Assets



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Stephen’s Storage Company: Long-term mortgage

a. $100,000 .09 = $9,000 interest expense.

b. $98,000 (=$100,000 – $2,000)

c. $98,000 .09 = $8,820 interest expense.

d. $95,820 (=$98,000 – $2,180)

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Grace’s Gems: Quarterly amortization of loan

|a. |Quarter |Carrying |Carrying Value .02 | |New Carrying |

| |Ending |Value |= Interest Expense |Payment |Value |

| |March 30 |$80,000.00 |$1,600.00 |$2,925 |$78,675.00 |

| |June 30 |$78,675.00 |$1,573.50 |$2,925 |$77,323.50 |

| |Sept. 30 |$77,323.50 |$1,546.47 |$2,925 |$75,944.97 |

| |Dec.31 |$75,944.97 |$1,518.90 |$2,925 |$74,538.87 |

b. Sum of the quarterly expenses = $1,600.00 + $1,573.50 + $1,546.47 + $1,518.90 = $6,238.87

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Calculating payments for various loans

1. PV(A) = PMT (factor for 5 periods, 7.5%)

OR

Using a financial calculator, we would input the following information for the truck:

Enter $30,000 and press PV for present value

Enter 0 and press FV for future value

Enter 7.5/12 or .625 and press I% for the interest rate per period

Enter 60 and press n for number of periods, monthly payments for 5 years.

Now we can press CPT and then PMT. Your answer should be $601.14 for the payment amount.

2. PV(A) PMT (factor for 5 periods, 10%)

OR

Using a financial calculator, we would input the following information for the land:

Enter $25,000 and press PV for present value

Enter 0 and press FV for future value

Enter 10 and press I% for the interest rate per period

Enter 5 and press n for number of periods, annual payments for 5 years.

Now we can press CPT and then PMT. Your answer should be $6,594.94 for the payment amount.

3. PV(A) = PMT (factor for 8 periods, 2%)

OR

Using a financial calculator, we would input the following information for the equipment:

Enter $4,000 and press PV for present value

Enter 0 and press FV for future value

Enter 8/4 or 2 and press I% for the interest rate per period

Enter 8 and press n for number of periods, quarterly payments for 2 years.

Now we can press CPT and then PMT. Your answer should be $546.04 for the payment amount.

4. PV(A) = PMT (Factor for 20 periods, 3.25%)

OR

Using a financial calculator, we would input the following information for the land and building:

Enter $45,000 and press PV for present value ($50,000 – $5,000 down payment)

Enter 0 and press FV for future value

Enter 6.5/2 or 3.25 and press I% for the interest rate per period

Enter 20 and press n for number of periods, semi-annual payments for 10 years.

Now we can press CPT and then PMT. Your answer should be $3,095.05 for the payment amount.

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Hewitt’s Paints: Calculating proceeds from bond issue and preparing an amortization schedule

There are two components for the bond proceeds: the annual payments and the lump sum. The equation for bond proceeds = PV (OA) + PV (lump sum).

Present Value of an ordinary annuity, for 5 years, with a market rate of 10%, PMT = $80,000 ($1,000,000 8%)

PV(OA) = PMT (factor for 5 periods, 10%)

PV(OA) = $80,000 (3.79079)

PV(OA) = $303,263.20

Present value of a future lump sum, $1,000,000, in 5 years, with a market rate of 10%

PV (lump sum) = FV (factor for 5 years, 10%)

PV (lump sum) = $1,000,000 (.62092)

PV (lump sum) = $620,920

Bond proceeds = PV (OA) + PV (lump sum) = $303,263.20

+ $620,920.00 = $924,183.20

Using this information, we can use the effective interest method to calculate the interest payments, interest expense and year-end carrying value:

| | |Carrying | |Interest | |Unamor- | |

| | |Value at |Interest |to Be | |tized | |

| | |Beginning |Expense |Paid |Amorti- |Bond |Carrying |

|Date |Period |of Period |= CV 10% |(Cash) |zation |Discount |Value |

|1/1/05 |0 | | | | |75,817 | 924,183 |

|12/31/05 |1 |924,183 |92,418 |80,000 |12,418 |63,399 | 936,601 |

|12/31/06 |2 |936,601 |93,660 |80,000 |13,660 |49,739 | 950,261 |

|12/31/07 |3 |950,261 |95,026 |80,000 |15,026 |34,713 | 965,287 |

|12/31/08 |4 |965,287 |96,529 |80,000 |16,529 |18,184 | 981,816 |

|12/31/09 |5 |981,816 |**98,184 |80,000 |18,184 | 0.00 |1,000,000 |

** The calculation is actually $98,182, but the number used is a bit larger to make the problem come out even—i.e., it’s a plug figure to get the carrying value of $1,000,000 at the end of year 5. This is needed because we rounded as we worked the problem.

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Julie’s Jewels: Bonds issued at a premium

a. Lower—that made our bonds look so good at 8% that buyers were willing to pay a premium for them.

b. $20,000 102 ½ = $20,500

c. $20,464.15 (see chart below)

| | | |Carrying | |Cash to Be | |Unamor- | |

| | | |Value at |Annual |Paid to | |tized | |

| | | |Beginning |Interest |Bond- |Amorti- |Bond |Carrying |

| |Date |Period |of Period |Expense |holders |zation |Premium |Value |

| |1/1 |0 | | | | |500.00 |20,500.00  |

| |12/31 |1 |20,500.00 |1,564.15 |1,600.00 |35.85 |464.15 |20,464.15  |

d. Interest expense gets smaller with each payment. See chart for the interest expense numbers for the first two payment dates.

| | | |Carrying Value |Semi- | | |Unamor- | |

| | | |at |annual |Interest | |tized | |

| | | |Beginning |Interest |to Be Paid |Amorti- |Bond |Carrying |

| |Date |Period |of Period |Expense |(Cash) |zation |Premium |Value |

| |7/1/X0 |0 | | | | |500.00 |20,500.00 |

| |12/31/X0 |1 |20,500.00 |782.08 |800.00 |17.92 |482.08 |20,482.08 |

| |6/30/X1 |2 |20,482.08 |781.39 |800.00 |18.61 |463.47 |20,463.47 |

e. Under straight-line, the interest expense each period would be the amount of cash paid to the bondholders minus the amortized premium. With semiannual payments, the amortization each period would be $500/20 = $25. Therefore, the interest expense each period = $800 – $25 = $775.

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