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.)

a. 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.
b. Established a plant remodeling 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 of this year.
c. 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.
d. Purchased a $170,000 machine on January 1 of this year for $34,000 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 the nearest whole dollar.)
2. In transaction (c), determine the present value of this obligation. (Round your answer to the nearest whole dollar.)
3-a. In transaction (d), what is the amount of each of the equal annual payments that will be paid on the note? (Round your answer to the nearest whole dollar.)
3-b. What is the total amount of interest expense that will be incurred? (Round your answer to the nearest whole dollar.)

Answer 1

1 PV: $ 103,951.96

2 PV) $ 290.800‬

3) a: $ 30,999.19

b: $ 18.995,95‬

Step-by-step explanation:

We have an annuity of 6,000 for 6 year plus a maturity of 115,000 at the end of the year

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 6,000.00

time 7

rate 0.07

`6000 * (1-(1+0.07)^(-7) )/(0.07) = PV\\`

PV $32,335.7364

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity $115,000.00

time 7.00

rate 0.07000

`(115000)/((1 + 0.07)^(7) ) = PV`

PV 71,616.2203

Total: $103,951.9567

we solve for the pv of each:

`(75000)/((1 + 0.07)^(1) ) = PV`

PV 70,093.4579

`(112500)/((1 + 0.07)^(2) ) = PV`

PV 98,261.8569

`(150000)/((1 + 0.07)^(3) ) = PV`

PV 122,444.6815

Total: 290.800‬

3) We have to solve for the balance and th n the installment

170,000 - 34,000 = 136,000

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 136,000.00

time 5

rate 0.07

`136000 / (1-(1+0.07)^(-5) )/(0.07) = C\\`

C $ 30,999.191

Interst: 30,999.19 x 5 - 136,000 = 18.995,95‬

Answer 2

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