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Flashcards in Present Value Fundamentals Deck (15):
1

White Airlines sold a used jet aircraft to Brown Company for $800,000, accepting a 5-year 6% note for the entire amount. Brown’s incremental borrowing rate was 14%. The annual payment of principal and interest on the note was to be $189,930. The aircraft could have been sold at an established cash price of $651,460. The present value of an ordinary annuity of $1 at 8% for five periods is 3.99. The aircraft should be capitalized on Brown’s books at

  1. $651,460
  2. $757,820
  3. $800,000
  4. $949,650

$651,460

Brown’s 14% incremental borrowing rate is significantly higher than the stated rate of 6%. Therefore, the stated rate is unreasonable and the acquisition should not be recorded at the face value ($800,000) of the note. The cost of the aircraft is the present value of the note and stated interest payments discounted at 14% or the fair market value of the aircraft, whichever is more clearly evident. Since the aircraft has an established cash price of $651,460, this amount is an appropriate basis for recording the transaction.

2

On January 1, year 1, Robert Harrison signed an agreement to operate as a franchisee of Perfect Pizza, Inc. for an initial franchise fee of $40,000.  Of this amount, $15,000 was paid when the agreement was signed and the balance is payable in five annual payments of $5,000 each beginning January 1, year 2. The agreement provides that the down payment is not refundable and no future services are required of the franchisor.  Harrison’s credit rating indicates that he can borrow money at 12% for a loan of this type.  Information on present and future value factors is as follows:

  • Present value of $1 at 12% for 5 periods .567
  • Future amount of $1 at 12% for 5 periods 1.762
  • Present value of an ordinary annuity of $1 at 12% for 5 periods 3.605

Harrison should record the acquisition cost of the franchise on January 1, year 1, at

  1. $29,175
  2. $33,025
  3. $40,000
  4. $44,050

$33,025

This answer is correct.  The acquisition cost is equal to the $15,000 down payment plus the present value of the $25,000 loan.  The loan is payable in 5 equal installments of $5,000 at the end of each year (ordinary annuity).

  • Down payment on 1/1/Y1$  15,000
  • Present value of ordinary annuity ($5,000 × 3.605) $18,025
  • Total acquisition cost $33,025

3

On January 1, year 1, Duripan Corp. invested $10,000 in 5-year certificates of deposit at 8% interest. Future value factors are as follows:

  • Future amount of $1 at 8% for 5 periods1.469
  • Future amount of $1 at 10% for 5 periods1.611
  • Future amount of an ordinary annuity of $1 at 8% for 5 periods5.867
  • Future amount of an ordinary annuity of $1 at 10% for 5 periods6.105

Assume that Duripan does not elect the fair value option to report its financial assets.  What will be the maturity value of these CDs, assuming that the market interest rate at maturity is 10%?

  1. $14,690
  2. $16,110
  3. $58,670
  4. $61,050

$14,690

If Duripan does not elect the fair value option to report financial assets, the market rate of interest at maturity is irrelevant because the $10,000 was invested at a fixed rate of 8%. Since a single lump-sum amount was invested, the future value factor at 8% for 5 periods is used. Therefore, the value of the investment at maturity is $14,690 ($10,000 x 1.469).

4

On January 1, year 2, Dorr Company borrowed $200,000 from its major customer, Pine Corporation, evidenced by a note payable in 3 years. The promissory note did not bear interest. Dorr agreed to supply Pine’s inventory needs for the loan period at favorable prices. The going rate of interest for this type of loan is 14%. Assume that the present value (at the going rate of interest) of the $200,000 note is $135,000 at January 1, year 2. What amount of interest expense should be included in Dorr’s year 2 income statement?

  1. $0
  2. $18,900
  3. $21,667
  4. $28,000

$18,900

This answer is correct.  ASC Topic 835 requires that the liability should be recorded at its present value by establishing a discount account.  The difference between cash proceeds and the present value of the note is credited to an unearned income account, which is recognized as revenue as the agreement is fulfilled.

  • Cash 200,000 
  • Discount on N/P 65,000 
    •  Note payable 200,000
    •  Unearned income 65,000

Interest expense is then recognized using the effective interest method.  For year 2, interest expense is equal to the present value of the note ($135,000) times the effective interest rate (14%), or $18,900.  The unearned income will be recognized as sales as the inventory is sold to Pine Corporation at favorable prices.

5

Esmond Bank approves a 10-year loan to Matt Schweitzer. In doing so, Esmond Bank incurs $2,000 of loan origination costs (attorney fees, title insurance, wages of employees’ direct work on loan origination). The loan origination fees shall be

  1. Deferred and recognized upon final payment of the loan.
  2. Reported as service fee income.
  3. Deferred and recognized over the life of the loan as an adjustment of yield (interest income).
  4. Recognized as revenue when the loan is granted.

Deferred and recognized over the life of the loan as an adjustment of yield (interest income).

The lender shall defer and recognize loan origination costs over the life of the loan when the costs relate directly to the loan and would not have been incurred but for the loan.

6

On September 30, World Co. borrowed $1,000,000 on a 9% note payable. World paid the first of four quarterly payments of $264,200 when due on December 30. In its income statement for the year, what amount should World report as interest expense?

