Discounting VS Interest charges

The reason that you do not include interest charges is that discounting is accounting for the interest. (If you included interest charges you would then be dealing with them twice.)

The discount rate is the after-tax rate - the cost to the company. The pre-tax rate is irrelevant for the company (it is the return to the investors, but the company gets tax relief on borrowing).

You always discount the nominal (actual) cash flows at the nominal (actual) cost of capital.

The formula you refer to is the Fisher formula (although on the formula sheet the symbol f does not appear - it is h !). This is only relevant if you are given the real cost of capital (i.e. the cost of capital ignoring inflation). In this case you need to use the formula (using h = the general rate of inflation) to calculate i (the nominal cost of capital). Then you continue as above.

Thank you very much:) you are the best in explanation, also you understood what I meant. Thank you for your time and help:)

You are welcome :)

Dear John, I've a similar question: how to account for interest charges? in many books it's said exactly what you said: finance cost is incorporated into a discount factor and you would be dealing with it twice, should you consider them separately. But i cant' figure out how it works, because finance charges are tax-deductible cash flows. There may be a gap in my knowledge... However i would appreciate some explanations (with a simple numeric example) on that issue, or at least a reference to an article or a book where it's clearly explained. Because it's difficult to explain to non-finance people and to some finance people as well what finance charges must be excluded from a project appraisal on the grounds the book say so. Kind regards.

I do not know how far you have got in your studies and whether or not you have covered the weighted average cost of capital. Without repeating all the chapter and lectures on this, there are two important points: One is that we use the after-tax cost of money when we discount. So if we are borrowing at 10% but the tax is (say) 30%, then the net cost after tax relief is only 7%. Secondly, for a project to be worthwhile it needs to not only cover the interest payable (after tax) on any borrowing, but it must also provide an adequate return to shareholders by way of increased dividends, and dividends are not tax allowable. You will see in the cost of capital chapters that we actually discount at a weighted average cost of capital, which takes into account the after-tax costs of borrowing but also the cost of equity (shareholder) finance.

Dear John, I've studied F9 syllabus, and i know that we should use after-tax cost of capital, about tax shield, about wacc, etc. You mentioned recently that: "Secondly, for a project to be worthwhile it needs to not only cover the interest payable (after tax) on any borrowing" the question is: how can we be sure that the project will cover the interest payable, and how can it be demonstrated? (may be the use of different words to explain could work) for example, a simple project: outlay=100 (loan) interest to pay a bank: 10% cashflows: year1: 100 year2: 70 tax rate: 30% variant1 (by the book): year 1 2 CFs 100 70 taxable CFs 100 70 tax -30 -21 net CFs 70 49 df @ 7% (tax relief) 0.9346 0.8734 pv 65.4 42.8 npv=108.2-100=8.2 (positive) === variant2 (interest charges included): year 1 2 CFs 100 70 interest@10% -10 -10 taxable CFs 90 60 tax -27 -18 net CFs 63 42 df @ 10% 0.9091 0.8264 pv 57.3 34.7 npv=92-100=(8.0) - negative npv with df@7% =95.6-100=(4.4) - negative === What is the methodological error? In the varian1 we would accept the project, in the varian2 we would reject it.

The error is the same as I explained before. In your variant 2, by charging interest and then discounting you are still accounting for the interest twice. The only reason ever for discounting is to account for the cost of money. In addition, we do not discount simply at the cost of he borrowing (after tax) – we need to also take into account the return needed by shareholders (the cost of equity) and so we discount at the WACC. You ask how it can be demonstrated – discounting at the WACC and seeing whether the NPV is positive or negative will demonstrate whether or not the project is giving a sufficient return. (Alternatively – never in the exam, but it may make it more clear to you – you can calculate the net terminal value. This cannot be asked in F9, but as you will know it is examinable in F3 and if you watch the F3 lectures then you will see that I work through an example.)

Let me give you a very simple example. Suppose you borrow 50 to invest in a project with interest at 10% per annum (and assume the interest is all tax allowable). The project lasts 1 year, and gives a cash inflow of 120 in one years time. At the end of the year, there is interest chargeable of 5, and so the taxable profit is 115 and therefore the tax payable is 115 x 30% which is 34.5. So the net cash receipt at the end of the year is 120 - 5 - 34.5 = 80.5. The initial cost was 50, and so the cash balance at the end of the year is 80.5 - 50 = 30.5. (This is the terminal value). It is positive i.e. a cash surplus, and therefore we would accept the project. However the conventional approach for F9 is to say that the cash flow in 1 year is 120 and the tax on it is 36 (30%) giving a net cash flow in 1 year of 84. The present value of this (discounting at an after tax 7%) is 78.5, and therefore the net present value is 78.5 - 50 = 28.5. It is positive and therefore we would accept the project. We can reconcile the two answers - 28.5 is the equivalent amount now, whereas 30.5 is the amount in 1 years time. If you add 7% (the after tax interest) to the 28.5 now, you end up with 30.5 in one year. What makes this too simple is that we have assumed that the tax is payable immediately (in the exam there is often a 1 year delay), and we have only used the cost of borrowing - in practice we need to use the WACC for the reasons already stated. As I wrote before, for Paper F3 you did need to know about the terminal value. For Paper F9 you do not. In F9 we always discount the after tax flows at the weighted average cost of capital and we never include interest flows because they are taken account of when we discount at the WACC.

PS You said that 'in many books it says the same as me'. It is all books! There is no exception :-)

Dear John, Thank you for your efforts and support. Best regards, Konstantin

You are welcome :-)

Dear John, This is me again. (: You continuosly repeat that we should use WACC as a discount factor, which has raised a doubt with me. Do we still need to use WACC even when the project is all loan-financed? If yes, when how shall it be calculated? According to my knowledge a calculation of WACC implies that we have to weigh the return required by shareholders with a portion of capital provided by them among the project financing pool? Thus, if a project is all loan financed the return to shareholders would be multiplied with zero, and resulting in just after-tax interest rate on the loan. Otherwise, we could combine the interests (a return to shareholders PLUS after-tax interest on the loan). Kind regards.

For Paper F9, the answer is yes - we will discount at the WACC. The flaw in what you write is that we use the WACC for the company (not for the project). The company will obviously have shares and so the weighting for the cost of equity is not zero. (In fact, we are assuming that the overall gearing of the company is not going to change significantly - certainly in the long-term - when we use WACC. When you come to P4 you will see that if the gearing is going to change significantly (because, for example, debt is used to finance the project and it is a large amount) then there is a better approach - adjusted present value - where we do look separately at the tax benefit associated with the debt borrowing. However this is only for P4 - it is not in the syllabus for F9)