Engineering Economic Analysis

318 UNCERTAINTY IN FUTURE EVENTS

What decision should be made on the new product summarized in Figure 1O-3?What is the

expected value of the product's PW? The firm uses an interest rate of 10% to evaluate projects.

If the product is terminated after one Year,the capital equipment has a salvage value of $550,000

for use with other new products. If the equipment is used for 8 years, the salvage valut?

is $0.

Evaluating decision trees is done by starting with the end outcome nodes and the decisions that

lead to them. In this case the decisions are whether to terminate after 1 year if sales volume is low

and whether to expand after 1 year if sales volume is high.

The decision to terminate the product depends on which is more valuable, the equipment's

salvage value of $550,000 or the revenue of $100,000per year for 7 more years. The worth (PW1)

of the salvage value is $550,000. The worth (PW1)of the revenue stream at the end of Year 1

shown in node 8 is:

PW1 for node 8= 100,000(PjA, 10%,7)

• 100,000(4.868) = $486,800

Thus, terminating the product and using the equipmentfor other products is better. We enter the

two "present worth" values at the end of Year 1 in nodes 7 and 8. We make the arc-tonode 7 bold,

and use a double hash mark to show that we're pruning the arc to node 8.

The decision to expand at node 6 could be based on whether the $800,000 first cost for

expansion can be justified based on increasing annual revenues for 7 years by $200,000 per year.

However, this is difficult to show on the tree. It is easier to calculate the "present worth" values

at the end of Year 1 for each of the two choices. The worth (PW1) of node 9 (expand) is:.~

PW1 for node 9 - -800,000 +600,000(P j A, 10%,7)

;::::; -800,000 + 600,000(4.868)

.$2,120,800

The value of node 10 (continue withoutexpanding) is:

:PW1 for pode 10. 400,000(Pj A, 10%,7)

.4OQ,0()O(4. 868)

--'=$1~947,200

This is $173,600 less.thaI}tIleexpaJ1sioJ).node,sothee)(pansion should happen if volume is high,

Figure 10=4suni1nanz~swjiat,w~iW.ff~~HiU"S~geofthepro~ess. '" ~ ~

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