Long-Term Liabilities. We determine the annuity PV factor from the table labeled Present Value of Ordinary Annuity of $1 (Appendix A, Table A-2). We use this table for annuities. We look down the 6% column and across the 5 periods row and find the annuity PV factor is 4.212. We finish our calculation as follows: Present value = Amount of each cash inflow X Annuity PV factor for i = 6%, n = 5 = $2,000 x 4.212 = $8,424 This means that an investment today of $8,424 at 6% will yield $2,000 per year for the next five years, or total payments of $10,000 over 5 years ($2,000 per year X 5 years). The reason is that interest is being earned on principal that is left invested each year. Let's verify the calculation: [1] Year Beginning Balance Previous [4] 0 2 $8,424 6,929 5,345 3,666 1,886 *rounded up by $1 [2] Interest [1] X6% $ 505 416 321 220 114* [3] Withdrawal $2,000 $ 2,000 2,000 2,000 2,000 2,000 [4] Ending Balance [1] + [2] [3] $8,424 6,929 5,345 3,666 1,886 0 The chart shows that the initial investment of $8,424 is invested for one year, earning $505 in interest. At the end of that period, the first withdrawal of $2,000 takes place, leav- ing a balance of $6,929 ($8,424 + $505- $2,000). At the end of the five years the ending balance is $0, proving that the present value of the $2,000 annuity is $8,424. Present Value of Bonds Payable We can use what we have just learned about the present value of a lump sum and present value of an annuity to calculate the present value of bonds payable. The present value of a bond its market price-is the sum of: the present value of the principal amount to be paid at maturity, a single amount (present value of a lump sum) plus the present value of the future stated interest payments, an annuity because it occurs in equal amounts over equal time periods (present value of an annuity). Present Value of a Bonds Payable Issued at a Discount Let's compute the present value of Smart Touch Learning's 9%, five-year bonds. The face value of the bonds is $100,000, and they pay (9% X 6/12) or 4.5% stated interest semian- nually. At issuance, the annual market interest rate is 10% (5 % semiannually). Therefore, the market interest rate for each of the 10 semiannual periods is 5%. We use 5% to compute the present value (PV) of the maturity value and the present value (PV) of the stated interest. The present value of these bonds is $96,149, computed as shown:

our ralculation in followe 12.0004212 = SR 474 the culculations rimonded up byst balase is 30 proving ther the persen value of the $2000 annerter is 58,424 Present Value of Rlonds Payable bonal-ats marliet price- is the vam of: value of a hinp num! Present Value of a Bends Payable lasued at a Disceunt