CAPITAL INVESTMENT
Capital Investment (Capital Budgeting) involves the allocation of large amounts of resources in long-term investments.
Examples:
1. Replacement of Equipment
2. Expansion of Existing Product Lines
3. Development of New Product Lines
4. Intangibles:
· Research & Development
· Patents
· Advertising campaigns
Success:
Texas Instruments - semiconductor in 1950s and 1960s; microchip in 1970s
Microsoft - Bought Quick and Dirty Operating System for $50,000
Failure:
BP oil company Deep Horizon oil well – estimated loss is $40 billion
Ford Edsel (Loss of $250 million in 1957-59, or approximately $1.85 billion today)
Once the Investment is made, it is almost impossible to back out. Unlike a surplus of inventory which can be quickly corrected, an unutilized refinery just sits vacant.
The firm's existence is a series of capital investment decisions that are necessary for the company to grow, remain competitive, etc.
Basic Concept: Accept all projects that yield a return that exceeds the cost of financing the project. Thus, if we are maximizing stockholder wealth, we would accept Projects A – D and reject the remainder:
Numerous investment alternatives exist and we want to identify those that add value to the firm. We need a means of ranking the projects from best to worst in order to select those that are most valuable to the firm; i.e., a means of evaluating and ranking proposals.
The primary concern in the investment decision is that of cash flows that occur:
· Incremental Revenues
· Incremental Costs
· Taxes
· Depreciation considerations
· Investment in Working Capital
· Cost Savings
Any cash inflow or outflow.
EVALUATION TECHNIQUES
A. Payback Period – How long it takes to recover the initial investment
Consider the net, after-tax cash flows of the following two investment alternatives:
Proj. A Proj. B
------
Year 0 (3,000) (3,000)
Year 1 1,000 2,000
Year 2 2,000 1,000
Year 3 3,000 4,000
Payback = 2 years Payback = 2 years
Both projects have a payback of two years, so the payback method indicates that the two projects are equally desirable.
Problems:
1) Ignores the Time Value of Money
2) Ignores cash flows beyond the payback period
Project B returns $1,000 a year earlier than Project A and also returns an additional $1,000 in the last year.
Present Value (Discounted) Payback, which utilizes the present value of each year's cash flow, overcomes the first problem, but not the second.
B) Present Value (Discounted) Payback
Proj. A Proj. B
------
Cash Flow PV of CF Cash Flow PV of CF
Year 0 (3,000) (3,000) (3,000) (3,000)
Year 1 1,100 1,000 2,200 2,000
Year 2 2,420 2,000 1,210 1,000
Year 3 3,000 2,254 4,000 3,005
PV Payback = 2 years PV Payback = 2 years
C) Net Present Value (NPV)
We need a methodology that takes into account all of the cash flows as well as the time value of money. Net Present Value is one such technique:
NPV = PV of Cash Inflows PV of Cash Outflows
Required Rate of Return = 10%
0 1 2 3
(4,000) 1,000 2,000 3,000
0.9091
909
0.8264
1,653
0.7513
2,254
NPV @ 10% = 816
To calculate the NPV on an HP 10B financial calculator,
Clear All
Enter 4000 and change the sign (+/-) and press CFj
Enter 1000 and press CFj again
Enter 2000 and press CFj
Enter 3000 and press CFj
Enter 10 and press I/YR
Press the shift key and press NPV
NPV represents the increase in the value of the firm that occurs by accepting the project. In other words, it represents the amount by which the value of the project exceeds its cost.
Proof:
Year 0 Investment 4,000 Cash Flow Year 1 1,000
Return of Investment (600) Less: Interest (400) (10%*$4,000)
-- --
Year 1 Investment 3,400 Return of Investment 600
Return of Investment (1,660)
-- Cash Flow Year 2 2,000
Year 2 Investment 1,740 Less: Interest (340) (10%*$3,400)
Return of Investment (2,826) ---
-- Return of Investment 1,660
Surplus Return (1,086)
PVIF10%,3 0.7513 Cash Flow Year 3 3,000
--- Less: Interest (174) (10%*$1,740)
Present Value 816 --
Return of Investment 2,826
The problem with NPV is that there is no consideration of cost, or what is referred to as size disparity.
Proj. A Proj. B
--
Present Value of Inflows 1,050 125
Cost (1,000) (100)
-
Net Present Value 50 25
If these are mutually exclusive projects (i.e., choose one or the other, but not both), the NPV criterion says to choose Project A. While Project A increases the value of the firm by twice the amount of Project B, it costs ten times as much. The NPV does not indicate how efficiently money has been invested.
Capital Rationing - the allocation of a scarce resource, in this case money.
