Chapter 6

Problem 5

(Analysis of Alternatives) Julia Baker died, leaving to her husband Brent an insurance policy contract that provides that the beneficiary (Brent) can choose any one of the following four options. a. $55,000 immediate cash. PV b. $4,000 every 3 months payable at the end of each quarter for 5 years. 62357 c. $18,000 immediate cash and $1,800 every 3 months for 10 years, payable at the beginning of each 3-month period. 64,315 d. $4,000 every 3 months for 3 years and $1,500 each quarter for the following 25 quarters, all payments payable at the end of each quarter. 20,549.34

Exercises 7

(Computation of Bond Prices) What would you pay for a $100,000 debenture bond that matures in 15 years and pays $5,000 a year in interest if you wanted to earn a yield of: a. 4%? b. 5%? c. 6%? A bond is the debt instrument issued by the companies or financial institutions to raise the capital from the market. a) Bond price = ($100,000 x PVF @ 4% at 15th year) + ($5,000 x PVAF @ 4% for 15 years) = ($100,000 x 0.55526) + ($5,000 x 11.1183) = $111,117.5 b) Bond price = ($100,000 x PVF @ 5% at 15th year) + ($5,000 x PVAF @ 5% for 15 years) = ($100,000 x 0.48102) + ($5,000 x 10.3796) = $100,000 c) Bond price = ($100,000 x PVF @ 6% at 15th year) + ($5,000 x PVAF @ 6% for 15 years) = ($100,000 x 0.41726) + ($5,000 x 9.71225) = $90,287.25

Applications of Time Value Concepts

1.Notes 2.Leases 3.Pensions and Other Postretirement Benefits4.Long-Term Assets 5.Stock-Based Compensation 6.Business Combinations 7.Disclosures 8.Environmental Liabilities

question 8 Will Smith will receive $80,000 5 years from now, from a trust fund established by his father. Assuming the appropriate interest rate for discounting is 12% (compounded semiannually), what is the present value of this amount today?

80000(1/(1+0.06)^10)=44671.58

Compound Interest Tables Comparison of Different Compounding Periods

A 9% annual interest compounded daily provides a 9.42% yield.Effective Yield for a $10,000 investment.

Future Value of an Ordinary AnnuityFormula

A formula provides a more efficient way of expressing the future value of an ordinary annuity of 1.

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.

Question 12

Assume the same situation as in Question 11, except that the four equal amounts are deposited at the beginning of the period rather than at the end. In this case, what amount must be deposited at the beginning of each period? (Round to two decimals.) Amount deposited each year = $200,000/5.10510 [future value of an annuity due at 10% for 4 years (4.64100 X 1.10)]. Amount deposited each year = $39,177.

Brief Ex 8

BE6.8 (LO 2) Refer to the data in BE6.7. Assuming quarterly compounding of amounts invested at 8%, how much of John Fillmore's inheritance must be invested to have enough at retirement to buy the boat? amount to be invested = 300,000/1.02^20 amount to be invested = 201,891.40 a) Amount to e invested = 300,000/1.08^5 amount to be invested = 204,174.96 b) amount to be invested = 300,000/1.02^20 amount to be invested = 201,891.40 FV = 300,000 n = 5 X 4 = 20 i = 8% / 4 = 2% PV = FV (PVFn,i) PV = 300,000 (0.67297) PV = $201,891

Preview of Chapter 6 Accounting and the Time Value of MoneyBasic

Basic Time Value Concepts •Applications •The nature of interest •Simple interest•Compound interest •Fundamental variables

Future Value of a Single Sum

Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at an interest rate of 6%.

Present Value Measurement

Concept Statement No. 7 introduces an expected cash flow approach that uses a range of cash flows and incorporates the probabilities of those cash flows. Choosing an Appropriate Interest RateThree Components of Interest: •Pure Rate •Expected Inflation Rate •Credit Risk Rate

question 7 Regina Henry deposited $20,000 in a money market certificate that provides interest of 10% compounded quarterly if the amount is maintained for 3 years. How much will Regina have at the end of 3 years?

Deposit = 20,000 R = 10%/4 = 2.5% (compounded quarterly) N = 3* 4 = 12 FV = 20000 * (1 + 2.5%)^12 = 20000 * (1.025)^12 = 20000 * (1.344888) = $26898

Learning Objective 1

Describe the Fundamental Concepts Related to the Time Value of Money

Compound Interest Tables Frequency of Compounding

Determine number of periods by multiplying number of years involved by number of compounding periods per year.