  1. $0
  2. $14,200
  3. $22,500
  4. $30,000

$22,500

The requirement is to determine the amount of interest expense that should be accrued. Interest expense is calculated as $1,000,000 x 9% x 3/12 months = $22,500.

7

A loan is granted in the amount of $500,000 with a stated interest rate of 10%. The lender incurs direct loan origination costs of $10,000 and charges the borrower a 3-point nonrefundable fee. The effective interest rate to the lender will be

  1. 10%
  2. Less than 10%
  3. Greater than 10%
  4. Greater than 9% but less than 10%.

Greater than 10%

The lender has a carrying amount of $495,000. This reflects the $500,000 less the $15,000 nonrefundable fee plus the $10,000 loan origination costs. A carrying amount less than the face amount will yield an effective interest rate greater than the stated interest rate of 10%.

Sometimes the lender incurs various loan origination costs when originating or acquiring a loan. According to ASC Subtopic 310-20, the lender shall defer and recognize these costs over the life of the loan only when the costs relate directly to the loan, and would not have been incurred but for the loan. Otherwise, the costs are considered indirect and are charged to expense as incurred.

Sometimes the lender charges the borrower a nonrefundable loan origination fee. According to ASC Subtopic 310-20, both lender and borrower shall defer and recognize the nonrefundable fee over the life of the loan. The fee is frequently assessed in the form of points, where a point is 1% of the face amount of the loan.

For example, assume that Bannon Bank grants a 10-year loan to VerSteiner, Inc. in the amount of $100,000 with a stated interest rate of 8%. Payments are due monthly, and are computed to be $1,213. In addition, Bannon Bank incurs $3,000 of direct loan origination costs (attorney’s fees, title insurance, wages of employees’ direct work on loan origination), and also charges VerSteiner a 5-point nonrefundable loan origination fee.

Bannon Bank, the lender, has a carrying amount of $98,000. This reflects the $100,000 face amount of the loan less the $5,000 nonrefundable fee, plus the $3,000 additional investment Bannon Bank incurs to generate the $145,560 total payments from the borrower, VerSteiner. The effective interest rate is approximately 8.5%.

VerSteiner, the borrower, receives 5% less than the face amount of $100,000, or $95,000, but is still required to pay $1,213 per month under the terms of the loan. VerSteiner’s carrying amount is then $100,000 – $5,000 = $95,000, with an effective interest rate of approximately 9.2%.

8

On January 1, year 1, Mill Co. exchanged equipment for a $200,000 noninterest-bearing note due on January 1, year 4. The prevailing rate of interest for a note of this type at January 1, year 1, was 10%. The present value of $1 at 10% for three periods is 0.75. What amount of interest revenue should be included in Mill’s year 2 income statement?

  1. $0
  2. $15,000
  3. $16,500
  4. $20,000

$16,500

Per ASC Topic 835, when property is exchanged for a note and neither the property nor the note has a known fair market value, interest is imputed using the prevailing rate of interest for a note of similar quality. Therefore, the note should be recorded at its present value of $150,000 ($200,000 × .75) by debiting notes receivable for $200,000 and crediting discount on notes receivable for $50,000 ($200,000 – $150,000).  ASC Topic 835 states that the discount should be amortized and recognized as interest revenue over the life of the note using the interest method.  Under the interest method, interest revenue/expense equals the carrying value of the note multiplied by the imputed interest rate.  For year 1, interest revenue is $15,000 ($150,000 × 10%). Discount on notes receivable is debited for the amount of interest revenue recognized ($15,000) which increases the carrying value of the notes to $165,000.  Thus, interest revenue reported in year 2 is $16,500 ($165,000 × 10%).

9

On November 1, year 1, a company purchased a new machine that it does not have to pay for until November 1, year 3. The total payment on November 1, year 3, will include both principal and interest. Assuming interest at a 10% rate, the cost of the machine would be the total payment multiplied by what time value of money concept?

  1. Present value of annuity of 1.
  2. Present value of 1.
  3. Future amount of annuity of 1.
  4. Future amount of 1.

Present value of 1.

The requirement is to determine what time value of money concept would be used to determine the cost of a machine when a payment (principal plus interest) is to be made in 2 years. Because the cost of the machine is to be recorded immediately, the cost of the present value of a lump-sum payment would be used.

10

Which of the following transactions would require the use of the present value of an annuity due concept in order to calculate the present value of the asset obtained or liability owed at the date of incurrence?

  1. A capital lease is entered into with the initial lease payment due upon the signing of the lease agreement.
  2. A capital lease is entered into with the initial lease payment due 1 month subsequent to the signing of the lease agreement.
  3. A 10-year 8% bond is issued on January 2 with interest payable semiannually on July 1 and January 1 yielding 7%.
  4. A 10-year 8% bond is issued on January 2 with interest payable semiannually on July 1 and January 1 yielding 9%.

A capital lease is entered into with the initial lease payment due upon the signing of the lease agreement.

An annuity due is an annuity with the first payment occurring at the beginning of the first period. In contrast, an ordinary annuity is an annuity with the first payment occurring at the end of the first period. This answer is an example of an annuity due.