D) Profitability Index (PI) (or Benefit-Cost Ratio) - a measure of efficiency of investment
PIA = 1.05 PIB = 1.25
The interpretation of PI is that of the amount of money in today's dollar terms that you get per dollar of investment. This indicates how efficiently you have invested money.
E) Internal Rate of Return (IRR)
Another measure of the efficiency of investment is the Internal Rate of Return. When someone asks what rate of return an investment is earning, they mean the Internal Rate of Return. The IRR can be defined as
PV of Inflows @ IRR = PV of Outflows @ IRR
or
NPV @ IRR = 0
This is the actual rate of interest that is being earned on the investment. While the present value and annuity tables can be used in certain cases, the more general situation of uneven cash flows requires that the IRR be found by trial and error. From the previous example, it is clear that more than 10% is being earned, since the NPV is $816.
Calculating the IRR on the HP 10B is almost identical to calculating the NPV:
Clear All
Enter 4000 and change the sign (+/-) and press CFj
Enter 1000 and press CFj again
Enter 2000 and press CFj
Enter 3000 and press CFj
Press the shift key and press IRR/YR
The Internal Rate of Return is 19.44%
Year 0 Investment 4,000 Cash Flow -- Year 1 1,000
Return of Investment (222) Less: Interest (778) (19.44% * $4,000)
Year 1 Investment 3,778 Return of Investment 222
Return of Investment (1,266)
Year 2 Investment 2,512 Cash Flow -- Year 2 2,000
Return of Investment 2,512 Less: Interest (734) (19.44% * $3,778)
Surplus Return 0 Return of Investment 1,266
Cash Flow -- Year 3 3,000
Less: Interest (488) (19.44% * $2,518)
Return of Investment 2,512
Conflicts in Rankings
Year 0 Year 1 Year 2 Year 3 NPV @ 10% PI @ 10% IRR
Project A (15,000) 10,000 10,000 0 2,355 1.16 21.5%
Project B (48,000) 30,000 30,000 0 4,066 1.08 16.3%
Which project is better? The major difference is the costs of the projects.
Year 0 Year 1 Year 2 Year 3 NPV @ 10% PI @ 10% IRR
Project C (10,000) 8,000 5,600 0 1,901 1.19 24.9%
Project D (10,000) 0 0 17,000 2,772 1.28 19.3%
Which project is better? The major difference is the timing of the cash flows.
Note that all three measures agree as to whether a project is acceptable or not. The conflict is in the ranking of the investment proposals.
Note also that the Profitability Index, a measure of efficiency of investment, does not always agree with IRR in terms of which is the most efficient use of funds.
III) THE REINVESTMENT ASSUMPTION
Consider the following two projects, their NPVs, PIs, and IRRs.
Project X
Year 0 Year 1 Year 2 Year 3
Cash Flows (886) 100 100 1,100
NPV @ 10% = 114
PI @ 10% = 1.13
IRR = 15.0%
Project Y
Year 0 Year 1 Year 2 Year 3
Cash Flows (886) 900 150 55
NPV @ 10% = 97
PI @ 10% = 1.11
IRR = 20.0%
Most academicians claim that the conflict is a consequence of the reinvestment assumption. Net Present Value and Profitability Index assume reinvestment at the discount rate. Internal Rate of Return can be thought of as a special case of NPV (when it equals zero). Hence, it assumes reinvestment at the IRR.
Realistically, investments are made to maximize future wealth. Even the Capital Asset Pricing Model's original derivation assumed that investors were terminal wealth maximizers (it was a single period model.) Present value (discounted cash flow techniques) are generally preferred in practice since we know the value of a dollar today. The reinvestment assumption is invoked in order to make the future value (terminal value) rankings consistent with the present value rankings. To see this, let's reinvest the cash flows of Projects X and Y at the discount rate of 10%.
Project X
Year 0 Year 1 Year 2 Year 3
Cash Flows (886) 100 100 1,100
1.21
121
1.10
110
Terminal Value = 1,331
Project Y
Year 0 Year 1 Year 2 Year 3
Cash Flows (886) 900 150 55
1.21
1,089
1.10
165
Terminal Value = 1,309
Since the costs are the same, the terminal values are both relative to the same size of investment. The $1,331 terminal value of Project X represents a 14.53% rate of return on an investment of $886 over three years while the $1,309 terminal value of Project Y is a 13.89% return on the initial investment. The difference in the terminal values of $22 has a present value of $17 which is the same as the difference in NPVs of the two projects (114 97 = 17). Thus, the terminal value rankings are consistent with the NPV and PI rankings that indicate Project X is superior to Project Y. Similarly, if the cash flows of each project are reinvested at their respective IRRs, the following is obtained:
Project X
Year 0 Year 1 Year 2 Year 3
Cash Flows (886) 100 100 1,100
1.3223
132
1.1500
115
Terminal Value = 1,347
Project Y
Year 0 Year 1 Year 2 Year 3
Cash Flows (886) 900 150 55
1.4400
1,296
1.2000
180
Terminal Value = 1,531
Again, since the costs are identical, it is clear that Project Y is better since it maximizes future wealth, and agrees with the rankings of the IRRs. Moreover, the terminal value of $1,347 of Project X represents a 15% return on the cost of the project, while the $1,531 terminal value of Project Y is a 20% return on the investment in Project Y. Of course, why the $100 from Project X in the first year could only be reinvested to earn 15% but the $900 from Project Y in the first year could be reinvested to earn 20% seems inconsistent.
