Time Value of Money EXAMPLES AND PRACTICE PROBLEMS

Transcription

1 Time Value of Money EXAMPLES AND PRACTICE PROBLEMS The following problems involve the business activities of Palouse Paper Industries. Use the compound interest tables in the textbook or a financial calculator or spreadsheet to work the following problems On July 1, Year 1, PPI issued $10 million of 20-year, 8% bonds, which paid interest semiannually. The bonds were issued to yield 10%. What were the proceeds of the bond issue? 1-2. On April 1, Year 1, PPI purchased a forklift by paying $5,000 down and $5,000 at the beginning of each of the next 19 calendar quarters. What was the cost of the forklift for financial accounting purposes if the rate of interest agreed upon was 16% compounded quarterly? 1-3. PPI needs to accumulate a $5 million trust fund with Idaho First Bank and Trust for the retirement of a bond issue in 10 years. The company plan to make 20 equal deposits of $186,078.54, starting in six months, to accumulate the $5 million fund. What annual interest rate is Idaho First Bank & Trust paying on the balance of the fund? 1-4. PPI also wants to accumulate $500,000 on December 31, Year 10, to retire some preferred stock. The company deposits $125,000 in a savings account on January 1, Year 1, which will earn interest at 6% compounded quarterly. PPI's controller asks you to figure out what additional amount PPI should deposit at the end of each quarter for 10 years to have the $500,000 available at the end of Year 10. The periodic deposits will also earn interest at the same 6% rate PPI received a promissory note from a customer in the amount of $300,000. The note calls for payment of $100,000 of principal at the end of each year, starting in three years, plus interest at the rate of 14% per year on the unpaid balance. Only interest is due at the end of the first two years. To accelerate the collection, PPI immediately discounts the note with Idaho First Bank & Trust which is charging a 12% annual interest rate. How much will PPI receive in cash from the bank? 1-6. PPI wants to make five equal annual savings account deposits beginning June 1, Year 4, in order to be able to withdraw $75,000 at six annual intervals beginning June 1, Year 9. The amount on deposit with Idaho First Bank & Trust will earn 8% per annum until the account is exhausted. The controller asks you to compute the amount of the deposits that will be needed On June 30, Year 3, PPI purchased a machine for $100,000. The downpayment was $15,000, and the balance will be paid in 48 equal monthly payments, including interest at 18% compounded monthly. What is the amount of the monthly payment if the first payment is due one month from the date of the purchase? 1-8. On April 1, Year 2, PPI made a deposit of $100,000 in a fund and left the fund undisturbed for four years to earn compound interest at a rate which did not change during the four-year period. At the end of the four years, the fund had accumulated to $132, If interest was compounded quarterly, what was the rate of interest earned each quarter? PV_examples_S10.doc Page 1 of 6

2 Assume you are confronted with the following happy circumstances. Use your knowledge of compound interest and present values to choose the alterative which makes the most sense from a financial point of view. Please do the computations even though the answer seems "obvious." 2-1. A distant relative has contacted you with a desire to help you get started with your career. She offers you your choice of $27,000 to be received in one of the following three patterns: (1) One thousand dollars at the end of each of the first three years, starting one year from now; $3,000 at the end of each of the next three years; and $5,000 at the end of each of the last three years. Your relative suggests that this might be preferable because you are young and will need more money as you get older, not only because you will learn to spend more, but also because inflation will increase your cost of living. (2) Three thousand dollars at the end of each of the next nine years, starting one year from now. Your relative points out that this option offers you the advantage of a steady cash flow. (3) Five thousand dollars at the end of each of the first three years, starting one year from now; $3,000 at the end of each of the next three years; and $1,000 at the end of each of the last three years. Your relative points out that she would not recommend this option to you because it would give you an excess of cash flow during the first three years which might raise your standard of living so that it would hurt to get less in the later years. She also points out that you could probably earn only 6% per annum while she can earn 10% annually in a bank in Singapore You have just been notified that you have won the jackpot in the Canadian lottery. You can accept your winnings in one of the following cashflow streams. Assume you are a Canadian citizen and therefore not liable for any income taxes on the winnings. Compare the alternatives assuming a long-term average interest rate on any investments of 8%. Would your answer change if you could earn only 6% or as much as 10% interest? [In other words, compare the options using 3 different interest rates] (1) $1,000,000 per year for ten years, first payment received immediately. (2) $550,000 per year for twenty years, first payment received immediately. (3) $70,000 per month for the next 15 years, beginning at the end of the first month. Note: Present Value of Ordinary Annuity interest factors for n=180 are as follows: 1/2 % /3 % /6 % PV_examples_S10.doc Page 2 of 6

3 Assume that you were recently hired at Genessee Engineering Consultants. The controller describes several recent transactions and asks you to prepare amortization or accumulation tables for each Today, we purchased a machine for $54,173. We paid $5,000 down and agreed to make six equal payments, including interest at 12% compounded semiannually, every six months starting six months from now We will need $200,000 five years from now to replace our elevator. We want to deposit five equal amounts in a fund starting one year from now so that we will have the money we need in five years. We have arranged to invest the money with Idaho First Bank and Trust at 8% compounded annually On January 1 of Year 1, we invested $37,368 with Rocky Mountain Insurance Company. The amount on deposit will earn 10% per year. We are planning to withdraw the amount on deposit in three equal annual installments beginning December 31, Year We want to accumulate $58,666 at Idaho First Bank & Trust at the end of five years by making five equal annual deposits starting one year from now. The fund will earn interest at 8% compounded annually On January 1, Year 1, we invested $199,635 at 8% compounded annually with Northwest Life. The amount invested and accrued interest are to be withdrawn in five equal installments starting on December 31, Year 1. PV_examples_S10.doc Page 3 of 6

