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.)

1. Borrowed $115,200 for eight years. Will pay $6,100 interest at the end of each year and repay the $115,200 at the end of the 8th year.
2. Established a plant remodeling fund of $490,150 to be available at the end of Year 9. A single sum that will grow to $490,150 will be deposited on January 1 of this year.
3. Agreed to pay a severance package to a discharged employee. The company will pay $75,100 at the end of the first year, $112,600 at the end of the second year, and $150,100 at the end of the third year.
4. Purchased a $170,500 machine on January 1 of this year for $34,100 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.

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

Solution:

1)

A sum $ 6,100 is to be paid at the end of each yer for 8 years and the principal amount $115,200 to be paid at the end of 8th year.

PV = $6,200/(1+0.08)^1 + $6,200/(1+0.08)^2 + $6,200/(1+0.08)^3 + $6,200/(1+0.08)^4 + $6,200/(1+0.08)^5 +$6,200/(1+0.08)^6 + $6,200/(1+0.08)^7 + $115,200/(1+0.08)^8

PV = $5,740.74 + 5,315.50 + 4,921.75 + 4,557.18 + 4,219.61 + 3,907.05 + 3,617.64 + 62,238.97

PV = $94,518.44

2a)

Let the single sum that will grow to $ 490,150 at 8% interest per annum at the end of 9 years be X

Fv = PV(1+i)^n

$490,150 = X(1+0.08)^9

X = $490,150/(1.07)^8

X = $490,150/1.7182

X = $285,269.468

Thus a single sum of $285,269.468 needs to be deposited for 9 years at 8% interest p a

2b)

The total amount of interest revenue is ($490,150 - $285,269) = $ 204,881

3)

PV = $75,100/(1.08)^1 + $112,600/(1.08)^2 + $150,100/(1.08)^3

PV = $69,537.58 + 96,536.14 + 119,154.43

PV = $285,230

Fv = $75,100*(1.08)^1 + $112,600*(1.08)^2 + $150,100*(1.08)^3

FV = $81,108 + $131,336 + 189,082

FV =$ 401,526

4a)

The cost of the machine is $170,500 immediate cash paid $34,100 . Loan amount is ($170,500 - $34,100) = $136,400

The PVA factor at 8% p.a compunded annually for 5 year is 4.1002

Thus , PMT = 136,400/4.1002

=$ 33,266

Thus the amount of each annual payment is $33,266 for 5 years

The total amount to be paid is ($34,100 + $33,266*5)

=$34,100 + 166,330

=$ 200,430

The interest expense is ($200,430 - $170,500)

=$29,930