chapter 10: comparing monetary returns over time
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Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Chapter 10: Comparing Monetary Returns
Over Time
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Objectives
• Find the payback time for a project
• Understand the concept of time value of money
• Calculate a net present value for a project
• Criticise the process
• Discuss the selection of discount factors
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Costs & Benefits
• Costs usually come at the beginning of a project
• Their level is often known with some certainty
• Benefits come over some future time period
• They are open to considerable variation
• They are also uncertain
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
PaybackThis method only takes into account how long it will take to pay back the initial investment in nominal termsIf we invest £1,000
and get back £500 in year 1 and £500 in year 2
Then it takes 2 years to payback
If the money back were £750 in year 1And £750 in year 2
Then it would take one and a third years to pay back
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Interest Calculations
Interest is earned on a sum of money invested over a period of timeThe amount of interest depends upon the interest rate and the time period,But also on the method of interest accumulation
SIMPLE INTEREST: Here the same amount is earned each yearSo if you invest £100 at 10% you get
£10 interest in year 1£10 interest in year 2
and so on ………..So the total interest is(the amount)x(interest rate)x(number of years)
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Compound InterestWith compound interest, the money earned is left invested from year to yearAnd hence you get interest on interest
If you invest £100 at 10%, you get£10 interest at the end of year 1
In year 2, you get £10 interest on your £100plus £1 interest on the £10
A formula has been developed to help work out the total amount:
A0(1+r)n
Where A0 is the initial amount, r is the decimal interest rate and n is the number of years
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Time-value of Money
Money which we get in the future will not buy as much as the same amount received now.
One reason is inflation.
To work out the present value of a sum of money, we need to assume a rate of interest.We can then use the formula:
tt
r
AA
10
A0 - start yearAt - in t years time
This is just a manipulation of the compound interest formula
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
TablesYou could work out the values of the present value formula:
by hand, or you could use a spreadsheet,
or you could use tables
To find the figure for4%
And 6 years
You get
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Present ValueFor example:
How much would you need to invest now at 10% interest, to have £242 in two years time?
At = £242 r =0.1
201.01
242
A = 242 * 0.826446
= £200
So invest £200 to get £242 two years from now
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Choosing between Opportunities
You are offered a choice between two dealsThe first gives you £700 in 4 years time
The second gives £850 in 6 years timeThe rate of interest is set at 8%
Option 1:
Option 2:
4008.1
700A = 700 * 0.735
= £514.50
6008.1
850A =850 * 0.6302
=£535.67CHOICE?
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Investment AppraisalBusinesses often have several competing uses for their fundsThey need to find a way of objectively comparing themThis needs to take account of the time value of money
Net Present Value calculations meet these criteria
Method: For each project or use of funds we need to determine
1. Initial cost2. Income in each year3. Costs in each year4. An interest rate to be used5. The projected life of the project or asset
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Example - 1A company needs to invest in new manufacturing capacity and can buy either two Xenion Producers at £50,000 each or one Yeoming Producer at £120,000
The Xenion Producer will need to be upgraded in year two at a cost of £20,000 per machine
There are no expected future costs with the Yeoming Producer during its lifetime
All Producers are expected to last for 6 years and have zero scrap value
Expected revenues are given in the table
A 8% interest rate is used
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Example - 2
Yr X Y
0 0 0
1 25000 20000
2 30000 25000
3 30000 40000
4 35000 40000
5 25000 30000
6 15000 20000
Expected Revenues Expected Costs
X Y
-100000 -120000
-40000
Net Revenues
X Y
-100000 -120000
25000 20000
-10000 25000
30000 40000
35000 40000
25000 30000
15000 20000
R - C
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Tables 2
To help answer this problem we need six years of present value factors
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Example - 3
X Y-100000 -120000
25000 20000-10000 2500030000 4000035000 4000025000 3000015000 20000
Net Revenues
0.92590.85730.79380.735
0.68060.6302
Present Value Factor PV1 PV2
-100000 -12000023147.5 18518
-8573 21432.523814 3175225725 2940017015 204189453 12604
CHOICE
-£9,418.15 £14,124.50
Net Revenue times Present Value Factor
Total Net Present Value
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Choosing r
No-one publishes a specific value of r to useThere are a range of alternatives:
• The rate of inflation
• The rate used in the past
• The rate of return on capital (from the accounts)
• The rate available on the stock market
• The rate currently paid on the bond market
• A rate to reflect the riskiness of the project
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Ranges of Benefits
We already know that the future is uncertain
But the future expected income may possibly be labelled
By the likelihood of it happening
And then we could assign probabilities to the sets of
outcomes
The next example considers this situation
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Ranges 2A company is assessing a project and has 3 sets of projections
of contribution. These are shown in the table below.
Year
Pessimistic General Optimistic
Cost
£100,000 £100,000 £100,000
Expected Contribution, Year 1
£10,000 £12,000 £20,000
Expected Contribution, Year 2
£20,000 £25,000 £40,000
Expected Contribution, Year 3
£40,000 £50,000 £70,000
Expected Contribution, Year 4
£25,000 £40,000 £60,000
Expected Contribution, Year 5
£10,000 £20,000 £30,000
The company uses a discount rate of 12% and you have determined the probabilities of the three scenarios as 0.2, 0.7 and 0.1 respectively.
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Ranges 3
£100,000£100,0
00 £100,000
-£100,00
0
-£100,00
0
-£100,00
0
£10,000£12,00
0 £20,0000.89285
7 £8,929 £10,714 £17,857
£20,000£25,00
0 £40,0000.79719
4 £15,944 £19,930 £31,888
£40,000£50,00
0 £70,000 0.71178 £28,471 £35,589 £49,825
£25,000£40,00
0 £60,0000.63551
8 £15,888 £25,421 £38,131
£10,000£20,00
0 £30,0000.56742
7
NPV -£25,094 £3,002 £54,723
Year Pessimistic
General
Optimistic PV1 PV2 PV3
Cost
Expected Contribution, Year 1
Expected Contribution, Year 2
Expected Contribution, Year 3
Expected Contribution, Year 4
Expected Contribution, Year 5 £5,674 £11,349 £17,023
The first step is to find NPV’s in the normal way
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
Expected NPV
(-£25,094 x 0.2) + (£3,002 x 0.7) + (£54,723 x 0.1)= £2,555.20
You then take each NPV and multiply it by the appropriate probability
Where there are several projects competing for the same funds, this method suggests that you choose
the one with the highest expected NPV
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Thomson Learning 2004
Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE
ISBN 1-86152-991-0 © Cengage
ConclusionsNet Present Value takes account of the time value of moneyOther methods are available:
Discounted Cash Flow Looks for the rate of return on the investment which gives zero NPV
Internal Rate of Return Accounting ratio
Payback period
Ignores time value of money
Just counts up income until total equals the cost
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