitability index of the project with equal cash flows is 1.54, and the profitability index for the project with unequal cash flows is 1.56.
Present Value of Cash Flows
Capital Budgeting and Risk and Uncertainty Analysis
Profitability Index =
Required Investment Equal Cash Flows = $ 230,452 / $ 150,000 = 1.54, and Unequal Cash Flows = $ 233,195 / $ 150,000 = 1.56 Internal rate of return
The internal rate of return also uses the present value concepts. The internal rate of return (IRR) determines the interest yield of the proposed capital project at which the net present value equals zero, which is where the present value of the net cash inflows equals the investment. If the IRR is greater than the company’s required rate of return, the project may be accepted. To determine the internal rate of return requires two steps. First, the internal rate of return factor is calculated by dividing the proposed capital investment amount by the net annual cash inflow. Then, the factor is found in the Present Value of an Annuity of 1 table using the service life of the project for the number of periods. The discount rate of the factor is the closest to is the internal rate of return. A project for Knightsbridge, Inc., has equal net cash inflows of $50,000 over its seven-year life and a project cost of $200,000. By dividing the cash flows into the project investment cost, the factor of 4.00 ($200,000 ÷ $50,000) is found. The 4.00 is looked up in the Present Value of an Annuity of 1 table on the seven-period line (it has a seven-year life), and the internal rate of return of 16% is determined.