Capital Investment

Penri James2005

2

Definition of Capital

• wealth in the form of money or property owned by a person

• business and human resources with an economic value

• assets available for use in the production of further assets

3

Sources of Capital

• Own Capital– Assets (net worth)

• Retained Profits• Capital Grants

– Government and Agencies

• Creditor Capital– Banks, private investors

4

Interest

• The reward to capital– Interest is the

payment to the lender for postponing the consumption of capital – PURE INTEREST

– Service charges - ADMINISTRATION

– Profits – REWARD FOR RISK

• Expressed as a % rate

Reward for Risk

Pure Interest

Administration

%

5

Interest Rates

• Interest Rates apply the charge on borrowing money

• Agreed percentage rate over a period of time

6

Variable Interest Rates

0

2

4

6

8

10

12

14

16• Vary throughout

duration of loan• Vary according to

cost of borrowing by lender

• Unpredictable and uncertain cost

7

Fixed Interest Rates

0

2

4

6

8

10 • Constant rate• Certain

predictable cost

8

Break Loans

• Changes between variable and fixed rate throughout duration of loan

time

%

9

Interest rates

• Base Rate• Annual Nominal Rate

– Applied to daily balance outstanding – Base rate + x%

• Period rate– Annual Nominal rate for periods of less than

a year

• Flat rate– % of original amount borrowed

10

Interest Rates (from LloydsTSB)

• GROSS RATE– The contractual rate of interest payable before deduction of income

tax at the rate specified by law• NET RATE

– The rate of interest which would be payable after allowing for the deduction of income tax at the rate specified by law.

• AER– AER stands for Annual Equivalent Rate and illustrates what the

interest rate would be if interest was paid and compounded once each year.  As every advert for a savings product will contain an AER you can compare more easily what return you can expect from your savings over time.

• TAX FREE RATE– The annual interest rate when interest is exempt from income tax.

Interest is normally paid at the net rate unless the Account falls within an exempt category or the Account holder qualifies to receive interest gross. Interest rates may vary from time to time. All rates are per annum except where stated.

11

Factors that affect Interest Rates

• Cost of money to financial institutions– Government policy (Bank of England Monetary Policy

Committee)– Oil prices– International interest rates– Supply and demand for money– Inflation

• Method by which financial institutions raise money– Deposit vs Current accounts (Loanable Funds Theory of

Interest)

• Fixed or variable rates• Risk factor

12

Loanable Funds Theory of Interest

• When DEMAND (Current) increases or SUPPLY (Deposit) decreases then interest rates rise

• When DEMAND (Current) decreases or SUPPLY (Deposit) increases then interest rates fall

13

Loanable Funds Theory of Interest

Interest rate

Quantity

demand

supply

demand increase

i

Q

14

Loanable Funds Theory of Interest

Interest rate

Quantity

demand

supply

i

Q

supply increase

15

Annual Percentage Rate

• Consumer Credit Act 1974• APR sets all quoted interest rates on an

equal basis

1001p

n+1=APR

p

where

n = nominal interest rate in decimal

p = number of instalments per year

16

1001

p

p

n+1=APR

Nominal rate = 15%Number of instalments = 4 (quarterly)

1001

4

4

0.15+1=APR

1001 40.0375 +1=APR

15.9%=APR

APR example

17

Annual Percentage Rate

Annual Percentage RateApproximate annual percentage rate equivalent (%)

Annual Nominal

Rate

Monthly Charging

Quarterly Charging

Half-Yearly Charging

5% 5.1% 5.1% 5.1%6% 6.2% 6.1% 6.1%7% 7.2% 7.2% 7.1%8% 8.3% 8.2% 8.2%9% 9.4% 9.3% 9.2%10% 10.5% 10.4% 10.3%11% 11.6% 11.5% 11.3%12% 12.7% 12.6% 12.4%13% 13.8% 13.6% 13.4%14% 14.9% 14.8% 14.5%15% 16.1% 15.9% 15.6%16% 17.2% 17.0% 16.6%17% 18.4% 18.1% 17.7%18% 19.6% 19.3% 18.8%19% 20.7% 20.4% 19.9%20% 21.9% 21.6% 21.0%

18

Interest Rate

• An Interest Rate is the exchange rate between today’s currency and money in tomorrow’s currency

Rate Interest currency sToday' currency sTomorrow'

