Question

At the beginning of 2018, VHF Industries acquired a equipment with a fair value of $9,112,050 by issuing a four-year, noninterest-bearing note in the face amount of $12 million. The note is payable in four annual installments of $3 million at the end of each year. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) Required: 1. What is the effective rate of interest implicit in the agreement? 2. to 4. Prepare the necessary journal entry. 5. Suppose the market value of the equipment was unknown at the time of purchase, but the market rate of interest for notes of similar risk was 11%. Prepare the journal entry to record the purchase of the equipment.

Answer 1

1) we can use the present value of an ordinary annuity formula to calculate the effective interest rate:

present value = annual payment x PV annuity factor (%, 4 periods)

9,112,050 = 3,000,000 x PV annuity factor (%, 4 periods)

PV annuity factor (%, 4 periods) = 9,112,050 / 3,000,000 = 3.03735

using a present value table, the % for 4 periods = 12%

2 to 4) January 2, 2018, equipment purchased by issuing non-interest-bearing note

Dr Equipment 9,112,050

Dr Discount on notes payable 2,887,950

Cr Notes payable 12,000,000

December 31, 2018, first installment paid on notes payable

Dr Notes payable 3,000,000

Dr Interest expense 1,093,446

Cr Cash 3,000,000

Cr Discount on notes payable 1,093,446

interest expense = 9,112,050 x 12% = 1,093,446

December 31, 2019, second installment paid on notes payable

Dr Notes payable 3,000,000

Dr Interest expense 864,660

Cr Cash 3,000,000

Cr Discount on notes payable 864,660

interest expense = 7,205,496 x 12% = 864,659.52 ≈ 864,660

December 31, 2020, third installment paid on notes payable

Dr Notes payable 3,000,000

Dr Interest expense 608,419

Cr Cash 3,000,000

Cr Discount on notes payable 608,419

interest expense = 5,070,156 x 12% = 608,418.72 ≈ 608,419

December 31, 2021, fourth installment paid on notes payable

Dr Notes payable 3,000,000

Dr Interest expense 321,425

Cr Cash 3,000,000

Cr Discount on notes payable 321,425

5) present value of equipment = 3,000,000 x 3.1024 (PV annuity factor, 115, 4 periods) = 9,307,200

Dr Equipment 9,307,200

Dr Discount on notes payable 2,692,800

Cr Notes payable 12,000,000