Question

Assume that I can borrow money at a rate of 10% per year, but that I only earn 2% per year on money I loan. A friend has recently offered me an investment opportunity; make a $5,000 investment today and receive a guaranteed $5,400 in one year. I currently have $10,000 in the bank, but I plan on consuming $9,000 – meaning that I only have $1,000 that I could invest. Can/should make the investment? How much consumption would I need to be willing to forego to make the investment? (Another way to think about this is what is the maximum amount that I would be willing to borrow to take the investment?)

Answer 1

Correction in answer

Case 1

If we take maximum loan amount that can be taken is $5000. Let's calculate Net profit/loss in such a situation

Total return on investment is $ 5400 on investment of $ 5000 (Taken in debt) in friends opportunity

And getting 2% return on Savings, i.e. $1000*2% = $20

Total cost of debt = 5000*(1+ .01) = $5500

Loss = 5400+20 -55000

=> Loss of $80

So this implies that we have to borrow such that its less than $5000 and is profitable

Let debt amount be x and y be the amount remaining after making the $5000 investment.

The conditions on

=> 5000 - x = 1000 - y

Returns here would be

Total return on investment is $ 5400 on investment of $ 5000 (Taken in equity and debt) in friends opportunity

And getting 2% return on Savings, i.e. (y)*2% = $20

Total cost of debt = x*(1+ .01) = $5500

So profit equation becomes,

Profit/Loss = .02y + 5400 - 1.1x

We have to maximize profit, such that x - y = 4000

If x = 5000 and y = 1000 (maximum possible values)

then we get a Loss of $ 80

If x = 4000 and y = 0 then (minimum possible values)

Total Proft = .02*0 + 5400 - $4000*1.1

=> Profit = $1000

Since its a linear equation $1000 is the maximum profit than can be made with constraint that the consumption being $9000.