IV. SEPARATION OF FINANCING FROM INVESTMENT
The Separation Theorem allows for the evaluation of an investment without regard to how it is financed as long as the required rate of return reflects the financing via the use of the Average Cost of Capital.
Assume the following:
Cost of Debt = 10%
Tax Rate = 40%
Aftertax Cost of Debt = 6%
Cost of Equity = 14%
Percent Debt Financing = 50%
Percent Equity Financing = 50%
Average Cost of Capital = Cost of Debt * (Percent Debt Financing) +
Cost of Equity * (Percent Equity Financing)
= 10% * (1-.4) * (.5) + 14% * (.5)
= 6% * (.5) + 14% * (.5)
= 10%
A) Project Cash Flows
Year 0 Year 1 Year 2 Year 3
Investment Cost (4,000)
Revenues 3,000 3,000 4,792
Costs (800) (800) (1,000)
Taxable Inc. 2,200 2,200 3,792
Taxes (40%) (880) (880) (1,517)
Net Cash Flows (4,000) 1,320 1,320 2,275
NPV @ 10% = 0
A NPV of zero indicates that both lenders and stockholders are earning their respective required rates of return as well as getting their investment back (with no surplus). Consider the financing explicitly with the payment of interest and a repayment of principal as follows:
B) Equity Cash Flows
Year 0 Year 1 Year 2 Year 3
Investment Cost (4,000)
Revenues 3,000 3,000 4,792
Costs (800) (800) (1,000)
Operating Inc. 2,200 2,200 3,792
Interest Expense (200) (154) (103)
Taxable Income 2,000 2,046 3,689
Taxes (40%) (800) (818) (1,475)
Net Income 1,200 1,228 2,213
Debt Payment 2,000 (460) (506) (1,034)
Equity Cash Flow (2,000) 740 722 1,179
IRR = 14%
Return of Principal Calculations:
Year 1 Cash Flow 2,200
Interest on Debt (200) (10% * 2,000)
Shareholder Rate of Return (280) (14% * 2,000)
Taxes (800)
Return of Principal 920
Return of Principal to Lenders = 460 (50%)
Return of Principal to Stockholders = 460 (50%)
Beg. Debt Balance Yr. 1: 2,000 Beg. Equity Balance Yr. 1 2,000
Debt Repayment (460) Equity Repayment (460)
Ending Debt Balance Yr. 1: 1,540 End. Equity Balance Yr. 1 1,540
Year 2 Cash Flow 2,200
Interest on Debt (154) (10% * 1,540)
Shareholder Rate of Return (216) (14% * 1,540)
Taxes (818)
Return of Principal 1,012
Return of Principal to Lenders = 506 (50%)
Return of Principal to Stockholders = 506 (50%)
Beg. Debt Balance Yr. 2: 1,540 Beg. Equity Balance Yr. 2 1,540
Debt Repayment (506) Equity Repayment (506)
Ending Debt Balance Yr. 2 1,034 End. Equity Balance Yr. 2 1,034
Year 3 Cash Flow 3,792
Interest on Debt (103) (10% * 1,034)
Shareholder Rate of Return (145) (14% * 1,034)
Taxes (1,475)
Return of Principal 2,068
Return of Principal to Lenders = 1,034 (50%)
Return of Principal to Stockholders = 1,034 (50%)
Beg. Debt Balance Yr. 3: 1,034 Beg. Equity Balance Yr. 3 1,034
Debt Repayment (1,034) Equity Repayment (1,034)
Ending Debt Balance Yr. 3: 0 End. Equity Balance Yr. 3 0
Cash Flows To Lenders Year 0 Year 1 Year 2 Year 3
Loan (2,000)
Interest 200 154 103
Principal 460 506 1,034
Net Cash Flows (2,000) 660 660 1,138
IRR = 10%
Cash Flows To Stockholders Year 0 Year 1 Year 2 Year 3