On January 1, 2014, Boston Company completed the following transactions (use a 7
ID: 2446843 • Letter: O
Question
On January 1, 2014, Boston Company completed the following transactions (use a 7 percent 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 $115,000 for seven years. Will pay $6,000 interest at the end of each year and repay the $115,000 at the end of the 7th year.
Established a plant addition fund of $490,000 to be available at the end of year 8. A single sum that will grow to $490,000 will be deposited on January 1, 2014.
Agreed to pay a severance package to a discharged employee. The company will pay $75,000 at the end of the first year, $112,500 at the end of the second year, and $150,000 at the end of the third year.
Purchased a $170,000 machine on January 1, 2014, and paid cash, $34,000. A five-year note payable is signed for the balance. The note will be paid in five equal year-end payments starting on December 31, 2014.
1. In transaction (a), determine the present value of the debt.
2-a. In transaction (b), what single sum amount must the company deposit on January 1, 2014?
2-b. What is the total amount of interest revenue that will be earned?
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?
On January 1, 2014, Boston Company completed the following transactions (use a 7 percent 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.)
Explanation / Answer
a) A sum of $6,000 is to be paid at the end of each year for 7 years and the principal amount $115,000 to be paid at the end of 7th year.
PV=$6,000/(1+0.07)^1 + $6,000/(1+0.07)^2 +$6,000/(1+0.07)^3 +$6,000/(1+0.07)^4 +$6,000/(1+0.07)^5 +$6,000/(1+0.07)^6 +$6,000/(1+0.07)^7 +$115,000/(1+0.07)^7
PV=$5,607.47 + $5,240.63 + $4,897.78 + $4,577.37 + $4,277.91 + $3,998.05 + $3,736.49 + $71,616.22
PV=$103,951.92
b) Let the single sum that will grow to $490,000 at 7% interest per annum at the end of 8 years be X
FV=PV(1+i)^n
$490,000 = X(1+0.07)^8
Thus,
X= $490,000/(1.07)^8
X = $490,000/1.7182
X = $285,182
Thhus, a single sum of $285,182 needs to be deposited for 8 years at 7% interest p.a.
The total amount of interest revenue is ($490,000-$285,182) = $204,818
c) PV = $75,000/(1.07)^1 + $112,500/(1.07)^2 + 150,000/(1.07)^3
PV = $70,093.45 + $98,261.85 + $122,444.68
= $290,800
FV =$75,000*(1.07)^1 + $112,500*(1.07)^2 + 150,000*(1.07)^3
= $80,250 + $85,867 + $91,878
= $257,995
d) The cost of the machine is $170,000. Immediate cash paid $34,000. Loan Amount is ($170,000-$34,000)=$136,000
The PVA factor at 7% p.a compounded annually for 5 years is 4.1002
Thus, the PMT = 136,000/4.1002
= $33,169
Thus, the amount of each annual payment is $33,169 for 5 years.
The total amount to be paid is ($34,000+$33,169*5)
=$34,000+$165845
=$199845
The interest expense is ($199845 - $170,000)
= $29,845
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