19

The concept of compounding

• Compounding gives the future value of money invested today

• It is a function of – Time – Interest (Discount) Rate– Amount invested

20

The concept of compounding

ni+1(£) capital Investing=(£) ValueFuture

wheren = number of yearsi = interest rate in decimal

i1n

factor gCompoundin

21

Compounding - example

• What is the future value of – £100 invested at 12% for 3 years

• Solution ni+1(£) capital Investing=(£) ValueFuture

30.12+1£100=(£) ValueFuture

1.405£100=(£) ValueFuture

£140.50=(£) ValueFuture

22

Compounding tables

1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14%0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0001 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120 1.130 1.1402 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210 1.232 1.254 1.277 1.3003 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.368 1.405 1.443 1.4824 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.518 1.574 1.630 1.6895 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 1.685 1.762 1.842 1.9256 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 1.870 1.974 2.082 2.1957 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.076 2.211 2.353 2.5028 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.305 2.476 2.658 2.8539 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 2.558 2.773 3.004 3.252

10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 2.839 3.106 3.395 3.70711 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 3.152 3.479 3.836 4.22612 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 3.498 3.896 4.335 4.81813 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 3.883 4.363 4.898 5.49214 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797 4.310 4.887 5.535 6.26115 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 4.785 5.474 6.254 7.13816 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 5.311 6.130 7.067 8.13717 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 5.895 6.866 7.986 9.27618 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 6.544 7.690 9.024 10.57519 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 7.263 8.613 10.197 12.05620 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727 8.062 9.646 11.523 13.743

Ye

ar

Rate

ni1 =factor Compound

23

The concept of discounting

• Discounting gives the present value of a sum received at a time in the future

ni+1

1=factor Discount

wheren = number of yearsi = interest rate in decimal

24

Discounting - example

ni+10 YearinMoney =3 YearinMoney

or

ni+1

3 YearinMoney =0 YearinMoney

1.405

£140.50=0 YearinMoney

100£=0 YearinMoney

25

Discounting tables

1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12%0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0001 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.8932 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.7973 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.7124 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.6365 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.5676 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.5077 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.4528 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.4049 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361

10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.32211 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.28712 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.25713 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.22914 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.20515 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.18316 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.16317 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.14618 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130

Yea

r

Rate

ni1

1=factor Discount

26

Loan characteristics

• Fixed amount– Principal of the loan

• Specific period• Interest rate• Charge period

27

A loan or a mortgage?

• Loan– Borrow money usually without security

• Mortgage– Mortgagor obtains a loan from a Mortgagee

on the security of a property– Deeds relating to the land are transferred

whilst loan is repaid– Mortgagee has the right to reposess on

repayment default

28

Reducing Balance Loan

• Easy to Calculate

• Equal Capital Repayments

• Interest Charged on outstanding balance at END of Charge Period

£0

£1,000

£2,000

£3,000

£4,000

£5,000

£6,000

£7,000

£8,000

£9,000

1 2 3 4 5 6 7 8 9 10

Repayment I nterest

29

Annuity Loan

where i = interest in decimal n = term of loan in years

i

i)+(1-1=FactorAnnuity

-n

FactorAnnuity

Loan of Principal=InstalmentPeriodic

Balance i=Payment Interest

Payment Interest-Instalment= Repayment

30

Annuity Loan

• Equal Repayments

• Increasing Capital Portion

• Decreasing Interest Portion

£-

£1,000

£2,000

£3,000

£4,000

£5,000

£6,000

£7,000

1 2 3 4 5 6 7 8 9 10

Repayment Interest

31

Endowment Loan

• Interest Charged on Total Through Term of Loan

• Premium Charge is dependent on status

• Loan Repayment on Maturity

• With Profits or Deficit• Not offered as an option

by lenders after mis-selling scandal

£0

£1,000

£2,000

£3,000

£4,000

£5,000

£6,000

£7,000

1 2 3 4 5 6 7 8 9 10

Interest Premium

32

Problems with endowment loans

£

time

80K

20 yrs

Deficit

With profits110K

good

bad

15 yrs

33

What is Investment Appraisal?

•Selecting investments where the benefits of the investment outweigh the costs

•Cash generated by the project more than outweighs the lost opportunity to invest in other projects.

34

Types of Investment

• Expansion of existing facilities

• Diversification into new products or new markets

• Cost reduction investments– Automation, mechanisation

• Safety and maintenance investments

35

Investment selection

Identify Objectives

Search for Investment

OpportunitiesInitial Screen

List Possible Outcomes

Select Investment

Projects

Measure Cashflow

Review investment

decision

THE BIN

36

Capital Budgets

• How much money is available for investment?

