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) (Use the 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.

a.) In transaction (a), determine the present value of the debt. (Round your answer to nearest whole dollar.)

b.) In transaction (b), what single sum amount must the company deposit on January 1 of this year? (Round your answer to nearest whole dollar.)

What is the total amount of interest revenue that will be earned? (Round your answer to nearest whole dollar.)

c.) In transaction (c), determine the present value of this obligation.

d.) In transaction (d), what is the amount of each of the equal annual payments that will be paid on the note?

What is the total amount of interest expense that will be incurred?

Thank you in advance!

Answer 1

Part a)

The present value of debt is calculated as below:

Present Value of Debt = Present Value of Annual Fixed Amount + Present Value of One Time Payment

_____

Using the values provided in the question and Present Value Tables:

Present Value of Annual Fixed Amount = Annual Fixed Amount*PVA(Rate,Years) = 7,200*PVA(7%,7) = 7,200*5.3893 = $38,802.96

Present Value of One Time Payment = One Time Payment*PV(Rate,Years) = 117,400*PV(7%,7) = 117,400*0.62275 = $73,110.85

Present Value of Debt = 38,802.96 + 73,110.85 = $111,913.81 or $111,914

_____

Part b)

The amount that must be deposited by the company on January 1 of this year and interest revenue is determined as below:

Amount of Deposit = Value of Plant Remodeling Fund*PV(Rate,Years) = 491,800*PV(7%,8) = 491,800*0.5820 = $286,227.60 or $286,228

Amount of Interest Revenue = Value of Plant Remodeling Fund - Amount of Deposit = 491,800 - 286,228 = $205,572

_____

Part c)

The present value of the obligation is arrived as follows:

Present Value of Obligation = Present Value of First Payment + Present Value of Second Payment + Present Value of Third Payment

_____

Using the values provided in the question and Present Value Tables:

Present Value of First Payment = Amount of First Payment*PV(Rate,Years) = 76,200*PV(7%,1) = 76,200*0.9346 = $71,216.52

Present Value of Second Payment = Amount of Second Payment*PV(Rate,Years) = 113,700*PV(7%,2) = 113,700*0.8734 = $99,305.58

Present Value of Third Payment = Amount of Third Payment*PV(Rate,Years) = 151,200*PV(7%,3) = 151,200*0.8163 = $123,424.56

Present Value of Obligation = 71,216.52 + 99,305.58 + 123,424.56 = $293,946.66 or $293,947

_____

Part d)

The value of annual payment is calculated as below:

Annual Payment = Value of Note/PVA(Rate,Years) = (176,000 - 35,200)/PVA(7%,5) = 140,800/4.1002 = $34,339.78 or $34,340

Total Amount of Interest Expense = Annual Payment*Years - Value of Note = 34,340*5 - 140,800 = $30,900

_____

Notes:

There can be a slight difference in final answers on account of rounding off values.