4 Time Value of Money Problems Homework #1 You are a staff accountant at the CPA firm of Gerald & Minn. In the course of your December 31 audit engagement for Palouse Paper Industries, you are required to apply present value concepts to the following situations. (Prepare journal entries with supporting documentation for the first three situations.) 4-1. A non-interest bearing note receivable in the face amount of $120,000 and maturing in three years was received on December 31 in partial payment of an account receivable. The accountant for the company credited the customer's account for $120,000 despite a written agreement that the customer was to receive credit for the "present value of the note discounted at 8% for three years, interest compounded semiannually." 4-2. The client company had agreed to pay $10,000 per year for five years to a retiring executive. The payments, which start three years from the end of the current year, were not recorded in the accounting records. The payments were in lieu of a year-end bonus which would have been taxed at a combined federal and state income tax rate of over 50%. The company regularly borrows money at 9% per annum On April 1 of this year the company issued $1,000,000 (face value) in bonds with a coupon interest rate of 10% and received $1,124, from the investment banking firm. The first interest payment was made as scheduled on October 1, and the next is due on April 1 of next year. The bonds will mature 9 years from the date of issue. The bookkeeper didn't know what to do with the premium, and had made no accruals at December 31. Therefore, the interest paid in cash is the only charge so far to interest expense. You determine that the effective interest method should be used to record interest expense PPI wants to accumulate a fund of $100,000 in six years (from December 31 of the current year) to retire a long-term note. Three years ago, the board of directors had passed a resolution instructing the treasurer to make ten equal annual deposits in a fund earning 8% compounded annually. Because no one knew how to compute the equal deposits, the treasure decided to deposit $10,000 at the end of each year. The fourth deposit was made on December 31 of the current year. What equal annual deposits should be made during the next six years, starting a year from now, if exactly $100,000 is to be accumulated in the fund? 4-5. The company recently purchased a computer for $500,000. The purchase contracts calls for 20 payments of $32,629 every three months starting immediately. You have been asked by the President of the company to compute the approximate rate of interest charged on this contract on an annualized basis. PV_examples_S10.doc Page 4 of 6

5 As a summer intern with the CPA firm of Gerald & Minn, you are presented with the following client questions. Prepare the appropriate computations and workpapers to support your answers to the clients A major sports team has just negotiated a contract with one of the top free agent players available this year. After months of negotiations, he signed a contract with the following terms: (1) An annual salary of $900,000 a year for four years, payable in monthly installments of $75,000 per month starting one month from now. (2) A deferred compensation package of $1,920,000, payable in monthly installments of $40,000 for four years, for services rendered during the four years of active service for the Spokane Stars. These payments commence one month after the last payment of $75,000 is made. Your client, the local newspaper, contacts you to verify that the value of the contract is $4,620,000. You do some checking and find that professional athletes generally have to pay an 18% compounded monthly rate of interest on personal loans. What is the actual present value of this contract? 5-2. Genessee Engineering just called to inquire whether a proposed transaction made economic sense. They had just sold a parcel of land for $51,000 and had the option of receiving $51,000 cash or $17,000 per year for four years, starting one year from now. Since they don't need the cash right now, but would like to earn at least 12% before income taxes on idle cash resources, the client asks you what interest rate is implied by the terms of the installment option Another client, Palouse Cedar Fence, wants to know how much they should pay to buy $100,000 face value of 8% bonds which mature in five years if interest is paid semiannually and if 12% compounded semiannually is a fair return for this type of investment. The bonds are not publicly traded Agriculture Micronomics, Inc., wants to make the first of four equal annual deposits in a fund that will earn 10% and will amount to $500,000 immediately after the last deposit on June 1, Year 5. The client wants to know the amount of each deposit and "proof" that $500,000 will actually be available on June 1, Year The president and principal stockholder of Palouse Cedar Fence is 50 years old today. He is worried about retirement and wants to start a pension fund for himself that would give him $30,000 per year for the rest of his life after he retires at age 65. The president wants to know how much the company will need to set aside each year (annual deposits beginning immediately) in order to accumulate enough to guarantee his retirement benefit. You use some IRS life expectancy tables to estimate that he will live to age 80. Assume that the payments after retirement would be made once a year at the beginning of each year, and that the company can earn 10% interest in all future periods. [Hint, first determine how much would need to be set aside in a fund on the day he turns 65.] PV_examples_S10.doc Page 5 of 6

6 Check Figures for Time Value of Money Problems 1-1 8,284, , % per annum compounded semiannually (i.e., 3% for 6 months) 1-4 5, , , , % per quarter 2-1 (1) 18,830 (2) 20,406 (3) 21, Using 8%: (1) 7,246, (2) 5,831, (3) 7,324, $9, or about $10, , , or about $20, , or about $10, , A/R 25, N/R 25, Salary Expense 32, Bonus Payable 32, /31/1:Correct erroneous 10/1/1 entry Prem on B/P 5, assumes interest rate is rounded off, else $4,853 Interest Expense 5, /31/1: Record accrued interest expense Prem on B/P 2, assumes no rounding of interest rate, else $2, Interest Expense 22, Interest Payable 25, , % per quarter Better answer: 12% compounded quarterly 5-1 3,219, % Acceptable answer: between 12 & 14% 5-3 $85, An amortization table would be proof 5-5 $7, or $7, depending on assumptions made PV_examples_S10.doc Page 6 of 6