Chapter 6 Notes Basic Time Value Concepts time value of money a dollar received today is worth more than a dollar promised some time in the future o you could receive the dollar today and receive interest on it making it worth more than it would be if you just received it tomorrow and didn t receive interest on it Applications of Time Value Concepts most useful fair value measures based on market prices o when market info on an asset or liability isn t readily available expectations on future cash flows related to the asset or liability can be used to estimate fair value Level 3 measures subjective Present Value Based Accounting Notes valuing noncurrent receivables and payables that carry no stated interest rate or a lower than market interest rate Leases valuing assets and obligations to be capitalized under long term leases and measuring the amount of the lease payments and annual leasehold amortization Pensions and Other Postretirement Benefits measuring service cost components of employer s postretirement benefits expense and postretirement benefits obligation Long Term Assets evaluating alternative long term investments by discounting future cash flows determining the value of assets acquired under deferred payment contracts measuring impairments of assets Stock Based Compensation determining the fair value of employee services in compensatory stock option plans Business Combinations determining the value of receivables payables liabilities accruals and commitments acquired or assumed in purchase Disclosures measuring the value of future cash flows from oil and gas reserves for disclosure in supplementary information Environmental Liabilities determining the fair value of future obligations for asset retirements The Nature of Interest interest payment for the use of money o excess cash received or repaid over and above the amount lent or borrowed principal multiple factors go into determining the interest rate o most important factor credit risk risk of underpayment Variables in Interest Computation principal the amount borrowed or invested interest rate a percentage of the outstanding principal time the number of years or fractional portion of a year that the principal is outstanding 3 relationships apply to interest rates o the larger the principal amount the larger the dollar amount of interest o the higher the interest rate the larger the dollar amount of interest o the longer the time period the larger the dollar amount of interest Simple Interest simple interest the return on or growth of principal for one time period Simple Interest p x i x n Compound Interest compound interest computed on principal and on any interest that has not been paid or withdrawn o the return on or growth of the principal for 2 or more periods uses the accumulated balance principal interest to date at each year end to compute interest in the succeeding year Interest Tables and Their Contents Future Value of 1 Table contains the amounts to which 1 will accumulate if deposited now at a specific rate and left for a specified number of periods Present Value of 1 Table contains the amounts that must be deposited now at a specified rate of interest to equal 1 at the end of a specified number of periods Future Value of an Ordinary Annuity of 1 Table contains the amounts to which periodic rents of 1 will accumulate if the payments rents are invested at the end of each period at a specified rate of interest for a specified number of periods Present Value of an Ordinary Annuity of 1 Table contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of 1 at the end of regular periodic intervals for the specified number of periods Present Value of an Annuity Due of 1 contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of 1 at the beginning of regular periodic intervals for the specified number of periods future value factor FVF 1 i n Fundamental Variables Rate of Interest an annual rate that must be adjusted to reflect the length of the compounding period if less than a year Number of Time Periods the number of compounding periods Future Value the value at a future date of a given sum or sums invested assuming compound interest Present Value the value now of a future sum or sums discounted assuming compound interest Single Sum Problems generally classified into 1 of the following categories o 1 computing the unknown future value of a known single sum of money that is invested now for a certain number of periods at a certain interest rate accumulate all cash flows to a certain point interest increases the amounts or values over time so the future value exceeds the present value o 2 computing the unknown present value of a known single sum of money in the future that is discounted for a certain number of periods at a certain rate discount all cash flows from the future to the present discounting reduces the amounts or values so the present value is less than the future value Future Value of a Single Sum Future Value PV FVFn i Present Value of a Single Sum present value amount needed to invest now to produce a known future value o always smaller than the future value due to earned and accumulated interest PVFn i 1 1 i n PV FV PVFn i Solving for Other Unknowns in Single Sum Problems Example Computation of the Number of Periods 1 Note the PV amount and the FV amount along with the interest rate 2 Solve for FVF PVF either works 3 Find FVF PVF and use table to find number of periods Example Computation of the Interest Rate 1 Note the FV amount the PV amount and the number of periods 2 Solve for FVF PVF 3 Find FVF PVF on table and find the interest rate Annuities annuity requires periodic payments or receipts of the same amount the samelength interval between payments and the compounding of interest once each interval o future value of an annuity the sum of all the payments plus the accumulated compound interest on them if payments are due at the end of the period it is an ordinary annuity if payments are due at the beginning of the period it is an annuity due Future Value of an Ordinary Annuity when computing the future value of an ordinary annuity the number of compounding periods will always be one less than the number of payments FVF OAn i 1 i 1 i Future Value of an Ordinary Annuity R FVF OAn i Future Value of an Annuity Due annuity due periodic payments occur at the beginning of each period o will accumulate interest