• Select capital project which gives greatest return on the investment– INVESTMENT APPRAISAL

• Quality of investment– showing a net benefit

• Capital constraints– financing method

37

Allocating Capital

Growth InvestmentLand purchaseDairy herd increaseNew pig unit

Safety investmentNew tractorWaste controlDust extractor

•Rank according to feasability

•Rank according to priority

– statutory

– strategy

•Rank according to benefits

38

Investment Appraisal Techniques

• Payback method• Discounted Payback method• Net Present Value• Internal Rate of Return• Profitability Index

39

Payback method

• Investment is recouped within a period of time

• Period length based on– past experience– forecasting accuracy

• Method - successive cash inflows are added together until cumulative cash inflow is greater than the cash outlay

40

Payback method example

• Self propelled forage harvester purchased for £80,000

• Calculate the payback periodYear Investment Cashflows Cumulative

cash inflow

0 -80,000£ 1 20,000£ 2 22,000£ 3 25,000£ 4 29,000£ 5 25,000£

41

Payback method solution

Year Investment Cashflows Cumulative cash inflow

0 -80,000£ -800001 20,000£ -600002 22,000£ -380003 25,000£ -130004 29,000£ 16000 Payback Year 45 25,000£ 41000 Additional Cashflow

80,000£ 121,000£

42

Payback method

• Advantages– Simple and quick

• Disadvantages– Takes no account of time element– Ignores cash flows ouside payback period– Cut off point is arbitrary - makes decision

subjective

• Short term only

43

Discounted Payback method

• Removes time criticism from Payback - others remain

44

Discounted Payback method example

• Self propelled forage harvester for £80,000 at a discount rate of 13%

• Calculate the payback period

Year Investment Cashflows Discount factors

Discounted cashflow

Discounted cumulative cashflow

0 -80,000£ 1 20,000£ 2 22,000£ 3 25,000£ 4 29,000£ 5 25,000£

45

Discounted Payback method solution

Discount rate 13%

Year Investment Cashflows Discount factors

Discounted cashflow

Discounted cumulative cashflow

0 -80,000£ 1.000 -80,000£ -80,000£ 1 20,000£ 0.885 17,699£ -62,301£ 2 22,000£ 0.783 17,229£ -45,072£ 3 25,000£ 0.693 17,326£ -27,745£ 4 29,000£ 0.613 17,786£ -9,959£ 5 25,000£ 0.543 13,569£ 3,610£ Payback Year 5

46

Problems with Payback (non discounted and

discounted)

time

cumulative £

constant cashflow

investment

payback paybacklater

paybackearlier

UNCERTAIN END RESULT WITH INCONSISTENT

CASHFLOW

47

Net Present Value (NPV)

• NPV compares today’s cash oulay with future cash inflows from the investment

• Convert future cash into today’s currency using discount factors

48

Net Present Value (NPV) - components

• Initial Cash Flow / Investment Cost• Net Cash Inflows

– additional revenue

• Lifespan of the Investment• Cost of Capital

– market rate of interest for an investment– linked to RISK

49

Net Present Value (NPV)

NPV

INITIAL INVESTMENT

CASH INFLOW

COST OF

CAPITALLIFESPAN

Estimated operating

costsEstimated

sales volume

EstimatedPrice

50

Net Present Valuemethodology

1. Initial Cash Flow (capital investmet) is estimated

2. Periodic net cashflows which result from investment are calculated

3. Terminal value (if any) is calculated and added to last year’s cash flow

4. Opportunity cost of capital is calculated and used as discount rate

5. Net Present Value calculated

51

NPV with regular cash flows

• Present Values are additive with both regular and irregular cash flows

• With regular cash flows discount factors are also additive - cumulative discount factor

Factor Discount Cumulative CashflowPeriodic NPV

52

NPV with regular cash flows - example

Year Cashflow Discount factor Present Value

1 40,000£ 0.870 34,783£

2 40,000£ 0.756 30,246£

3 40,000£ 0.658 26,301£

4 40,000£ 0.572 22,870£

2.855 114,199£ Discount rate 15%

2.855£40,000=NPV

£114,199=

53

NPV on Excel

• NPV can be calculated using the function

=NPV(rate, value1, value2, ...)

• Modelling– Cash flow

• Receipts• Payments

– Opportunity cost

54

Internal Rate of Return (IRR)

• Discounted cash flow approach similar to NPV

• Calculates the rate of return required to make the NPV of the investment zero

• At what rate of return will the NPV of the investment be zero?

55

IRR

• Projects are accepted if the IRR is less than the opportunity cost of borrowing capital

• The IRR is the maximum cost of capital without incuring a loss on the investment

56

IRR

ACCEPT REJECT

BORROWING RATE

IRR

Increasing rate

57

IRR

• 3 methods of calculation– Interpolation– Calculator– Computer model

58

IRR - interpolation

• Calculate NPV using high discount rate – to give negative NPV

• Calculate NPV using low discount rate– to give positive NPV

• Plot on graph• High and low rates should be close to

IRR

59

IRR - interpolation

• As discount rate increases then NPV decreases

• On a graphic representation of NPV and discount rate - at a point where NPV=0 then an approximation of IRR can be made on the discount rate axis

