Farm Management

Chapter 17 Investment Analysis

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Chapter Outline

• • • •

Time Value of Money Investment Analysis Financial Feasibility Income Taxes, Inflation, and Risk

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Chapter Objectives

1. Explain the time value of money and its use 2. Illustrate the process of compounding 3. Demonstrate the process of discounting 4. Discuss the payback period, simple rate of return, net present value and internal rate of return 5. Show how to apply these concepts 6. Explain how income taxes, inflation, and risk affect investment analysis

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Time Value of Money

A dollar today is preferred to a dollar in the future:

1. The dollar could be invested to earn interest 2.

If dollar is spent on consumption, we’d prefer to get the enjoyment now 3. Risk is also a factor as unforeseen circumstances could prevent us from getting the dollar 4. Inflation may diminish the value of the dollar over time

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Present Value and Future Value

• Present Value (PV): the number of dollars available or invested at the current time or the current value of some amount to be received in the future • Future Value (FV): the amount to be received at some future time or the amount a present value will be worth at some future date when invested at a given interest rate © Mcgraw-Hill Companies, 2008

• • • •

More Terms

Payment (PMT): number of dollars to be paid or received in a time period Interest Rate (

i

): also called the discount rate



the interest rate used to find present and future values, often equal to opportunity cost of capital Time Periods ( n ): the number of time periods used to compute present and future values Annuity: a term used to describe a series of periodic payments

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Table 17-1 Future Value of $1,000

Year 1 2 3 Value at beginning of year 1000.00

1080.00

1166.40

Interest rate (%) 8 8 8 Interest earned ($) 80.00

86.40

93.31

Value at end of year ($) 1080.00

1166.40

1259.71

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Figure 17-1 Illustration of the concept of future value for a present value and for an annuity

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Figure 17-2 Relation between compounding and discounting

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Computing Future Value

FV = PV ( 1 +

i

)

n

FV = $1,000 ( 1 + 0.08 )3 = $1,259.70

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Future Value of an Annuity

FV = PMT



( 1

+

i

)n



1

i

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Present Value

PV = FV (1

+

i

)n or FV



1 (1

+

i

)n

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Present Value of an Annuity

PV = PMT



1



( 1

+

i

)-n

i

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Figure 17-3 Illustration of the concept of present value for a future value and for an annuity

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Table 17-2 Value of an Annuity

Year 1 2 3 Amount ($) 1,000.00

1,000.00

1,000.00

Present value factor 0.92593

0.85734

0.79383

Total Present value ($) 925.93

857.34

793.83

2,577.10

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Investment Analysis

• • • • •

Investment analysis, also called capital budgeting, involves determining profitability of an investment Initial cost: investment actual total expenditure for the Net cash revenues: cash expenses Terminal value: value cash receipts minus usually the same as salvage Discount rate: opportunity cost of capital

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Payback Period

The payback period is the number of years it would take an investment to return its original cost. If net cash revenues are constant each year, the payback period (P) is: C P = E where C is original cost and E is the expected annual net cash revenue © Mcgraw-Hill Companies, 2008

Table 17-3 Net Cash Revenues for Two $10,000 Investments

Total cash revenues Less initial investment Net Cash Revenues Average net revenue/yr Year 1 2 3 4 5 Net revenues ($) Investment A Investment B 3,000 3,000 3,000 3,000 3,000 15,000 -10,000 5,000 1,000 1,000 2,000 3,000 4,000 6,000 16,000 -10,000 6,000 1,200

no terminal value

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Finding Payback Period

The payback period for investment A is 3.33 years ($10,000 ÷ 3) The payback for investment B is 4 years, which is found by summing the revenues until they reach $10,000.

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Limitations of the Payback Period

The payback period is easy to calculate and identifies the investments with the most immediate cash returns. But it ignores returns after the end of the payback period as well as the timing of cash flows. © Mcgraw-Hill Companies, 2008

Simple Rate of Return

Rate of return =

average annual net revenue initial cost

$1,000 Investment A = $10,000 x 100% = 10% Investment B = $1,200 $10,000 x 100% = 12% © Mcgraw-Hill Companies, 2008

Net Present Value

Net Present Value (NPV) is the sum of the present values of each year’s net cash flow minus the initial investment.

P 1 P 2 NPV = + + + (1 +

i

) 1 (1 +

i )

2 . .

P n (1 +

i

) n  C © Mcgraw-Hill Companies, 2008

Table 17-4 Net Present Value and Internal Rate of Return for Two Investments of $10,000

Year Net cash flow ($) 1 2 3 4 5 3,000 3,000 3,000 3,000 3,000 Investment A Present value factor 0.9090

0.8260

0.7510

0.6830

0.6210

Total Less initial cost Net present value Internal rate of return Present value ($) 2,727 2,478 2,253 2,049 1,863 11,370 10,000 1,370 15.2% Net cash flow ($) Investment B Present value factor Present value ($) 1,000 2,000 3,000 4,000 6,000 0.9090

0.8260

0.7510

0.6830

0.6210

909 1,652 2,253 2,732 3,726 Total Less initial cost Net present value Internal rate of return 11,272 10,000 1,272 13.8%

10% discount rate and no terminal values

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Internal Rate of Return

The internal rate of return (IRR) is the discount rate that would make the NPV of an investment equal to zero.

The IRR is usually calculated by computer or with a financial calculator.

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Annual Equivalent and Capital Recovery

The annual equivalent is an annuity that has the same present value as the investment being analyzed. Investment A: $1,370  Investment B: $1,272  0.2638 = $361.41

0.2638 = $335.55

The amortization factor for 10% and 5 years is 0.2638 (Appendix Table 1) © Mcgraw-Hill Companies, 2008

Financial Feasibility

• The methods presented so far analyze economic profitability • Investors also need to look at financial feasibility • Will the investment generate sufficient cash flow at the right times to meet required cash outflows?

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Table 17-5 Cash Flow Analysis

Year Net cash revenue 1 2 3 4 5 3,000 3,000 3,000 3,000 3,000 Investment A Debt payment Net cash flow 2,800 2,640 2,480 2,320 2,160 200 360 520 680 840 Net cash revenue Investment B Debt payment Net cash flow 1,000 2,000 3,000 4,000 6,000 2,800 2,640 2,480 2,320 2,160 -1,800 -640 520 1,680 3,840

$10,000 loan at 8% interest with equal principal payments

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Income Taxes, Inflation, and Risk

• Different investments may have different effects on income taxes so they should be compared on an after-tax basis • If net cash revenues and terminal values are adjusted for expected inflation, the discount rate should also be adjusted • Investments with higher risk should be assigned a higher discount factor © Mcgraw-Hill Companies, 2008

Sensitivity Analysis

Sensitivity analysis is a process of asking several “what if” questions. What if net cash revenues are higher or lower?

What if the timing is different? What if the discount rate were higher or lower?

Change one or more values and recalculate NPV and IRR. © Mcgraw-Hill Companies, 2008

Summary

The future value of a sum of money is greater than its present value because of the interest that could be earned. Investments can be analyzed using payback period, simple rate of return, net present value, and internal rate of return.

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