## Advanced Individual Income TaxationSouth Texas College of Law Houston Yamamoto, Kevin M.

Advanced Federal Income Tax, Yamamoto, Spring 2013
Time Value of Money (TVM)
Using the BA-II Plus Calculator
·         Steps
o   First: Clear the time value of money worksheets.  Hit “2nd”, then “CLR TVM”
o   Second: Enter the variables present in the problem
§  N = number of periods (normally years)
§  I/Y = interest rate
§  PV = Present value
§  FV = Future value
§  Note: With any three variables you may figure out the fourth.  However you must always have, or be calculating, N and I/Y.
o   Third: Set the payments per period (P/Y) and compounding periods per period (C/Y).  P/Y is best set at 1.  The C/Y is set by hitting “2nd” and then “P/Y” and the up or down arrow key.  Set C/Y  equal to the number of compounding periods (annually =1, semi-annually = 2, etc.).  After this hit “ENTER”, then “2nd” and “Quit” to get back to the time value of money calculations.
§  Note: The same result can be achieved by multiplying the periods (N) by the compounding periods, and dividing the interest rate (I/Y) by the same number.  I would suggest you try this to complete the annuity calculations.
o   Fourth: Compute the variable you desire.  Hit “CPT” and the variable you wish to compute (i.e. N, I/Y, PV, PMT or FV).

·         Example:  The first PV problem would be computed in the following manner.
o   First – Clear the TVM worksheet.
o   Second – Put in the variables.
o   N = 10                I/Y = 12    FV = \$5,000
o   Third – Set C/Y to 1 (“2nd”, “P/Y”, up-arrow, “1”, “enter”, “2nd”, “Quit”)
o   Fourth – Compute PV of -\$1,609.8662.  (“CPT”, “PV”)
Definitions
·         pure rate of interest = what rate would be if risks did not exist
·         inflation premium = cost covering loss in purchasing power from rising prices
·         maturity premium = cost offsets the risk associated with committing funds for longer periods
·         default premium = cost reflects risk that the borrower will default on the loan and the lender will lose the principal and any accrued interest
·         illiquidity premium = compensates a lender for lack of marketability and resulting price concession if lender is forced to sell debt instrument
Computation
·         Interest = Principal * Rate * Time
o   principal = amount of money borrowed before interest
o   rate = stated cost of borrowing one dollar per unit of time
o   time = number of units of time that the principal remains unpaid
·         Simple Interest = borrower pays interest on the original principal amount only, regardless of any unpaid accrued interest
o   ex: P = \$10K, Rate = 8% per yr, Time = 1 yr
§  at the end of the each year, borrower owes…
(\$10K * 0.08/yr * 1 yr) = \$800 interest
·         Complex Interest = borrower pays interest on the unpaid interest of past periods plus the original principal amount
o   interest on interest
o   ex: at the end of the second year, borrower owes…
(\$10,800 * 0.08/yr * 1 yr) = \$864 interest
Future Value
·         Single Amounts
o   future amount of \$1 = amount to which a current P will grow at the end of N periods of time invested at I compound interest rate
§  ex: P = \$10K, N = 10 yr, I = 12%
·         future value = \$31,058.50
§  Rule of 72 – Doubling Investment
·         72 ÷ __% (compounded annually) = # yrs for investment to double
·         Annuities
o   ordinary annuity = investor makes payments at the end of the period
o   annuity due = makes payments at the beginning of each period
§  yields more!
§  represents the sum accumulated one period after the last payment
Present Value
·         Single Amounts
o   PV of \$1 = amount that will grow at the end of N periods of time in the future at a compound interest rate
o   Discounted = start with a larger known amount in the future and determine the lower PV
o   PV + interest = FV
·         Annuities
o   as if one invested a lump sum compounding interest with a series of equal withdrawals at regular intervals zeroing out after final withdrawal
o   ordinary annuity vs. annuity due à timing of withdrawal/payment
§  annuity due à discount each withdrawal for one LESS period than with ordinary annuity
·         must invest more initially to have same outcome as ordinary annuity?????
o   Perpetual Annuity = investor may only withdraw interest ea

interest
·         Lender:
o   deemed to make a gift on 12/31 of amt of forgone interest
o   include forgone interest in gross income
·         Borrower:
o   initial transfer of interest to B is a gift ≠ gross income (102)
o   deemed to make an interest payment
o   potentially deductible (163) depending on what B spent loan on
Exceptions
·         If gift loan between individuals does NOT exceed \$10,000, then no imputed interest (7872c2A) – de minimis
o   …unless Borrower spends loan money on income-producing assets, then 7872(a) applies. (7872c2B)
·         If gift loan between individuals does NOT exceed \$100,000, then Lender’s interest income is limited to Borrower’s net investment income (7872d1A)
o   …unless a principal purpose was Federal tax avoidance (7872d1B)
o   only applies to Borrower à Lender interest income
§  b/c initial transfer Lender à Borrower = gift
o   Borrower: potentially limits deduction correspondingly
o   if Borrower’s net investment income does NOT exceed \$1,000, then no imputed interest (7872d1Eii)