Exercise 20.

E6.20 (LO 5) (Expected Cash Flows) For each of the following, determine the expected cash flows. Cash FlowEstimateProbabilityAssessment a. $ 4,800 20% 960 6,300 50% 3150 7,500 30% 2250 b. $ 5,400. 30% 1620 7,200 50% 3600 8,400 20% 1680 c. $(1,000. 10% -100 3,000 80% 2400 5,000 10% 500

Compound Interest Tables

Formula for future value factor (FVF) for 1 FVF I,n,=(1+i)^n Where:FVFn,i= future value factor for n periods at i interestn = number of periodsi = rate of interest for a single period

Simple Interest (1 year)

Interest computed on the principal only.Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at a simple interest rate of 8% per year. Compute the total interest to be paid for the 1 year. Annual Interest= p × i × n= $10,000 × .08 × 1= $800

Problem 14

P6.14 (LO 4, 5) (Expected Cash Flows and Present Value) At the end of 2020, Sawyer Company is conducting an impairment test and needs to develop a fair value estimate for machinery used in its manufacturing operations. Given the nature of Sawyer's production process, the equipment is for special use. (No secondhand market values are available.) The equipment will be obsolete in 2 years, and Sawyer's accountants have developed the following cash flow information for the equipment.

question 4 What are the components of an interest rate? Why is it important for accountants to understand these components?

Part A: Interest rates in common parlance refers to the cost of capital i.e. some portion of principal amount which is charged by the lender from the borrower. Some of the key components of interest rates are given below:- Component 1: the Real rate of interest: This is the first element of interest rate. as we are aware of the fact that nothing is free in this world. everything bears some cost. Likewise, the real interest rate is nothing but the cost of capital charged by the lender of the money. Component 2: Inflation differentials: Inflation simply means a general increase in the price level of the goods and services in the economy. Inflation has a huge impact on the interest rates. The increase in Inflation leads to increase in interest rates and vice versa. Component 3: Credit risk : Credit risk refers to the risk of default or non-payment of a loan or due amount. Like in the case of equity, credit risk is high but vice versa in case of government securities. Part B: For an accountant, it is very essential to understand all the components of interest rates due to the following reasons:- Reason 1: Real interest rate: From real interest rate, an accountant can determine interest coverage ratio in order to determine the long-term solvency of the company. Reason 2: Inflation: From inflation, an accountant have to make a technical estimation of different kinds of functional budgets like the cost of raw material, wages of labor and cash flows etc. Reason 3: Credit Risk: From credit risk premium, the accountant can come to know about the liquidity as well as solvency position of the company. Even it is helpful in the creation of a provision for doubtful debts Accountants must have knowledge about these components because these components are essential in identifying an appropriate interest rate for a given company or investor at any given moment..

Simple Interest (3 months)

Partial Year Interest= p × i × n= 10,000*0.08*3/12

Valuation of Long-Term Bonds

Present Value of Interest TABLE 6.4 PRESENT VALUE OF AN ORDINARY ANNUITY OF 1

Valuation of Long-Term Bonds

Present Value of Principal

Annuities (Present Value)

Present Value of an Ordinary Annuity •Present value of a series of equal rents to be withdrawn or received at equal intervals. •Periodic rents occur at the end of the period.

Future Value Single Sum

Problems Solving for an Unknown Number of Periods

Future Value of an Annuity Due Computation of Accumulated Value

Referring to the "future value of an ordinary annuity of 1" table for 8 periods at 6%, Sue finds a factor of 9.89747. She then multiplies this factor by (1 + .06) to arrive at the future value of an annuity due factor. As a result, the accumulated value on Howard's eighteenth birthday is $8,393.06 below.

Future Value of an Annuity Due

Rents occur at beginning of each period •Interest will accumulate during 1st period •Annuity Due has one more interest period than Ordinary Annuity •Factor = multiply future value of an ordinary annuity factor by 1 plus interest rate

Preview of Chapter 6

Single-Sum Problems •Future value of single sum •Present value of single sum •Solving for other unknowns Annuities (Future Value) •Future value of ordinary annuity •Future value of annuity due •Examples of FV of annuity

Learning Objective 3

Solve Future Value of Ordinary and Annuity Due Problems

Learning Objective 2

Solve Future and Present Value of 1 Problems

Learning Objective 5

Solve Present Value Problems Related to Deferred Annuities, Bonds, and Expected Cash Flows

Learning Objective 4

Solve Present Value of Ordinary and Annuity Due Problems

Compound Interest Tables

Table 6.1 - Future Value of 1 Table 6.2- Present Value of 1 Table 6.3- Future Value of an Ordinary Annuity of 1 Table 6.4- Present Value of an Ordinary Annuity of 1Table 6.5 - Present Value of an Annuity Due of 1 Number of Periods = number of years × the number of compounding periods per year.Compounding Period Interest Rate = annual rate divided by the number of compounding periods per year.

