Toughnut plc is considering a two-year project that has the following probabilit

Question

Toughnut plc is considering a two-year project that has the following probability distribution of returns: <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Year 1

Year 2

Return $

Probability

Return $

Probability

8,000

.1

4,000

.3

10,000

.6

8,000

.7

12,000

.3

The events in each year are independent of other years (that is, there are no conditional probabilities). An outlay of 15,000 is payable at Time 0 and other cash flows are receivable at the year ends. The risk-adjusted discount rate is 11 percent.

Calculate

a.            The expected NPV

b.            The standard deviation of NPV

Year 1

Year 2

Return $

Probability

Return $

Probability

8,000

.1

4,000

.3

10,000

.6

8,000

.7

12,000

.3

Explanation / Answer

Expected NPV 0 (15,000)

                         1 (800+ 6,000+3,600)= 10,400/1.11= 9369,37

                          2 (1,200+5,600)= 6,800/1.11^2= 5519.03

So (15,000) +9369.37+ 5519.03= (111.60)

Stanford deviation would be a hassle. Probabilities would be

.03    8,000, 4000     (prob, year 1,year 2)

.07    8,000 8,000

.18    10,000 4,000

.42    10,000 8,000

.09    12,000 4,000

.21 12,000, 8000

Compute NPV of all those scenarios. Square the difference between them and the expected value and multiply by the probability. Add them all together and take the square root and you would have the standard deviation. I'll let you crunch through the numbers, or perhaps someone else can come up with an easier method.

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