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.) Borrowed $117,200 for nine years. Will pay $7,100 interest at the end of each year and repay the $117,200 at the end of the 9th year. Established a plant remodeling fund of $491,650 to be available at the end of Year 10. A single sum that will grow to $491,650 will be deposited on January 1 of this year. Agreed to pay a severance package to a discharged employee. The company will pay $76,100 at the end of the first year, $113,600 at the end of the second year, and $151,100 at the end of the third year. Purchased a $175,500 machine on January 1 of this year for $35,100 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. (Round your answer to nearest whole dollar.)

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

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

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

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

4-b. What is the total amount of interest expense that will be incurred?

Answer 1

1. The present value of the debt in transaction (a) would be $110,003.

In the transaction, the annual payments for 9 years would be $7,100. Using the PVA of $1 table, the factor for 9 years at 7% are of interest is 6.5152. Multiplying $7,100 by 6.5152 gives $46,258 which is the PV of the annual payments

At the end of 9th year the company needs to pay $117,200. Hence we need to use the PV of $1 table and get the factor for 9th year at 7% which is 0.5439. Hence the PV of $117,200 would be $117,200 x 0.5439 = $63,745

Thus, the present value of the debt would be $46,258 + $63,745 = $110,003

2-a. In transaction (b) the the single sum that the company must deposit on January 1 this year would be $249,906

In order to make available a sum of $491,650 at the end of Year 10, we need to find the factor for 10th year at 7% interest using the PV of $1 table which is 0.5083. Multiplying $491,650 by 0.5083 we get $249,906 which is the sum to be deposited by the company this year.

2-b. The total amount of interest revenue earned would be $241,744 i.e. the difference between $491650 and the PV of $491,650 i.e. $249,906 which is $241,744

3. The present value of the obligation would be $293,684

Using the factors for Year 1, 2 and 3 for 7% interest in the PV of $1 table i.e. 0.9346 for Year1, 0.8734 for Year2 and 0.8163 for Year3 we multiply the factor for each year with each years payout i.e. $76,100, $113,600 and $151,100 at the end of Years 1, 2 & 3 respectively we get the PVs as $71,123, $99,218 and $123,343 for Year 1, 2 & 3 respectively. Adding the PVs we get $293,684 which is the present value of the obligation.

4-a. In transaction (c), the amount of equal annual payment to be paid on the note would be $34,244

Using the FVA of $1 table for Year 5 for 7% interest we get the factor of 0.2439 which when multiplied by the note amount which is $175,500 - $35,100 i.e. $ 140,400 gives the annuity amount of $34,244 which is the annual amount to be paid at the end of every year for 5 years.

4-b. The total amount of interest expense that will be incurred would be ($34,244 x 5) - $140,400 = $30,820