CAPITAL BUDGETING TECHNIQUES CHAPTER 21

Capital Budgeting Techniques PAY-BACK AVERAGE RATE OF RETURN DISCOUNTED CASH FLOW

PAYBACK FORMULA INVESTMENT PAYBACK = CASH FLOW

PAYBACK EXAMPLE Investment = $100,000 Cash Flows: Year 1 $ 5,000

SOLUTION TO PAYBACK Unrecovered Investment Year 1 5,000 95,000 Year 2 20,000 75,000 Year 3 35,000 40,000 Year 4 60,000 -20,000 Year 5 45,000 -65,000 The payback is: 3 2/3 years

PAYBACK EXERCISE INVESTMENT OF $250,000 CASH FLOWS: YEAR 1 $-10,000 CALCULATE THE PAYBACK

SOLUTION TO EXERCISE Unrecovered Investment Year 1 -10,000 260,000 Year 2 60,000 200,000 Year 3 90,000 110,000 Year 4 120,000 -10,000 Year 5 100,000 -110,000 Year 6 -20,000 - 90,000 The payback is:3 years and 11 months

PAYBACK The payback method estimates the length of time it takes to recover the investment Payback is widely used. It is simple to understand and apply HOWEVER It lacks economic substance, it disregards The time value of money Cash flows after the payback period

AVERAGE RATE OF RETURN FORMULA Average Positive Cash Flow R of R = Investment

RATE OF RETURN EXAMPLE Investment = $100,000 Cash Flows: Year 1 $ 5,000 Year 2 20,000 Year 3 35,000 Year 4 60,000 Year 5 45,000

RATE OF RETURN SOLUTION Profit 165,000 – 100,000 = $65,000 Average Profit $65,000 / 5 = $13,000 per year Average Rate of Return 13,000 / 100,000 = 13%

RATE OF RETURN EXERCISE INVESTMENT OF $250,000 CASH FLOWS: YEAR 1 $ -10,000 YEAR 2 60,000 YEAR 3 90,000 YEAR 4 120,000 YEAR 5 100,000 YEAR 6 -20,000 CALCULATE THE RATE OF RETURN

SOLUTION Profit = 340,000 - 250,000 = $ 90,000 Average profit = 340,000 - 250,000 = $ 90,000 Average profit = $90,000 / 6 = $15,000 Rate of Return = $15,000 / $250,000 = 6%

AVERAGE RATE OF RETURN The average rate of return estimates the average rate of return over the life of the project It is simple to apply Considers the cash flow after payback HOWEVER Like payback, it ignores the time value of money

DISCOUNTED CASH FLOW There are two discounted cash flow techniques Internal Rate of Return - The economic (real) rate of return on the investment Net Present Value - The net cash value after charging a capital cost

FUTURE AMOUNT OF ONE INVEST $1,000 IN THE BANK AT 10% YEAR O INVESTMENT IS $1,000 YEAR 1 INVESTMENT IS $1,100 YEAR 2 INVESTMENT IS $1,210 YEAR 3 INVESTMENT IS $1,331

FORMULA FOR THE FUTURE AMOUNT OF ONE AMOUNT = INVESTMENT ( 1 + r ) n Where r = rate of return n = number of years (periods) AMOUNT is the future value INVESTMENT is the amount put in initially, or the PRESENT VALUE

PRESENT VALUE FORMULA FOR SINGLE AMOUNT Simple math on the amount formula yields Present Value = AMOUNT / ( 1 + r ) n

APPLY FORMULA Present value = $1,331 / (1.00 + 0.10) 3 = 1,331 / (1.1) 3 = 1,331 / 1.331 = $1,000

WHAT TO DO WHEN WE HAVE MANY CASH FLOWS?

NET PRESENT VALUE FORMULA Where: r = minimum acceptable rate of return and = cash flow in period n

DETERMINING THE INTERNAL RATE OF RETURN The Internal Rate of Return is that rate which yields a Net Present Value of zero. If cash flows are not uniform, then the solution is found by trial-and-error.

PROBLEMS WITH THE INTERNAL RATE OF RETURN There are two majors problems with the Internal Rate of Return method: Mathematically, there can be more than one internal rate of return, one for each change in direction of cash flow and The important thing is not the rate of return but the amount of money earned.

