Question

Becky needs another $1,100 in her vehicle fund to purchase the car she wants. Her parents offer to loan her the money, but want to teach her about the time value of money. They offer to have her repay the loan in the future using money from freelance work. They agree that she will repay $475 at each of her next three booked engagements. These events are 3, 9 and 16 months from now. Assume a 5% cost of capital. Assume there is no risk of default, and that compounding is monthly. What is the NPV of the loan from her parents' perspective? (Enter just the number in dollars without the $ sign or a comma and round off decimals to the closest integer, i.e., rounding $30.49 down to $30 and rounding $30.50 up to $31.)

Answer 1

Given That the Cost of Capita is 5%

Now, Since the compiunding is monthly, therefore per month Interest Cost = 5%/12
=0.42%

Now we need to get the present value of Cash Inflows
Present Value of 1st Loan Repayment @ 3months = $475/(1.042)^3

=420

Present Value of 2nd Loan Repayment @ 9months = $475/(1.042)^9

=328

Present Value of 3rd Loan Repayment @ 16months = $475/(1.042)^16

= 246

Adding all the above Computed Present Values and deducting the same from the inital Loan Amount would help us get our required NPV

= 994 - 1100

= - 106

Therefore the NPV of the loan is -106