11

Gold Co. purchased equipment from Marshall Co. on July 1. Gold paid Marshall $10,000 cash and signed a $100,000 noninterest-bearing note payable, due in three years. Gold recorded a $24,868 discount on notes payable related to this transaction. What is the acquired cost of the equipment on July 1?

  1. $75,132
  2. $85,132
  3. $100,000
  4. $110,000

$85,132

Facts state that $10,000 cash was paid and a long-term noninterest bearing note ($100,000 with a $24,868 discount) was given. If a note (receivable or payable) has a life longer than one year, it should be recorded at its present value. Therefore, the acquisition cost of the equipment would be equal to $85,132 = $10,000 + $75,132 ($100,000 − $24,868).

12

On January 1, year 1, Beal Corporation adopted a plan to accumulate funds for a new plant building to be erected beginning July 1, year 6, at an estimated cost of $1,200,000.  Beal intends to make five equal annual deposits in a fund that will earn interest at 8% compounded annually.  The first deposit is made on July 1, year 1.  Present value and future amount factors are as follows:

  • Present value of 1 at 8% for 5 periods 0.68
  • Present value of 1 at 8% for 6 periods 0.63
  • Future amount of ordinary annuity of 1 at 8% for 5 periods 5.87
  • Future amount of annuity in advance of 1 at 8% for 5 periods 6.34

Beal should make five annual deposits (rounded) of

  1. $151,200
  2. $163,200
  3. $189,300
  4. $204,400

$189,300

The desired fund balance on July 1, year 6 ($1,200,000) is a future amount.  The series of five equal annual deposits is an annuity in advance.  Whether this is an ordinary annuity or an annuity in advance can be determined by looking at the last deposit.  The last deposit (7/1/Y5)) is made one year prior to the date the future amount is needed.  Therefore, these are beginning-of-year payments, and this is an annuity in advance.  The deposit amount is computed below.
 

           Future amount 
           F.A. factor=$1,200,000 
     6.34=$189,274

13

Able, Inc. had the following amounts of long-term debt outstanding at December 31, year 1:

  • 14 1/2% term note, due year 2 $3,000
  • 11 1/8% term note, due year 5 107,000
  • 8% note, due in 11 equal annual principal payments, plus interest beginning December 31, year 2 $110,000
  • 7% guaranteed debentures, due year 6 $100,000
  • = Total $320,000

Assume Able does not elect the fair value option to value financial liabilities.  Able’s annual sinking-fund requirement on the guaranteed debentures is $4,000 per year.  What amount should Able report as current maturities of long-term debt in its December 31, year 1 balance sheet?

  1. $4,000
  2. $7,000
  3. $10,000
  4. $13,000

$13,000

The portion of bonds, notes, and other long-term debt that matures within the next year is called current maturities of long-term debt and is reported as a current liability. When only a part of certain long-term debt is to be paid in the next 12 months (such as with installment notes or serial bonds), the maturing part is reported as current and the balance as long-term. Therefore, Able should report $13,000 as current maturities of long-term debt ($3,000 note due in year 2, plus $10,000 installment of 8% note due in year 2). The sinking fund requirement ($4,000) is not debt.

14

On December 27, year 1, Holden Company sold a building, receiving as consideration a $400,000 noninterest bearing note due in 3 years. The building cost $380,000 and the accumulated depreciation was $160,000 at the date of sale. The prevailing rate of interest for a note of this type was 12%. The present value of $1 for three periods at 12% is 0.71. In its year 1 income statement, how much gain or loss should Holden report on the sale?

  1. $20,000 gain.
  2. $64,000 gain.
  3. $96,000 loss.
  4. $180,000 gain.

$64,000 gain.

The gain (loss) is the difference between the value of the consideration received and the book value of the building sold.  The consideration received is a 3-year, noninterest-bearing, $400,000 note. Per ASC Topic 835, such receivable is to be recorded at its present value.

  • Note receivable $400,000 
  • Accum. depr. $160,000 
    • Discount on N/R $116,000
    • Building $380,000
    • Gain $64,000

15

On January 1, year 2, the Carpet Company lent $100,000 to its supplier, Loom Corporation, evidenced by a note, payable in 5 years. Interest at 5% is payable annually with the first payment due on December 31, year 3. The going rate of interest for this type of loan is 10%. The parties agreed that Carpet’s inventory needs for the loan period will be met by Loom at favorable prices. Assume that the present value (at the going rate of interest) of the $100,000 note is $81,000 at January 1, year 2. What amount of interest income, if any, should be included in Carpet’s year 2 income statement?

  1. $0
  2. $4,050
  3. $5,000
  4. $8,100

$8,100

The solutions approach is to recognize that (1) a note has been issued for cash and a future benefit, and (2) the provision for interest on the loan is not reasonable (per ASC Topic 835). The difference between the face value of the note ($100,000) and its present value ($81,000) represents interest on notes receivable of $19,000. Using an effective interest approach, interest income for Carpet is computed as follows:

  • $81,000 (carrying value of note) x 10% (imputed interest rate) = $8,100 interest income