Financial and Managerial Accounting

Business

Quiz 27 :

The Time Value of Money: Future Amounts and Present Values

Quiz 27 :

The Time Value of Money: Future Amounts and Present Values

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Explain what is meant by the phrase time value of money.
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Time value of money is an important concept and is used for making several business decisions specially when evaluating an investment prospect.
The concept of the time value of money assumes future amount always higher than present value, and value of a dollar today always higher than a dollar in a future date.
In investment decision the most fundamental concept is the time value of money. Under this concept we consider the amount of money available today can be invested today for higher amount in the future. Hence, we can consider value of money available today is equivalent to the higher amount would be available in the future date. In other words, time value of money is the concept of equivalent value of different amount of money between two point of time. These amount of money at two different point of time are considered as present value (money available today) and future amount (higher amount in the future).
Example:
Mr. A invest today $1,000 safely in bank at the interest rate of 5% per annum for two years. After 2 years Mr. A will get higher accumulated amount of principal amount and interest on the investment.
img img Thus, Mr. A will get future amount $1,102.5 after 2 years.

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Using Future Amount Tables Use Table FA-1 (in Exhibit B-2) and Table FA-2 (in Exhibit B-4) to determine the future amounts of the following investments: a. $50,000 is invested for 10 years, at 6 percent interest, compounded annually. b. $240,000 is to be received five years from today, at 10 percent annual interest. c. $20,000 is invested in a fund at the end of each of the next 10 years, at 8 percent interest, compounded annually. d. $80,000 is invested initially, plus $6,000 is invested annually at the end of each of the next three years, at 12 percent interest, compounded annually. EXHIBIT B-2 The Future Value of $1 img EXHIBIT B-4 Future Value of an Ordinary Annuity img
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The concept, time value of money is based on the analogy that an amount of money available today is equal to a larger sum of money after a period of time. For example, an amount of Rupees 100 available today is equal to a sum of money more than Rs100 basing upon the discounting rates. The amount available today is known as present value of money and the amount available on a future date is known as future value of money.
a.
Future amount = Present value X Factor
Future value of $50,000 invested today for 10 years at 6% interest,
compounded annually = $50,000 X 1.791 = $89,550
b.
Present value = Future amount / Factor
Present value of $240,000 to be received after a period of 5 years from today at 10% annual interest = $240,000 / 1.611 = $148,976
c.
Future amount of an annuity = Periodic payment X Factor
Future value of $20,000 invested annually at the end of each of the next 10 years at 8% interest, compounded annually = $20,000 X 14.487 = $289,740
d.
Future amount = Present value X Factor
Future amount of an annuity = Periodic payment X Factor
Future value of $80,000 invested today for 3 years at 12% interest,
compounded annually = $80,000 X 1.405 = $112,400
Future value of $6,000 invested annually at the end of each of the next 3 years at 12% interest, compounded annually = $6,000 X 3.374 = $20,244

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Explain why the present value of a future amount is always less than the future amount.
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Reason for the lower value of present value of future amount than the future amount:
• The interest factor is the main reason for the difference between the lower values of the present value of the future amount as compared to future value. The time value of money is based on the fact that a dollar received today is worthiest than a dollar to be received in future.
• The reason behind this is the dollar received today can be saved or invested and will be worth more than a dollar a year from today. Hence, the dollar to be received one year from today is currently worth less than a dollar today.