60

IRR

+

-

npv rate

NPV> 0

NPV< 0

61

IRR interpolation exercise

Year Cash Flow 10% 15%1 -20,000£ 18,182-£ 17,391-£ 2 10,000£ 8,264£ 7,561£ 3 10,000£ 7,513£ 6,575£ 4 5,000£ 3,415£ 2,859£

NPV 1,011£ 396-£

1. Plot chart - Rate (x axis) vs NPV (y axis)

2. Estimate IRR

62

Interpolation exercise summary

Average

Actual 13.48Inaccuracy

63

IRR - interpolation problems

• IRR involves compound interest calculations

• Progression between two points is a curve and not linear

• The further apart the high and low rates then the less accurate the interpolation

64

IRR - interpolation problems

rate

NP

V

65

IRR - interpolation problems

-£400.00

-£200.00

£0.00

£200.00

£400.00

£600.00

£800.00

£1,000.00

£1,200.00

10% 11% 12% 13% 14% 15%

66

IRR – calculator (10% & 15%)

rateNPV High+rateNPVLow

rate%Low -rate% HighrateNPVLow rate%Low =IRR%

£396+£1011

10%-15%£10%=IRR%

1011

1407

505510%=IRR%

13.59%=IRR%

67

IRR – calculator (12% & 14%)

rateNPV High+rateNPVLow

rate%Low -rate% HighrateNPVLow rate%Low =IRR%

£139+£410

12%-14%£12%=IRR%

410

549

82012%=IRR%

13.49%=IRR%

68

IRR - Excel

• = IRR(values, guess)

• Values is the values for a cash flow series for which you want to calculate the internal rate of return.

• Guess is a number that you guess is close to the result of IRR.

69

IRR - a critique

• No need to specify the opportunity cost of capital

• Returns a % and not a value• Not suitable for making

comparisons over different time horizons

70

Profitability Index

• Rearrangement of NPV

Profitability Index =Present Value

Initial Cash Outflow

If Profitability Index is greater than 1 then the project is worthwhile.

71

The effect of tax on investment appraisal

• A successful investment will increase taxable profit

• Capital allowances are available for capital investment

• Businesses not making a profit have no tax liability

72

The effect of tax - capital allowances

• A capital allowance will reduce the tax burden

• Cash benefits arise from a capital allowance

• Capital allowances are available in the year following the purchase of an asset

73

Investment appraisal - tax

GROSS ANNUAL CASH FLOWlessCAPITAL ALLOWANCESlessINTEREST ON INVESTMENT LOAN(if not already included in overheads)equalsTAXABLE INCOME

74

Investment appraisal - tax

TAXABLE INCOMEmultiplied byMARGINAL TAX RATEequalsTAX BURDEN

• Tax is payable in the year after the profit is assessed

75

Inflation

• An increase in prices in an economy and consequent fall in the purchasing value of money

• Devaluing the worth of money – (Discounting is the time value of

money)

• Headline rate measured using Retail Price Index (RPI)

76

Inflation

• Caused by– Excess demand in the economy -

demand-pull inflation– High production costs - cost-push

inflation– Excessive increase in money supply -

monetarism

77

The effect of inflation

Unit cost

No. purchased

£0.00

£2.00

£4.00

£6.00

£8.00

£10.00

£12.00Y

ea

r 1

Ye

ar

3

Ye

ar

5

Ye

ar

7

Ye

ar

9

Ye

ar

11

Ye

ar

13

Ye

ar

15 0

500

1,000

1,500

2,000

2,500

Unit cost

No. purchased

£10,000 sum with 5% inflation

78

Inflation and Investment

• Real returns exclude the effect of inflation

• Money returns include the effect of inflation (NOMINAL RETURN)

• Work consistently either in real or money terms - never mix both states

79

How to adjust for inflation

rate

rate Inflationrate discount Real+1=discount

Nominal

11

Inflation rate and discount rate both expressed as decimal

Inflation has a compounding effect

80

The compounding effect of inflation

Nominal Cashflow (£) = Real Cashflow (£) 1+ i n

Compounding factor = 1+ i n

wheren = number of yearsi = inflation rate in decimal

81

Appraising an option

• Gather Information• Set up CASH FLOWS

– Receipts– Payments

• Calculate CAPITAL ALLOWANCES• Calculate TAX BURDEN• Calculate NET CASH FLOW• Allow for INFLATION• Calculate NPV , IRR

82

When to use alternative appraisal methods

• Do not rely entirely on one appraisal technique - use as many as possible

83

Setting criteria for any investment appraisal

technique

• It needs to take account of the time value of money

• Discount rate needs to accommodate the risk factor of the project

• It needs to cover the working life of the investment

• Objective measurement based on past not best performance