NPV EXAMPLE Investment = $100,000 Cash Flows: Year 1 $ 5,000 Discount Rate of 9%

SOLUTION TO NPV EXAMPLE Cash Flows PV factor PV Investment = $-100,000 1.00 $ -100,000 Year 1 5,000 .917 4,585 Year 2 20,000 .842 16,840 Year 3 35,000 .772 27,020 Year 4 60,000 .708 42,480 Year 5 45,000 .649 29,205 Net Present Value $ 20,130

NPV EXERCISE CALCULATE THE NET PRESENT VALUE WITH A 10% DISCOUNT RATE INVESTMENT OF $250,000 CASH FLOWS: YEAR 1 $ -10,000 YEAR 2 60,000 YEAR 3 90,000 YEAR 4 120,000 YEAR 5 100,000 YEAR 6 -20,000 CALCULATE THE NET PRESENT VALUE WITH A 10% DISCOUNT RATE

SOLUTION TO NPV EXERCISE Cash Flows PV factor PV Investment $ -250,000 1.000 -250,000 YEAR 1 -10,000 .909 -9,090 YEAR 2 60,000 .826 49,560 YEAR 3 90,000 .751 67,590 YEAR 4 120,000 .683 81,960 YEAR 5 100,000 .621 62,100 YEAR 6 -20,000 .564 -11,280 NET PRESENT VALUE - 9,160

NET PRESENT VALUE The Net Present Value method resolves all of the problems inherent in the other methods. It considers all flows, It considers the time value of money, There is a unique solution, and It solves for profit in excess of capital costs

APPLICATION OF NPV Often the NPV method is applied without regard to the relative risk of the cash flows. Only one discount rate is applied to all cash flow estimates. This approach should, inadvertently, lead to higher risk opportunities.

ADJUSTING FOR RISK There are two methods used to adjust for risk: Adjust the cash flow or Adjust the discount rate. The cash flow can be adjusted to the Certainty Equivalent (CE) cash flow. The Discount Rate can be adjusted directly. Conventionally, there is a direct relationship between the discount rate and risk.

Estimating the Certainty Equivalent Estimate the Cash Flow in a period: e.g., $ 1,000,000 in year 3 Evaluate the risk of that cash flow Estimate the amount you would be willing to receive, with certainty, instead of the $1,000,000 e.g., $ 850,000 Discount these CEs at the risk-free rate of return

ADJUSTING THE DISCOUNT RATE Estimate the cash flow in a period: e.g., $1,000,000 in year 3 Determine the minimum rate of return that would be acceptable for the particular cash flow.

RELATIONSHIP OF RISK TO DISCOUNT RATE

RELATIONSHIP OF DISCOUNT RATE TO NET PRESENT VALUE NPV

CONFLICT OF NEGATIVE CASH FLOWS If cash flows are negative, investors should prefer lower net present values. Lower net present values result from higher discount rates. THEREFORE

THERE SHOULD BE AN INVERSE RELATIONSHIP OF RATE OF RETURN TO RISK. THAT IS, THE GREATER THE RISK, THE LOWER THE DISCOUNT RATE.

GRAPHICALLY Discount Rate 0 RISK

PROPOSED SOLUTION Group cash flows according to the activities that drive the cash flows. If the net cash flow is positive, discount in the conventional method, i.e., the greater the risk, the greater the discount rate. If the net cash flow is negative, adjust the discount rate inversely to risk.

WHAT METHODS ARE GENERALLY USED? Studies indicate that the payback method is widely used, probably the most used. Net present value, without adjusting for risk, is the second most common method. Many companies use a combination of these two methods. However, I suspect that the MOST commonly used method is:

I WANT IT

IMPACT OF TAXES ONE OF THE NICE ASPECTS OF CAPITAL BUDGETING IS THAT YOU ARE CONCERNED ONLY WITH CASH FLOW. TAXES ARE A CASH OUT-FLOW, SO, REDUCE THE CASH FLOW FOR THE TAX EFFECTS

DEPRECIATION DEPRECIATION IS A TAX DEDUCTION, THUS IT MAY BE A REDUCTION OF CASH OUTFLOW. FOR ANALYTICAL PURPOSES, THE TAX EFFECT OF DEPRECIATION CAN BE TREATED AS A CASH INFLOW, BUT YOU SHOULD KNOW THAT IT IS NOT A CASH INFLOW.

EXAMPLE NET CASH FLOW FROM OPERATIONS, DISREGARDING TAXES, WAS: YEAR 1 $13,000 YEAR 2 $20,000 YEAR 3 $30,000 YEAR 4 $20,000 YEAR 5 $13,000 ASSET COST $60,000 WITH A 5 YEAR LIFE. USE STRAIGHT-LINE DEPRECIATION TAX RATE IS 40%

NET CASH FLOWS OPER CF DEPR TI TAX NET CF 13,000 12,000 1,000 400 12,600 20,000 8,000 3,200 16,800 30,000 18,000 7,200 22,800