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Tilman Company is required by a bond indenture to make equal annual payments to a bond sinking fund at the end of each of the next 20 years. The sinking fund will earn 8 percent interest and must accumulate to a total of $500,000 at the end of the 20-year period. Instructions a. Calculate the amount of the annual payments. b. Calculate the total amount of interest that will be earned by the fund over the 20-year period. c. Make the general journal entry to record redemption of the bond issue at the end of the 20-year period, assuming that the sinking fund is recorded on Tilman's accounting records at $500,000 and bonds payable are recorded at the same amount. d. What would be the effect of an increase in the rate of return on the required annual payment? Explain.
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Identify the two factors that determine the difference between the present value and the future amount of an investment.
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Use Table PV-1 (in Exhibit B-7) and Table PV-2 (in Exhibit B-9) to determine the present values of the following cash flows: a. $15,000 to be paid annually for 10 years, discounted at an annual rate of 6 percent. Payments are to occur at the end of each year. b. $9,200 to be received today, assuming that the money will be invested in a two-year certificate of deposit earning 8 percent annually. c. $300 to be paid monthly for 36 months, with an additional "balloon payment" of $12.000 due at the end of the thirty-sixth month, discounted at a monthly interest rate of img percent. The first payment is to be one month from today. d. $25,000 to be received annually for the first three years, followed, by $15,000 to be received annually for the next two years (total of five years in which collections are received), discounted at an annual rate of 8 percent. Assume collections occur at year-end.
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Describe three basic investment applications of the concept of the time value of money.
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Present Value and Bond Prices On June 30 of the current year, Rural Gas Electric Co. issued $60,000,000 face value, 9 percent, 10-year bonds payable, with interest dates of December 31 and June 30. The bonds were issued at a discount, resulting in an effective semiannual interest rate of 5 percent. Instructions a. Compute the issue price for the bond that results in an effective semiannual interest rate of 5 percent. (Hint: Discount both the interest payments and the maturity value over 20 semiannual periods.) b. Prepare a journal entry to record the issuance of the bonds at the sales price you computed in part a. c. Explain why the bonds were issued at a discount.
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Briefly explain the relationships between present value and (a) the length of time until the future cash flow occurs, and (b) the discount rate used in determining present value.
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On December 1, Showcase Interiors purchased a shipment of furniture from Colonial House by paying $10,500 cash and issuing an installment note payable in the face amount of $28,800. The note is to be paid in 24 monthly installments of $ 1,200 each. Although the note makes no mention of an interest charge, the rate of interest usually charged to Showcase Interiors in such transactions is img percent per month. Instructions a. Compute the present value of the note payable, using a discount rate of img percent per month. b. Prepare the journal entries in the accounts of Showcase Interiors on: 1. December 1, to record the purchase of the furniture (debit Inventory). 2. December 31, to record the first $1,200 monthly payment on the note and to recognize interest expense for one month by the effective interest method. (Round interest expense to the nearest dollar.) c. Show how the liability for this note would appear in the balance sheet, at December 31. (Assume that the note is classified as a current liability.)
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Define financial instruments. Explain the valuation concept used in initially recording financial instruments in financial statements.
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Capital Leases: A Comprehensive Problem Custom Truck Builders frequently uses long-term lease contracts to finance the sale of its trucks. On November 1, 2015, Custom Truck Builders leased to Interstate Van Lines a truck carried in the perpetual inventory records at $33,520. The terms of the lease call for Interstate Van Lines to make 36 monthly payments of $1,400 each, beginning on November 30, 2015. The present value of these payments, after considering a built-in interest charge of 1 percent per month, is equal to the regular $42,150 sales price of the truck. At the end of the 36-month lease, title to the truck will transfer to Interstate Van Lines. Instructions a. Prepare journal entries for 2015 in the accounts of Custom Truck Builders on: 1. November 1, to record the sale financed by the lease and the related cost of goods sold. (Debit Lease Payments Receivable for the $42,150 present value of the future lease payments.) 2. November 30, to record receipt of the first $1,400 monthly payment. (Prepare a compound journal entry that allocates the cash receipt between interest revenue and reduction of Lease Payments Receivable. The portion of each monthly payment recognized as interest revenue is equal to 1 percent of the balance of the account Lease Payments Receivable, at the beginning of that month. Round all interest computations to the nearest dollar.) 3. December 31, to record receipt of the second monthly payment. b. Prepare journal entries for 2015 in the accounts of Interstate Van Lines on: 1. November 1, to record acquisition of the leased truck. 2. November 30, to record the first monthly lease payment. (Determine the portion of the payment representing interest expense in a manner parallel to that described in part a. ) 3. December 31, to record the second monthly lease payment. 4. December 31, to recognize depreciation on the leased truck through year-end. Compute depreciation expense by the straight-line method, using a 10-year service life and an estimated salvage value of $6,150. c. Compute the net carrying value of the leased truck in the balance sheet of Interstate Van Lines at December 31, 2015. d. Compute the amount of Interstate Van Lines's lease payment obligation at December 31, 2015.
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Are normal accounts receivable and accounts payable financial instruments? Are these items shown in the balance sheet at their present values? Explain.
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On December 31. Richland Farms sold a tract of land, which had cost $930,000, to Skyline Developers in exchange for $150,000 cash and a five-year, 4 percent note receivable for $900,000. Interest on the note is payable annually, and the principal amount is due in five years. The accountant for Richland Farms did not notice the unrealistically low interest rate on the note and made the following entry on December 31 to record this sale. img Instructions a. Compute the present value of the note receivable from Skyline Developers at the date of sale, assuming that a realistic rate of interest for this transaction is 12 percent. (Hint: Consider both the annual interest payments and the maturity value of the note.) b. Prepare the journal entry on December 31 to record the sale of the land correctly. Show supporting computations for the gain or loss on the, sale. c. Explain what effects the error made by Richland Farms's accountant will have on ( 1 ) the net income in the year of the sale arid.( 2 ) the combined net income of the next five years. Ignore income taxes.
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Assuming no change in the expected amount of future cash flows, what factors may cause the present value of a financial instrument to change? Explain fully.
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