Question 11

The Kellys are planning for a retirement home. They estimate they will need $200,000 4 years from now to purchase this home. Assuming an interest rate of 10%, what amount must be deposited at the end of each of the 4 years to fund the home price? (Round to two decimal places.) Amount deposited each year = $200,000/4.64100 (future value of an ordinary annuity at 10% for 4 years).Amount deposited each year = $43,094. n= 4 i= 10% FV= 200,000 FV-OA= R (FVF-OAn,i) 200,000=R (4.64100) R= $43,094

Basic Time Value Concepts

Time Value of Money •A relationship between time and money. •A dollar received today is worth more than a dollar promised at some time in the future.

Other Time Value of Money Issues Valuation of Long-Term Bonds

Two Cash Flows:•Periodic interest payments (annuity).•Principal paid at maturity (single-sum).

Single-Sum Problems

Two Categories

Present Value of a Single-Sum

Value now of a given amount to be paid or received in the future, assuming compound interest.

BE6.7 (LO 2) John Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. John has recently come into an inheritance of $400,000. He estimates that the boat he wants will cost $300,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 8% (compounded annually) to buy the boat at retirement?

We need to find out the present value of the $300,000 at 5th year PV= FV * PV factor annually at 8%,5th year PV =300,000 * PVF (8%,5th year) PV= 300,000*0.680583 PV=$204175 FV = 300,000 n = 5 i = 8% PV = 300,000 (0.68058) PV= $204,174

Present Value of an Ordinary Annuity Formula

Where:R = periodic rent (ordinary annuity)PVF-OAn,i = present value of an ordinary annuity of 1 for nperiods at i interest

question 1 What is the time value of money? Why should accountants have an understanding of compound interest, annuities, and present value concepts?

time value of money indicates a relationship between time and money—that a dollar received today is worth more than a dollar promised at some time in the future. Why? Because of the opportunity to invest today's dollar and receive interest on the investment. Financial reporting uses different measurements in different situations—historical cost for equipment, net realizable value for inventories, fair value for investments.Fair value hierarchy Money has value because with it one can acquire assets and services and discharge obligations.The holding, borrowing or lending of money can result in costs or earnings. And the longer thetime period involved, the greater the costs or the earnings. The cost or earning of money as afunction of time is the time value of money.Accountants must have a working knowledge of compound interest, annuities, and present valueconcepts because of their application to numerous types of business events and transactionswhich require proper valuation and presentation. These concepts are applied in the followingareas: (1) sinking funds, (2) installment contracts, (3) pensions, (4) long-term assets, (5) leases,(6) notes receivable and payable, (7) business combinations, (8) amortization of premiums anddiscounts, and (9) estimation of fair value

Compound Interest

•Computes interest on •principal and •interest earned that has not been paid or withdrawn •Typical interest computation applied in business situations

Preview of Chapter 6 Other Time Value of Money Issues

•Deferred annuities •Valuation of long-term bonds •Effective-interest method of bond discount/premium amortization •Present value measurement

The Nature of Interest

•Payment for the use of money •Excess cash received or repaid over the amount lent or borrowed (principal) Variables in Interest Computation 1.Principal. The amount borrowed or invested. 2.Interest Rate. A percentage of the outstanding principal. 3.Time. The number of years or fractional portion of a year that the principal is outstanding.

Present Value of an Annuity Due

•Present value of a series of equal rents to be withdrawn or received at equal intervals. •Periodic rents occur at the beginning of the period.

Preview of Chapter 6Annuities (Present Value)

•Present value of ordinary annuity •Present value of annuity due •Examples of PV of annuity

Fundamental Variables

•Rate of Interest •Number of Time Periods •Future Value •Present Value

Other Time Value of Money Issues Deferred Annuities

•Rents begin after a specified number of periods •Future Value of a Deferred Annuity - Calculation same as future value of an annuity not deferred •Present Value of a Deferred Annuity - Must recognize interest that accrues during deferral period

Annuities Future Value of an Ordinary Annuity

•Rents occur at the end of each period •No interest during 1st period