Simple valuation

6.3 Simple valuation

Thus the total NPV of costs is

57.4 16.29 13.65 87.3 million USD The NPV for the scenario-weighted revenue is

10% 40.2 80% 121.7 10% 322.28 133.7 million USD As a result the final NPV is 133.7 87.3 46.4 million USD

6.3.2 Fuzzy DCF valuation

As we are working with a cash flow forecast that is scenario weighted and divided into three categories, it is obvious that we should use triangular fuzzy numbers to our fuzzy valuation approach, which we presented in section 4.1.

To calculate the fuzzy NPV we need to rearrange the forecasted cash flow differently than in the standard scenario-weighted cash flow forecast by the use of the fuzzy pay-off method presented in section 4.1.1. The fuzzy cash flow (hereafter referred to as FCF) is constructed in order to model the most extreme cash flows possibly. For the bad case FCF we use the bad case total costs and the bad case total revenue to depict the worst possible cash flow scenario and vice versa for the good case, while the base case remains the same.

Total revenue for the good case is calculated as the highest estimated sales minus lowest estimated production costs. Appendix 20 shows the FCF for the three cases. The summarized FCF forecast is outlined in table 6.8.

Table 6.8: Own construction

The NPV of the FCF for each case is shown below, which are used to generate the fuzzy NPV (hereafter referred to as FNPV).

57.6 million USD 40.5 million USD

App.

2011e 2012e 2013e 2014e 2015e 2016e 2017e 2018e 2019e 2020e 2021e 2022e 2023e 2024e 2025e 2026e 2027e 2028e 2029e 2030e 2031e FCF ‐ Bad ‐3.8 ‐3.8 ‐3.8 ‐3.8 ‐2.5 ‐2.5 ‐5.5 ‐5.5 ‐20.0 ‐20.0 ‐20.0 ‐4.0 ‐7.3 2.3 8.8 14.4 17.2 18.5 17.2 14.7 8.2 FCF ‐ Base ‐1.4 ‐1.4 ‐1.4 ‐1.4 ‐2.3 ‐2.3 ‐5.3 ‐5.3 ‐15.0 ‐15.0 ‐15.0 ‐3.0 1.7 23.9 40.4 50.6 55.7 56.7 52.9 45.3 26.1 FCF ‐ Good ‐0.4 ‐0.4 ‐0.4 ‐0.4 ‐2.0 ‐2.0 ‐5.0 ‐5.0 ‐10.0 ‐10.0 ‐10.0 ‐2.0 21.3 75.4 116.7 138.9 150.0 150.9 140.8 120.6 70.1

Lead Opt./Preclinical phase Phase 1 Phase II Phase III Market

240.6 million USD

The resulting FNPV (-57.6, 50.5, 240.6) is the pay-off distribution for the project.

In section 4.1.1 the fuzzy pay-off method to calculate the fuzzy real option value (hereafter referred to as FROV) was presented. Hence we will lead out with identifying our ‘a’, (a – α) and (a + β):

57.6 million USD

40.5 million USD ‘a’

240.6 million USD

Thus the value of α is 40.5— 57.6 98.1 and the value of β is 240.6 40.5 200.1 As the method stipulates we have to find the mean value of the positive side of the triangle, denoted E(A+). Also we have to compute the relationship between the positive area and the negative area of the triangle.

The mean value of the positive area E(A+) is found by equation (4.6).

E A 40.5 200.1 98.1 6

98.1 40.5

6 · 98.1 60.79

The relation between the positive area and the negative area is found by simple mathematics as it is actually two right-angled triangles. The fact that we are working with two triangles with a limit of 0 and 1 as shown in figure 4.1 makes the calculation simpler. Appendix 21 shows the calculations as well as a figure to help the understanding. In order to compute the area

relationship we have to determine the intercept of the y-axis so we can compute the area of the negative side.

We already have the known points of (40.5; 1) along with (0; -57.6) and (0; 240.6). The next step is to compute the slope of the lines, going from peak ‘a’ to the two extreme points, so we end up with the formulas of the lines. This presents a situation where we in order to calculate the area relationship have to solve two equations with two unknowns.

Given the points mentioned we can form two equations that follow the traditional guidelines of

simple equations and thus we end up with

0 57.6 and 1 40.5 .

This gives us the possibility to eliminate one of the factors and replace it in the other equation in order to find a. So if we rearrange the first equation we will get 0 57.6

0 57.6 57.6 . With our b-value expressed as a function of a, we substitute the equation into the remaining equation to find a

1 40.5 1 40.5 57.6 0,0102

With the finding of a, we can easily calculate the value of b

0 57.6 0 0,0102 57.6 0,587

Now we have all the values to calculate the positive and negative area, respectively. To calculate the area relationship we have to split the area in three different pieces, the positive areas from ‘a’

to β and from 0 to ‘a’ as well as the negative area from α to 0. The areas are calculated from the area formula for right-angled triangles given as ½

The area of the negative side is then 0 ½ 0,587 57.6 16.915. Next we find the positive areas in the same way, and thus get ‘a’ 100.07 and 0 ‘a’ 32.11 Hence the relation between the positive and entire area is _. ^. _. ^. _. 0.8866 This means that we can compute the final FROV from equation 4.4.

60.79 0.8866 53.89 million USD 6.3.3 Review of the DCF valuation versus the fuzzy DCF valuation

Both methods produced a positive value for the CNS project, which was expected as none of the methods take the risk of failure into account but assumes that the project will be completed. The classic DCF method yields a value of USD 46.4 million while the fuzzy DCF method gives a value of 53.9 million USD. As advocated in section 4.1.1 the fuzzy DCF approach yields a

higher value than the traditional DCF approach as it puts more emphasis on the potential upside than the potential downside. Thus the results obtained are in line with the theoretical arguments.

According to the results of both the classic DCF model and the fuzzy DCF model the project should be initiated as the results provide significantly positive values.

However as none of the approaches include the risk of failure as mentioned above we will next evaluate the project with a simple DCF model that now incorporates the success rates for completing each phase.

6.4 Valuation with a real option perspective