Question

On january 1, boston company completed the following transactions (use a 7% annual interest rate for all transactions): (fv of $1, pv of $1, fva of $1, and pva of $1) note: use appropriate factor(s) from the tables provided. promised to pay a fixed amount of $7,200 at the end of each year for seven years and a one-time payment of $117,400 at the end of the 7th year. established a plant remodeling fund of $491,800 to be available at the end of year 8. a single sum that will grow to $491,800 will be deposited on january 1 of this year. agreed to pay a severance package to a discharged employee. the company will pay $76,200 at the end of the first year, $113,700 at the end of the second year, and $151,200 at the end of the third year. purchased a $176,000 machine on january 1 of this year for $35,200 cash. a five-year note is signed for the balance. the note will be paid in five equal year-end payments starting on december 31 of this year. required: 1. in transaction (a), determine the present value of the debt.

Answer 1

The present value of the debt in transaction (a) is $113,222.81.

Step-by-step explanation:

To determine the present value of the debt in transaction (a), we need to calculate the present value of the promised payments of $7,200 at the end of each year for seven years and the one-time payment of $117,400 at the end of the 7th year. To calculate the present value, we can use the present value of an annuity (PVA) formula and the present value of a future amount (PVF) formula.

For the promised payments of $7,200 for seven years, we can use the PVA formula:

PVA = Payment x [1 - (1 + r)^(-n)] / r

Using the formula with a payment of $7,200, an interest rate of 7%, and a number of periods (n) of 7, we find:

PVA = $7,200 x [1 - (1 + 0.07)^(-7)] / 0.07 = $35,210.60

For the one-time payment of $117,400 at the end of the 7th year, we can use the PVF formula:

PVF = Future Amount / (1 + r)^n

Using the formula with a future amount of $117,400, an interest rate of 7%, and a number of periods (n) of 7, we find:

PVF = $117,400 / (1 + 0.07)^7 = $78,012.21

To find the present value of the debt, we add the present values of the promised payments and the one-time payment:

Present Value of Debt = $35,210.60 + $78,012.21 = $113,222.81