Question

Book: An applied course in real options valuation; Shockley. The price of a unit to be...

Book: An applied course in real options valuation; Shockley.

The price of a unit to be manufactured can follow one of three potential paths with equal probability:

Path Period 0 Period 1 Period 2

A $35 $40 $45

B $35 $40 $40

C $35 $35 $35

D $35 $30 $25

A) What is NPA of a project that will allow the firm to manufacture 200 units each year for periods 1 and 2, assuming a cost of $12,800 and a discount rate of 10%?

B) Assuming that half the cost ($6,400) can be spent now and the rest after period 1, what is the NPV?

C) Suppose that after period 1 the price is $35 or $30, then what is the NPV of investing the second half of the $12,800?

D) Suppose that after period 1 the price is $40, then what is the NPV of investing the second half of the $12,000? is the 10$ discount rate appropriate here?

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Answer #1
  • all paths A, B, C, and D have equal probability of 0.25 or 25%
  • assuming 200 units are manufactured and taking present value discount factor at 10%(0.909 for year1 and 0.826 for year2
  • PATH A
  • present value of cash inflows= $40 * 200 *0.909 + $45*200 *0.826= 7272+ 7434= 14706
  • PATH B
  • present value of cash inflows= 40*200* 0.909 + 40*200 *0.826= 7272+6608= 13880
  • PATH C
  • present value of cash inflows= 35*200*0.909 +35*200*0.826 =6363+5782= 12145
  • PATH D
  • present value of cash inflows= 30 *200* 0.909 + 25*200 *0.826= 5454+4130=9584
  • applying PROBABILITY the present value of cash inflows will be
  • 14706* 0.25 + 13880* 0.25 + 12145* 0.25 + 9584* 0.25= $12578.5
  • cost/outflow= $12800
  • NPV = present value of cash inflows - present value of cash outflows
  • = 12578.5-12800= -$ 221.5(negative NPV)
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