What decision should be made on the new product summarized in Figure 10-3? 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

Question

What decision should be made on the new product summarized in Figure 10-3? 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 value is $0.

Accepted Answer

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 lowand 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 $100,000 per year for 7 more years. The worth [latex]\left( PW _{1} ight.[/latex]) of the salvage value is $550,000. The worth [latex]\left( PW _{1} ight.[/latex]) of the revenue stream at the end of Year 1 shown in node 8 is

[latex]\begin{aligned}PW _{1} ext { for node } 8 &=100,000(P / A, 10 \%, 7) \&=100,000(4.868)=\$ 486,800\end{aligned}[/latex]

Thus, terminating the product and using the equipment for 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 to node 7 bold to indicate that it is our preferred choice at node 4.We use a double hash mark to show that we’re pruning the arc to node 8 to indicate that it has been rejected as an inferior choice at node 4.

The decision to expand at node 6 could be based on whether the $800,000 first cost for expansioncan 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 [latex]\left( PW _{1} ight.[/latex]) of node 9 (expand) is

[latex]\begin{aligned}PW _{1} ext { for node } 9 &=-800,000+600,000(P / A, 10 \%, 7) \&=-800,000+600,000(4.868) \&=\$ 2,120,800\end{aligned}[/latex]

The value of node 10 (continue without expanding) is

[latex]\begin{aligned}PW _{1} ext { for node } 10 &=400,000(P / A, 10 \%, 7) \&=400,000(4.868) \&=\$ 1,947,200\end{aligned}[/latex]

This is $173,600 less than the expansion node, so the expansion should happen if volume is high. Figure 10-4 summarizes what we know at this stage of the process.

The next step is to calculate the PW(Time 0) at nodes 4, 5, and 6.

[latex] ext { PW at node } 4=(100,000+550,000)(P / F, 10 \%, 1)=650,000(0.9091)=\$ 590,915[/latex]

[latex] ext { PW at node } 5=(200,000)(P / A, 10 \%, 8)=200,000(5.335)=\$ 1,067,000[/latex]

PWat node 6 [latex]\begin{array}{l}=[400,000-800,000+600,000(P / A, 10 \%, 7)](P / F, 10 \%, 1) \=[-400,000+600,000(4.868)](0.9091)=\$ 2,291,660\end{array}[/latex]

Now the expected value at node 2 can be calculated:

EV at node 2 = 0.3(590,915) + 0.6(1,067,000) + 0.1(2,291,660) = $1,046,640

The cost of selecting node 2 is $1,000,000, so proceeding with the product has an expected PWof $46,640. This is greater than the $0 for not building the project. So the decision is to build. Figure 10-5 is the decision tree at the final stage.

Question 10.10: What decision should be made on the new product summarized i...

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