Golden corp is considering the purchase of new equipment costing $80,000.The exp

Question

Golden corp is considering the purchase of new equipment costing $80,000.The expected life of the equipment is 10 years.It is expected that the new equipment can generate an increase in net income for the next 10 years. The probabilities for the increase in net income depend on the state of the economy.

probabilities        after tax net income                   expected value of EAT

recession                         .3                                                 ($15,000)

normal                              .5                                                   $25,000

boom                                .2                                                    $35,000

the equipment will be depreciated using straight line depreciation.Goldens cost of the capital is %14.What is the expected NPV?should they purchase the equipment?

Explanation / Answer

I must assume that the "2" offered in the "boom" scenario is an error, and that it should be "0.2", because otherwise the sum of probabilities does not equal unity (1) -- which is scientifically impossible, because the set of all possibilities cannot be greater than the aggregate total of all individual probabilities.

Additionally, the hypothetical is impossible, because it unequivocally states that the probability of a "normal" landing is 0.5. If this is true, then the normal landing "is" the expected value, regardless of the other outcomes, and the recession and boom scenarios are irrelevant to the calculation.

In other words, if the probabily of normal is 50%, and that scenario will produce a $25,000 return, then that scenario MUST be the expected value, otherwise it could not have a 50% probability, because expected value is what occurs at the 50% point on the normal probability distribution curve.

Given the dramatic mathematical problems present in the hypothetical, I will assum that the only relevant values are those found in the "normal" scenario.

Based on the above assumption, Golden's capital cost over 10 years is the future value of borrowing $200,000 at 14% (1.4% per year), or $229,831.50.

Golden's income stream over the same period is $25,000 times 10, or $250,000.

The difference between income and capital cost over 10 years is a profit of $20,168.50.

The NPV of that income stream over the same period, assuming no payments made or income received for the 10 years, is $17,550.69.

Multplying that times the probability of 0.5 gives the "expected value" of $8,775.34.

Should Golden invest the money?

A: the pure mathematical answer is yes, because the result is positive. If you were asking me for a business decision, my answer would be: "I need better info, because this hypothetical is seriously flawed."

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.