Exercise 4-3 Investment decision making under uncertainty -

Risk analysis A leisure park's management intends to buy a little train, which provides the visitors of the parks with the possibility to take round trips. The estimated investment costs are € 630,000 for the little train and another € 1.5 Mio. for the restoration of already existing rails on which the train should run. For all equipment the economic life is estimated as 20 years after having started the business.

The management has gathered the following information:

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At the beginning of year 1 they have to pay a planning cost of € 80,000 for engineering consultants.

The payments for the rails occur one half each at the beginning of the first year and at the end of the first year.

The train is paid for at the beginning of the first year and immediately put into operation.

Consequently, there are assumed no time delays throughout construction.

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Current maintenance costs occur at the end of the respective period at the annual amount of€ 5,000.

With the purchase of the railway the management expects the number of visitors to rise by 200 people daily each paying a fare of € 3.00. We assume that these cash inflows of a year occur as a whole at the end of the respective year.

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A discount rate of 4 % is judged appropriate.

a) Compute the net present value of the investment project under certainty.

b) Now, run a risk analysis under the following conditions:

• 1) Selection of the uncertain input variables We assume that the cash inflow is uncertain. They can be 30 % under, but also 30 %

above the value under certainty. Accordingly the following figures for the cash inflow are possible: € 153,300, € 219,000 or € 284,700.

• 2) Estimate of the probability distributions of the uncertain input variables Table 4-27Probability distributions ofthe uncertain input variable Sales revenues in € 153,300 219,000 284,700 Probability 0.4 0.5 0.1

• 3) Allocation and generation of random numbers for the uncertain input variables Table 4-28 Allocation ofrandom numbers to the uncertain input variable Sales revenues in € 153,300 219,000 284,700 Allocated random 1,2,3,4 5,6,7,8,9 10 numbers Table 4-29 Generated random numbersfor the uncertain input variable 'sales revenues'
Replicate 1 2 3 4 5 6 7 8 Random num- 6 3 9 1 2 10 9 3 bers for the revenues Now calculate the related net present values. Prepare calculations for the relative frequencies of the net present value and derive a risk profile. Make appropriate investment recommendations.