The Optimum Solution to above Problem...
Working Note 1: The following assumptions have been made: i) the initial cost of investment at Rs 10,00,000 or extraction cost per ounce at Rs 4,600 is not expected to change;
ii) there are no additional expenses;
iii) the entire quantum of extracted gold will be sold, and there will be no stock in hand, at the end of first, second or third periods;
iv) there is no gestation period; production and sale commence immediately and are accrued at the end of the year;
v) the question states that the price will change at the beginning of a year. Hence, the price prevailing today will be the price at the end of the first year, and so on.
Working Note 2: For the first full year cash inflow per ounce will be Rs 400, being the difference between selling price of Rs 5,000 less extraction cost of Rs 4,600. For the 2nd year, the cash flow per ounce will be the same at Rs 400, as shown in Table 1. For the third year, too, the cash inflow position will be the same at Rs 400, as in Table 2 (cash flow per ounce). The workings can also be presented in a summarised form as in Table 3. Flowing from this, it is clear that, given a 50/50 rise or fall of Rs 500 per annum, and on account of neutralising effect, the expected cash flow will continue to be Rs 400 per ounce per annum, if the current price of gold is Rs 5,000
Working Note 3: The net present value (NPV) computations are shown in Table 4. Two conclusions can be reached. First: NPV is negative at Rs 5,600 and the mine should not be opened now. Also, we cannot open the mine when the selling price of gold is ruling below Rs 5,000 per ounce.
Evaluation, Part (a): Consider Working Notes 1 to 3. Scenario one: Since the NPV is negative at Rs 5,600 (Table 4), the mine should not be opened immediately.
Scenario two: i) Opening of mine is delayed by one year; and ii) the price is Rs 5,500. Since the expected price is Rs 5,500, taking into account 50/50 rise or fall of Rs 500, the price for all future periods will only be Rs 5,500 (comparable to computations in Tables 2 and 3). This is so because, if the gold price rises at year 1 to Rs 5,500 the rise and fall of Rs 500, on 50/50 basis thereafter will throw up only a uniform price of Rs 5,500. Profit per ounce, per annum will then be Rs 900 (Rs 5,500 less Rs 4,600). NPV computations are shown in Table 5. This throws up a positive amount of Rs 11,24,909. The expected value of this strategy is Rs 5,62,454 (Table 6). The mine can be opened, if (and only if) the price at the beginning of second period stands at Rs 5,500. Scenario three: i) Opening of mine is delayed by one year; and ii) the price is Rs 4,500. Considering that the project yields a negative NPV at an initial price of Rs 5,000, there is bound to be negative NPV at any price less than Rs 5,000.
Therefore, if after a wait of one year, the price rules at Rs 4,500, the mine should not be opened. Here it is assumed that the mine's life is three years from date of opening. Part (b), strategy 1: See Tables 7, 8 and 9. At this point, we have to decide whether the mine should be closed at t-1 or not. It is clear that when the price is Rs 4,500 at t-1, the mine should not be closed, but should be closed if the price is Rs 4,000 at t-2. When the price is ruling at Rs 4,000, the expected loss will be Rs 6,00,000 in that year. The probability of this loss is 0.25. Therefore, the value of option to close will emerge as shown in Table 10. Evaluation of strategy 1: When mine is opened when price is Rs 5,000 (t-0). i) Without an option to abandon, it has a negative NPV of Rs 5,600 (Table 4); and ii) Value of option to abandon is the saving of loss amounting to Rs 1,12,685.
Therefore, NPV with an option to abandon at t-2 is Rs 1,07,085 (being the difference between Rs 1,12,685 and Rs 5,600)
Strategy 2: i) Let us assume that the mine is opened, after a one-year wait, with a starting price of Rs 5,500. ii) For this alternative, the mine has to be abandoned at t-3, if the price reaches Rs 4,500. iii) The rationale is that there is likely to be a loss of Rs 1,00,000, and the probability of this occurring is 0.125. The expected value is presented in Table 11. Evaluation of Strategy 2: i) Without an option to abandon, the expected value for this alternative is Rs 5,62,454 (Table 6) ii) The NPV with an option to abandon is Rs 5,62,454 + 8,536, that is, Rs 5,70,990 Conclusion: i) value of option to abandon the mine under strategy 1 is Rs 1,07,085; ii) Value of option to abandon the mind under strategy 2 is Rs 5,70,990; and iii) Strategy 2 is optimal, and provides a better value, that is, wait for one year, open the mine if the price is Rs 5,500.
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