Answer to Question #188258 in Financial Math for Inara Shah

Question

 

              Question 3 

A potential client has offered the possibility to sign a contract, starting in 6 years, with a duration of 8 years (so it will produce 8 payments), to purchase a specific part that we can produce, but that will require a total reconversion of the whole factory. This contract is signed for annual revenues of $400,000. To do this, we must replace the machinery and the production plant must be reconverted. 

 

a)     What is the maximum amount of money we could afford to invest if we want a profitability of at least 4%?

 

b)     If we ask for a loan to be paid back in 5 years in constant equal monthly payments of $30,000, how much will we pay in total for the loan? 

                        

Answer 1

Given, we will receive annually $ 400,000 for 8 consecutive years, starting 6 years from now. In order to determine the amount we can invest, we need to discount this annuity to bring it at present value today.

1. Discounting to arrive at present value 6 years from now
2. Discounting amount received above to arrive at the present value today

Here, after discounting and bringing to present value, we can see that we can pay $2,128,294.

Here, is the back working for excel.

(b)

In order to find the amount we will pay for the loan, we need to discount the future monthly payments of $30,000 to the present value.

Note here that as the payments are monthly, the number of periods is 12*5 = 60 periods.

Also, the rate of interest has been divided by 12 in the formula, to arrive at a monthly rate of interest.

Thus, at the present value, we will be paying $1,628,972 for the loan.