Mr.Smith has an income of $40,000 this year and $60,000 next year.He can invest in a project that costs $30,000 this year,which generates an income of $36,000 next year.The market interest rate is 10%.What will be his consumption next year if Mr.Smith invests in the project and consumes $50,000 this year?
A)$40,000
B)$52,000
C)$60,000
D)$62,000

Question

Quizplus · Accepted Answer

If Mr. Smith doesn't invest in the project, his consumption next year will be $60,000 + ($60,000 x 10%) = $66,000.

If he invests in the project, his total income next year will be $60,000 (from his regular income) + $36,000 (from the project) = $96,000.

With a market interest rate of 10%, the present value of the project is: 
$36,000 ÷ (1 + 10%) = $32,727.27

So if he invests, his total wealth at the end of this year will be: 
$40,000 + ($60,000 ÷ (1 + 10%)) - $30,000 = $68,181.82

Therefore, his consumption next year will be: 
$68,181.82 - $50,000 = $18,181.82

If he doesn't invest, his consumption is $66,000, which is clearly higher than $18,181.82.

However, if he invests, his total wealth is higher than if he doesn't invest. Therefore, the best choice for Mr. Smith would be to invest in the project and consume $18,181.82 next year, for a total consumption of: 
$50,000 + $18,181.82 = $68,181.82

So the answer is: 
Choice B. $52,000.

MrSmith Has an Income of $40,000 This Year and $60,000