Question

P9-11 (Algo) Computing Present Values LO9-7, 9-8

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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. Promised to pay a fixed amount of $7,700 at the end of each year for eight years and a one-time payment of $118,400 at the end of the 8th year.
2. Established a plant remodeling fund of $492,550 to be available at the end of Year 9. A single sum that will grow to $492,550 will be deposited on January 1 of this year.
3. Agreed to pay a severance package to a discharged employee. The company will pay $76,700 at the end of the first year, $114,200 at the end of the second year, and $151,700 at the end of the third year.
4. Purchased a $178,500 machine on January 1 of this year for $35,700 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 transactions (1-4), determine the present value of the debt. (Round your answer to nearest whole dollar.)

	Present value

Answer 1

Solution :-

A)

A sum of $7,700 is to be paid at the end of each year for 8 years and the principal amount $118,400 to be paid at the end of 8th year.

PV = $7,700/(1+0.07) + $7,700/(1+0.07)2 + $7,700/(1+0.07)3 + $7,700/(1+0.07)4 + $7,700/(1+0.07)5 + $7,700/(1+0.07)6 + $7,700/(1+0.07)7 + $7,700/(1+0.07)8 + $118,400/(1+0.07)8

PV = $7196.26 + $6725.48 + $6285.49 + $5874.293 + $5489.99 + $5130.835 +

$4795.173 + $4481.47 + $68909.9

PV = $114,889

B)

Let the single sum that will grow to $492,550 at 7% interest per annum at the end of 9 years be X

FV=PV(1+i)^n

$492,550 = X * (1+0.07)9

Thus,

X= $492,550 / (1.07)9

X = $492,550 / 1.8385

X = $267,914.6

Thhus, a single sum of $267,914.6 needs to be deposited for 9 years at 7% interest p.a.

C)

PV = $76,700 / (1.07) + $114,200 / (1.07)2 + 151,700 / (1.07)3

PV = $71,682.24 + $99,746.7 + 123,832.4

Present Value of obligation = $295,261.3

D)

Value of Machine today = 178,500

Paid in Cash today = 35,700

Remaining amount Repaid = 178,500 - 35,700 = 142,800

Interest Amount = 7%

Repiad in years = 5

Installment amount = 142,800 / PVAF(7% , 5 ) = 142,800 / 4.1002 = 34,827.59

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