The contents of this chapter include all of the following: Solve future value of ordinary and annuity due problems, solve present value of ordinary and annuity due problems, solve present value problems related to deferred annuities and bonds, apply expected cash flows to present value measurement.
PART II: Corporate Accounting Concepts and Issues Lecture 25 Accounting and Annuities Learning Learning Objectives Objectives Solve future value of ordinary and annuity due problems Solve present value of ordinary and annuity due problems Solve present value problems related to deferred annuities and bonds Apply expected cash flows to present value measurement Accounting Accounting and and the the Time Time Value Value of of Money Money Annuities Future value of ordinary annuity Future value of annuity due Examples of FV of annuity Present value of ordinary annuity Present value of annuity due Examples of PV of annuity More Complex Situations Deferred annuities Valuation of long-term bonds Effectiveinterest method of bond discount/ premium amortization Present Value Measurement Choosing an appropriate interest rate Example of expected cash flow Basic Basic Annuities Annuities An annuity is a series of equal periodic payments Period 1 Period 2 Period 3 Period 4 $10,000 $10,000 $10,000 $10,000 Annuities Annuities Annuity requires: (1) Periodic payments or receipts (called rents) of the same amount, (2) Same-length interval between such rents, and (3) Compounding of interest once each interval Two Types Ordinary Annuity - rents occur at the end of each period Annuity Due - rents occur at the beginning of each period LO Solve future value of ordinary and annuity due problems Annuities Annuities Future Value of an Ordinary Annuity Rents occur at the end of each period No interest during 1st period Future Value Present Value $20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000 LO Solve future value of ordinary and annuity due problems Future Future Value Value of of an an Ordinary Ordinary Annuity Annuity Illustration: Assume that $1 is deposited at the end of each of years (an ordinary annuity) and earns 12% interest compounded annually Following is the computation of the future value, using the “future value of 1” table (Table 6-1) for each of the five $1 rents LO Solve future value of ordinary and annuity due problems Future Future Value Value of of an an Ordinary Ordinary Annuity Annuity A formula provides a more efficient way of expressing the future value of an ordinary annuity of Where: R = periodic rent FVF-OA n,i = future value factor of an ordinary annuity i = rate of interest per period n= number of compounding periods LO Solve future value of ordinary and annuity due problems Future Future Value Value of of an an Ordinary Ordinary Annuity Annuity Illustration: What is the future value of five $5,000 deposits made at the end of each of the next years, earning interest of 12%? = $31,764.25 LO Solve future value of ordinary and annuity due problems Alternate Future Value of an Ordinary Annuity Future Value of an Ordinary Annuity Calculation Illustration: What is the future value of five $5,000 deposits made at the end of each of the next years, earning interest of 12%? What table we use? 10 LO Solve future value of ordinary and annuity due problems More More Complex Complex Situations Situations Deferred Annuities Rents begin after a specified number of periods Future Value - Calculation same as the future value of an annuity not deferred Present Value - Must recognize the interest that accrues during the deferral period Future Value Present Value 37 100,000 100,000 100,000 19 20 LO Solve present value problems related to deferred annuities and bonds More More Complex Complex Situations Situations Valuation of Long-Term Bonds Two Cash Flows: Periodic interest payments (annuity) Principal paid at maturity (single-sum) 2,000,000 38 $140,000 140,000 140,000 140,000 140,000 140,000 10 LO Solve present value problems related to deferred annuities and bonds Valuation Valuation of of Long-Term Long-Term Bonds Bonds Present Value $140,000 140,000 140,000 140,000 140,000 2,140,000 10 Clancey Inc issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end The current market rate of interest for bonds of similar risk is 8% What amount will Clancey receive when it issues the bonds? 