Time Value of Money Measurement of recording of liabilities are based on the concept of the time value of money Time value of money compound interest Compound vs simple interest o Earns interest on the principle invested Compound interest previously earned interest Four Time Value Money Cases 1 Future Value of a lump sum 2 Present Value of a lump sum 3 Future Value of annuity 4 Present Value of annuity earns interest on bot principal invested as well as all o In each of these you need to use table factors Number of periods n Interest rate i In the future value of a lump sum case we know the value of some amount today and we want to know the value at some point in the future o FV PV FV factor Example 1 Compounding frequency with which interest is added to the principal o If ever different then being compounded annually must adjust interest rate and number of periods o i of compounds per year o n of compounds per year These adjustments must be made in all time value money cases FV factors can be calculated by 1 i n o Use table factors provided in the present value of a lump sum case we know the value of some amount in the future and we want to know the value today PV FV PV factor Example 2 discounting Key Point o Figuring out how much a future amount is worth today is called o The PV of a lump sum and the FV are reciprocals opposites of each other they can be used interchangeably to solve problems o As compounding frequency increases FV increases and PV decreases The more frequent the compounding the more interest earned on interest Annuity Lump sum single payment payment having the same time interval between them a series of equal payments either received or paid with each o A series of equal annual payments o A series of equal semi annual payments An annuity with payments occurring at the end of each period is known as an ordinary annuity An annuity with payments occurring at the beginning of each period is known as annuity due In the FV of an ordinary annuity case we want to know the value of a series of equal cash flows occurring at the end of each period at the same point in the future FV of annuity payment FV annuity factor Key Points 1 The payment in the above formula represents the amount of each individual equal payment do not add these payments together 2 The FV and PV of annuities are NOT reciprocal to each other and therefore can not be used interchangeably to solve problems Example 4 o To find the FV of an annuity due table factor multiply the ordinary annuity factor by 1 i PV of an ordinary annuity payment PV annuity factor Key Points 1 The payment in the above formula represents the amount of each individual equal payment Do not add these together 2 The FV and PV at annuities are NOT reciprocal to each other and therefore can not be used interchangeably to solve problems Example 5 o To find the pV of an annuity due table factor multiply the ordinary annuity factor by 1 i Example 6 Adequately evaluate different alternatives you must be able to compare each option at the same point in time o It is always easiest to compare alternatives using PV rather than FV Example 7 Example 8 Debt Financing When a company borrows money from he bank for longer than a year the obligation is a long term note payable These liabilities are typically repaid in equal installments part of which are repayment of principal and part of which are interest A major objective is determining how much of each loan is interest and how To spread the loan payments between interest and principal reduction use an much is a payment amortization table Example 1 Mortgage is a special type of note payable The liability is initially required for each installment payment usually monthly payments with each payment consisting of both interest and principal reductions Example 2 a contract that specifies the terms under which the owner of an asset Lease agrees to transfer the right to use the asset to another party Lessee the leases Lesser Two Types of Leases the owner of the property that is rented leased to another party the party that is granted the right to use property under the terms of 1 Operating Lease o Lessee assumes no risk of ownership o Each lease payment is classified as rent expense o At the end of loose term right to use the property reverts back to lesser 2 Capital Lease o Treated as if the lessee had purchased the asset o Lessee assumes rights and risk of ownership o Lessee records an asset on their balance sheet with related liabilities and depreciation Example 3 o Capital lease lessee records a leased asset and a leased liability on their balance sheet PV of lease payments The leased asset must be depreciated over the lease term The leased liability is amortized to separate the payment into interest and principal reduction o In last year the lease balance must be zero However there is always a rounding error Simply make the reduction to last liability balance Companies would prefer to categorize all leases as an operating lase o Reason companies are not required to record a liability on the balance sheet related to the lease Allows for better financial position Allows for better debt ratios Operating leases are referred to as off balance sheet financing Companies would prefer to categorize all leases as operating lease because of this concept of off balance sheet financing FASB issued SFAS No 13 which sets forth specific criteria that requires leases to be recorded as capital leases Financial Ratios relating to Debt 1 Debt to Equity Ratio measures the percentage of funds being provided by creditors versus stockholders o Total liabilities total equity ratio o Provides a measure of how protected creditors are in event of company not being able to pay its debts o All things equal the higher the Debt to equity ratio the higher the risk to creditors o The higher the ratio the higher creditors claims on assets so the higher the likelihood an individual creditor would not be paid in full if the company is unable to meet its obligations o Higher ratio there is a higher interest rate charged 2 Times Interest Earned Ratio measures the company s ability to meet its interest payments as they come due o Higher is better o Can be thought of as a margin of safety to creditors o The higher the more income the company has to pay interest and the less likely the company is to default on these payments Equity Financing No responsibility to pay Investors take risk Investors rewarded by company s future success