Three periods – given structure

The multi-period example will be limited to the method based on given cap- ital structure. An approach which assumes a fixed level of debt, and that has a changing capital structure, will be presented in Chapter 2 together with meth- ods of determining the cost of capital in such a context.

The general case will be illustrated by an example of a company with an in- vestment horizon of three years. The example is general enough, since methods used to cope with problems encountered here are helpful when dealing with a three-period (and more) case as well.

Example 8.

The company conducts operations for three years. Initially, 200 is invested in land. At the end of each of the three years, EBIT of 80, 90 and 70 respectively is gener- ated.

It is assumed that the value of land will not change and it can be sold as soon as the company terminates its operations. The company is financed 40% by debt. Other necessary parameters are as follows: T = 30%, k_D = 10%, k_E = 28%.

Method based on FCF

WACC has already been calculated (Example 6): WACC = 19.60%. Let us proceed to calculating free cash flow for each of the years and dis- counting it at WACC. Year 1 2 3 EBIT 80.00 90.00 70.00 Tax 24.00 27.00 21.00 FCF 56.00 63.00 249.00 PV 46.82 44.04 145.55

The value of the whole company is obtained by summing the present values of free cash flows: V = 236.41. The values of debt and equity can now easily be found using the following formulae:

Now we can take advantage of the values and determine cash flow in the first year. First, however, let us see what the value of company is each year.

The discounted cash flow from the end of year 3 represents the value of the company at the end of year 2, and the discounted cash flows from years 2 and 3 represent the value of the company at the end of year 1. The same result is obtained if cash flow and the value of company are discounted at the end of year 2:

There is also another way to show the present value:

For each of the years, let us split V into debt and equity according to the as- sumed capital structure:

Year 0 1 2 3

FCF 56.00 63.00 249.00

V 236.41 226.75 208.19

D 94.57 90.70 83.28

E 141.85 136.05 124.92

Now, cash flows (CF) can be determined for each of the periods. They are going to serve as data for a comparison analysis with the CF method that is to follow. Net profits must be calculated first.

Year 1 2 3 EBIT 80.00 90.00 70.00 Interest 9.46 9.07 8.33 EBT 70.54 80.93 61.67 Tax 21.16 24.28 18.50 EAT 49.38 56.65 43.17

Finding the value of cash flow needs a great deal of attention. At the end of year 3, the value of assets (after they are sold) must be added, and the debt (that is paid back) can be deducted:

At the end of year 2, another correction has to be made: the value resulting from a changed level of debt must be added. Debt diminishes, so every year cash flow is lower than net profit.

Cash flows discounted at 28% generate the value of E = 141.85. We can also find the value of equity each year (in the same fashion we did for the value of company V) :

Year 0 1 2 3

CF 45.52 49.23 159.89

E 141.85 136.05 124.92

For example, 136.05 is calculated by discounting the sum of 45.52 and 124.92 using a 28% discount rate.

The convergence between the two methods is striking. Still, it does not prove that the CF-based method will give the same result, since CFs were calculated with the use of values obtained via FCF based method. Let us calculate the ap- propriate values separately.

Method based on CF

Let us pore over the one-period example and use the experience to deal with an investment horizon of many periods. This time, however, we will limit ourselves to numerical solutions. Solving systems of equations for the multi-period case is viable but it would involve very complicated notation. We will relax these restrictions later and present graphically how such systems of equations might work. For the time being, a numerical solution will do – it is good enough to draw conclusions of a general nature.

Temporarily, debt is assumed to be fixed at 50 every year. The formula for CF takes into account changes in the level of debt, although now it is irrelevant since debt does not change.

Year 0 1 2 3 EBIT 80.00 90.00 70.00 D 50.00 50.00 50.00 Interest 5.00 5.00 5.00 EBT 75.00 85.00 65.00 Tax 22.50 25.50 19.50 EAT 52.50 59.50 45.50

The value of equity E each year is the discounted value of cash flow from the years to follow, or a discounted sum of one cash flow and the value of equity from the following year. It can be seen that the level of debt must be adjusted, because the capital structure is different from the one that was assumed. The assumed ratio of D/E is 2/3 and the adjustment are entered into the appropriate cells: Year 0 1 2 3 EBIT 80.00 90.00 70.00 D 94.57 90.70 83.28 Interest 9.46 9.07 8.33 EBT 70.54 80.93 61.67 Tax 21.16 24.28 18.50 EAT 49.38 56.65 43.17 CF 45.52 49.23 159.89 E 141.85 136.05 124.92

The order of putting the formulae into the spreadsheet also matters. Let us begin with the debt at the end of year 2. The numbers in bold are safe in that re- spect as their values are not related to other cells.

In conclusion, for the multi-period case and a fixed capital structure, both methods (CF and FCF-based) give identical results. The case of fixed debt will be considered in Chapter 2.