39 LO Solve present value problems related to deferred annuities and bonds i=8% n=10 Valuation Valuation of of Long-Term Long-Term Bonds Bonds PV of Interest $140,000 x Interest Payment 40 6.71008 Factor = $939,411 Present Value LO Solve present value problems related to deferred annuities and bonds i=8% n=10 Valuation Valuation of of Long-Term Long-Term Bonds Bonds PV of Principal $2,000,000 Principal 41 x 46319 Factor = $926,380 Present Value LO Solve present value problems related to deferred annuities and bonds Valuation Valuation of of Long-Term Long-Term Bonds Bonds Clancey Inc issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end Present value of Interest $939,411 Present value of Principal 926,380 Bond current market value Date Account Title Cash Bonds payable 42 $1,865,791 Debit Credit 1,865,791 1,865,791 LO Solve present value problems related to deferred annuities and bonds Valuation Valuation of of Long-Term Long-Term Bonds Bonds Schedule of Bond Discount Amortization 10-Year, 7% Bonds Sold to Yield 8% Cash Interest Paid Date 1/1/10 12/31/10 12/31/11 12/31/12 12/31/13 12/31/14 12/31/15 12/31/16 12/31/17 12/31/18 12/31/19 140,000 140,000 140,000 140,000 140,000 140,000 140,000 140,000 140,000 140,000 * 43 Interest Expense 149,263 150,004 150,805 151,669 152,603 153,611 154,700 155,876 157,146 158,533 * Bond Discount Amortization 9,263 10,004 10,805 11,669 12,603 13,611 14,700 15,876 17,146 18,533 Carrying Value of Bonds 1,865,791 1,875,054 1,885,059 1,895,863 1,907,532 1,920,135 1,933,746 1,948,445 1,964,321 1,981,467 2,000,000 rounding LO Solve present value problems related to deferred annuities and bonds Valuation Valuation of of Long-term Long-term Leases Leases Certain longterm leases require the recording of an asset and corresponding liability at the present value of future lease payments 44 Valuation Valuation of of Long-term Long-term Leases Leases On January 1, 2011, Todd Furniture Company signed a 20year non cancelable lease for a new retail showroom. The lease agreement calls for annual payments of $25,000 for 20 years beginning on January 1, 2011. The appropriate rate of interest for this longterm lease is 8%. Calculate the value of the asset acquired and the liability assumed by Todd (the present value of an annuity due at 8% for 20 years) 45 Valuation Valuation of of Pension Pension Obligations Obligations Some pension plans create obligations during employees’ service periods that must be paid during their retirement periods. The amounts contributed during the employment period are determined using present value computations of the estimate of the future amount to be paid during retirement. 46 Valuation Valuation of of Pension Pension Obligations Obligations On January 1, 2011, Todd Furniture Company hired a new sales manger for the new showroom. The sales manager is expected to work 30 years before retirement on December 31, 2040. Annual retirement benefits will be paid at the end of each year of retirement, a period that is expected to be 25 years. The sales manager will earn $2,500 in annual retirement benefits for the first year worked, 2011. How much must Todd contribute to the company pension fund in 2011 to provide for $2,500 in annual pension benefits for 25 years that are expected to begin in 30 years. Todd’s pension fund is expected to earn 5% 47 Valuation Valuation of of Pension Pension Obligations Obligations This is a two part calculation. The first part requires the computation of the present value of a 25year ordinary annuity of $2,500 as of December 31, 2040. Next we calculate the present value of the December 31, 2040 amount. This second present value is the amount Todd will contribute in 2011 to fund the retirement benefit earned by the sales manager in 2011 48 Present Present Value Value Measurement Measurement Expected cash flow approach that uses a range of cash flows and incorporates the probabilities of those cash flows Choosing an Appropriate Interest Rate Three Components of Interest: 49 Pure Rate Expected Inflation Rate Credit Risk Rate Risk-free rate of return IASB states a company should discount expected cash flows by the riskfree rate of return LO Apply expected cash flows to present value measurement Present Present Value Value Measurement Measurement Keith Bowie is trying to determine the amount to set aside so that she will have enough money on hand in years to overhaul the engine on her vintage used car While there is some uncertainty about the cost of engine overhauls in years, by conducting some research online, Angela has developed the following estimates Instructions: How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that she will have enough money on hand in years to pay for the overhaul? 50 LO Apply expected cash flows to present value measurement Present Present Value Value Measurement Measurement Instructions: How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that she will have enough money on hand in years to pay for the overhaul? 51 LO Apply expected cash flows to present value measurement ... deferred annuities and bonds Apply expected cash flows to present value measurement Accounting Accounting and and the the Time Time Value Value of of Money Money Annuities Future value of ordinary... of ordinary and annuity due problems Solving Solving for for Unknown Unknown Values Values in in Present Present Value Value Situations Situations In present value problems involving annuities, ... future value of ordinary and annuity due problems Annuities Annuities Future Value of an Annuity Due Rents occur at the beginning of each period Interest will accumulate during 1st period