golden corpoation is considering the purchase of new equipment costing $80,000.
ID: 2702333 • Letter: G
Question
golden corpoation 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.
The equipment will be depreciated using straight line depreciation. Golden's cost of capital is 14%. What is the expected NPV? Should they purchase the new equipment?
Probabilities
After-tax
Net Income
Expected Value
of EAT
Recession
.3
($15,000)
Normal
.5
25,000
Boom
.2
35,000
Probabilities
After-tax
Net Income
Expected Value
of EAT
Recession
.3
($15,000)
Normal
.5
25,000
Boom
.2
35,000
Explanation / Answer
I have done the calculation by using .... Golden Corporation is considering the purchase of new equipment costing $200,000.
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."
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