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Farm Management

Chapter 17Investment 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

1. The dollar could be invested to earn interest2. If dollar is spent on consumption, we’d

prefer to get the enjoyment now3. 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

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

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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

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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

Value atbeginning of Interest rate Interest earned Value at end

Year year (%) ($) of year ($)

1 1000.00 8 80.00 1080.002 1080.00 8 86.40 1166.403 1166.40 8 93.31 1259.71

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Figure 17-1Illustration of the concept of future value

for a present value and for an annuity

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Figure 17-2Relation 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 1i

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Present Value

PV = FV

(1 + i )nor 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 17-3Illustration 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 Amount ($) Present value factor Present value ($)

1 1,000.00 0.92593 925.932 1,000.00 0.85734 857.343 1,000.00 0.79383 793.83

Total 2,577.10

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Investment Analysis

• Investment analysis, also called capital budgeting, involves determining profitability of an investment

• Initial cost: actual total expenditure for the investment

• Net cash revenues: cash receipts minus cash expenses

• Terminal value: usually the same as salvage value

• Discount rate: opportunity cost of capital

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Payback Period

The payback period is the number ofyears it would take an investment toreturn its original cost. If net cash revenues are constant each year, thepayback period (P) is:

P =

C

E

where C is original costand E is the expected annual net cash revenue

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

Year Investment A Investment B

1 3,000 1,0002 3,000 2,0003 3,000 3,0004 3,000 4,0005 3,000 6,000

Total cash revenues 15,000 16,000Less initial investment -10,000 -10,000Net Cash Revenues 5,000 6,000

Average net revenue/yr 1,000 1,200

Net revenues ($)

no terminal value

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Finding Payback Period

The payback period for investment Ais 3.33 years ($10,000 ÷ 3)

The payback for investment B is 4 years, which is found by summingthe 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 ignoresreturns after the end of the payback periodas well as the timing of cash flows.

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Simple Rate of Return

Rate of return =

Investment A =

Investment B =

average annual net revenue

initial cost

$1,000

$10,000x 100% = 10%

$1,200

$10,000x 100% = 12%

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Net Present Value

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

NPV = + + + CP1 P2 Pn

(1 + i )1 (1 + i )2 (1 + i )n . .

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Table 17-4 Net Present Value and Internal Rate of Return

for Two Investments of $10,000

Net cash Present Present Net cash Present PresentYear flow ($) value factor value ($) flow ($) value factor value ($)

1 3,000 0.9090 2,727 1,000 0.9090 909 2 3,000 0.8260 2,478 2,000 0.8260 1,652 3 3,000 0.7510 2,253 3,000 0.7510 2,253 4 3,000 0.6830 2,049 4,000 0.6830 2,7325 3,000 0.6210 1,863 6,000 0.6210 3,726

11,370 11,27210,000 10,0001,370 1,27215.2% 13.8%

Investment B

Total

Investment A

TotalLess initial cost

Net present valueNet present valueInternal rate of returnInternal rate of return

Less initial cost

10% discount rate and no terminal values

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Internal Rate of Return

The internal rate of return (IRR) is thediscount rate that would make the NPVof 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 thathas the same present value as theinvestment being analyzed.

Investment A: $1,370 0.2638 = $361.41Investment B: $1,272 0.2638 = $335.55

The amortization factor for 10% and 5 yearsis 0.2638 (Appendix Table 1)

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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

Net cash Debt Net cash Net cash Debt Net cashYear revenue payment flow revenue payment flow

1 3,000 2,800 200 1,000 2,800 -1,800 2 3,000 2,640 360 2,000 2,640 -640 3 3,000 2,480 520 3,000 2,480 520 4 3,000 2,320 680 4,000 2,320 1,6805 3,000 2,160 840 6,000 2,160 3,840

Investment BInvestment A

$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

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Sensitivity Analysis

Sensitivity analysis is a process ofasking several “what if” questions. Whatif net cash revenues are higher or lower?What if the timing is different? What ifthe discount rate were higher or lower?Change one or more values andrecalculate NPV and IRR.

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Summary

The future value of a sum of money isgreater than its present value becauseof the interest that could be earned. Investments can be analyzed usingpayback period, simple rate of return,net present value, and internal rate ofreturn.