ABANDONMENT PROBLEM



ABANDONMENT PROBLEM 2

Burger Inc. is now (at time 0) evaluating the purchase of an asset, Asset X, which can now be acquired for $650 (all figures in $thousands). Assume that the discount rates for discounting future cash are as follows:

• For discounting cash flows back from time 2 to time 1:

▪ If the time 1 cash flow is $300, the discount rate is 8 percent.

▪ If the time 1 cash flow is $500, the discount rate is 10 percent.

• For discounting cash flows back from time 1 to time 0 the discount rate is 11 percent.

The table below shows the cash flows from the asset. The time 1 cash flow from using the asset (either $300 or $500) is received at time 1 whether or not the asset is abandoned at time 1. The amounts in brackets are the abandonment values. Thus, if the time 1 cash flow is $300, the time 1 abandonment value is $400; and if the time 1 cash flow is $500, the time 1 abandonment value is $550. Therefore, if the time 1 cash flow is $300 and the asset is abandoned at time 1, the total time 1 cash payoff (cash flow plus abandonment value) is $700 ($300 cash flow plus $400 abandonment value).

If Asset X is purchased, it will be held for no more than two time periods and will be abandoned either at time 1 or at time 2. Should your firm now purchase Asset X? Show all work.

Table 1: Future Cash Flow Probability Distribution for Asset X

|Time 1 | |Time 2 |

|Cash Flow and Abandonment Value | | |Cash Flow and Abandonment Value |Conditional Probability |

| |Probability | | | |

|$300 [$400] |.6 | |$ 0 [$200] |.3 |

| | | |$100 [$250] |.6 |

| | | |$200 [$300] |.1 |

| | | | | |

| | | | | |

|$500 [$550] |.4 | |$100 [$300] |.2 |

| | | |$300 [$400] |.5 |

| | | |$500 [$400] |.3 |

Solution

The asset should be purchased if its time 0 net present value [pic] is positive, where the [pic] is computed taking into account the ability in the future to abandon the asset. We will work back from time 2 to determine the [pic].

• If the asset generates $300 at time 1, then the expected (as of time 1) time 2 payoff from holding the asset to time 2 is computed as follows:

Expected time 2 payoff = .3 ($0 + $200) + .6 ($100 + $250) + .1 ($200 + $300) = $320 (1)

where the amounts in parentheses are the time 2 cash flow plus time 2 abandonment value. As of time 1, the present value of the $320 (using the 8 percent discount rate stated at the beginning of the problem) is:

Time 1 present value = [pic][pic][pic] (2)

Since the $296 time 1 present value from holding the asset to time 2 is less than the time 1 abandonment value of $400, the asset is abandoned at time 1. Therefore, if the firm receives a $300 time 1 cash flow from using the asset, it will at time 1 abandon the asset for $400, producing a time 1 total cash payoff of $700.

• If the asset generates $500 at time 1, then the expected (as of time 1) time 2 payoff from holding the asset to time 2 is computed as follows:

Expected time 2 payoff = .2 ($100 + $300) + .5 ($300 + $400) + .3 ($500 + $400) = $700 (3)

where the amounts in parentheses are the time 2 cash flow plus time 2 abandonment value. As of time 1, the present value of the $700 (using the 10 percent discount rate stated at the beginning of the problem) is:

Time 1 present value = [pic][pic][pic] (4)

Since the $636 time 1 present value from holding the asset to time 2 exceeds the time 1 abandonment value of $550, the asset is not abandoned at time 1. Therefore, if the firm receives a $500 time 1 cash flow from using the asset, it will keep the asset to time 2. For this case, the time 1 total cash payoff is $500.

Given the above information, we have the revised payoff distribution shown in Table 2.

Table 2: Future Cash Flow Probability Distribution for Asset X

|Time 1 | |Time 2 |

|Cash Flow plus Abandonment Value | | |Cash Flow plus Abandonment Value |Conditional Probability |

| |Probability | | | |

|$700 |.6 | |$ 0 |1.0 |

| | | | | |

| | | | | |

|$500 |.4 | |$400 |.2 |

| | | |$700 |.5 |

| | | |$900 |.3 |

The time 2 Cash Flow plus Abandonment Value amounts of $400, $700, and $900 shown in Table 2 are computed by adding the time 2 cash flow plus abandonment value from Table 1 since we know that, if the firm holds the asset to time 2, it will abandon the asset at time 2 and therefore will receive, at time 2, both the cash flow and the abandonment value (i.e., $400 = $100 + $300, $700 = $300 + $400, and $900 = $500 + $400).

We next use the Table 2 data to compute the present value of the future cash flows from Asset X. First bring the time 2 cash flows of $400, $700, and $900 back to time 1 and add that present value to the $500. The time 1 present value of the time 2 payoff is $636 [see equations (3) and (4) above]. Now add the $636 to the time 1 payoff of $500, producing a time 1 present value of payoff of $1,136 having a time 0 probability of .4. We can now compute the present value of the future cash flows from Asset X. Using the 11 percent discount rate for discounting the time 1 payoff to time 0 (see discount rate assumptions at the beginning of the problem):

[pic] = [pic] (5)

Therefore, given the required initial outlay of $650, the net present value of Asset X is:

[pic] $788 ($650 = $138 (6)

Asset X has a positive net value and should therefore be purchased.

10/25/2003

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