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exercise
Exercise

A friend of yours can invest in a multiyear project. The cost is $14,000. Annual cash flows are estimated to be $5,000 per year for six years but could vary between $2,500 and $7,000. Your friend estimates that the cost of capital (interest rate) is 11%, but it could be as low as 9.5% and as high as 12%. The basis of decision to invest will be whether the project has a positive net present value.

Construct a tornado diagram for this problem. On the basis of the tornado diagram, advise your friend regarding either (1) whether to invest or (2) what to do next in the analysis.

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Variable

Base Value

Lower Bound

Upper Bound

When X1=X2=∙∙∙= $5,000 and r=11%, NPV=$7,152.69

Cash flow

$2,500

$7,000

$5,000

When X1=X2=∙∙∙= $2,500 and r=11%, NPV=$-3,423.67

Interest rate

9.5%

12%

11%

When X1=X2=∙∙∙= $7,000 and r=11%, NPV=$15,613.76

When X1=X2=∙∙∙= $5,000 and r=9.5%, NPV=$8,099.13

When X1=X2=∙∙∙= $5,000 and r=12%, NPV=$6,557.04

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$2,500

$7,000

Cash flows

Interest rate

12%

9.5%

-$3,423. 67

$15,613.76

-$4,000

0

$4,000

$8,000

$12,000

$16,000

NPV

Conclusion: NPV is not sensitive to the change of the interest rate but very sensitive to the range of cash flows. Therefore, it would be appropriate to set the interest rate at 11% for the analysis but to model the uncertainty about the cash flows with some care.