Logical tests

Logical tests Consider an income tax system in which a fixed allowance of £4000 is awarded against gross income, i.e. no tax is paid on first £4000 earned. First £16000 is taxed at 20% Over £16000 the rate is 25%

Continued… If you earn £30000 Taxable income (TI) = £30000 - £4000 = £26000 First £16000 of this is taxed at 20%; 20/100*£16000 = £3200 The remaining £10000 is taxed at 25%; 25/100*£10000 = £2500 Therefore total tax bill is £3200+£2500=£5700 Net income is £30000-£5700=£24300

In Excel… We can use the IF statement Let G be gross income A be the tax free allowance Taxable income, TI=G-A Check to see where any tax should be paid =IF(G-A<0,0, G-A)

… Now to calculate the amount of tax If TI is less than the upper limit, M, then the tax is simply = lower rate * TI If TI is greater than M, then the tax is lower rate*TI + upper rate * (TI-M) Translating into an IF statement, =IF(G-A<=M, lower*(G-A), lower*M+upper*(G-A-M))

Naming cells To assign a name to a cell, highlight the cell and from the menu choose INSERT>NAME>DEFINE This can be very useful in keeping track of entries in formulae, especially as it means you do not have to use $ to fixed the cell you are referring to.

… Note that the cells A, tl, th, M, G, TI, TD and NI are all named cells Note lower rate = tl, higher rate =tu Try this on your own without naming the cells, what do you think will happen?

Vertical lookups How do we deal with situations where there may be more than two or three embedded IF statements, when it may get rather messy? Imagine a firm is selling kitchen units offers a range of discount rates depending on the size of the order.

Example For orders less than 10 units, there is no discount Orders >=10 but <25 a 4% discount is offered Orders >=25 but <45 a 6% discount is offered Orders >=45 but <75 a 7% discount is offered Orders >=75but <100 a 7.5% discount is offered Orders >=100 a 9% discount is offered

… We use the VLOOKUP statement

Define the lookup table The order size is stored in cell B3 The different discount rates are stored in cells D3:E8 We want to return the values from column 2 of the lookup table The statement is therefore = VLOOKUP(B3, D3:E8, 2)