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
§ PMT = Payments made
§ 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
o about 2-3% per year
· 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)
Non-Gift Loans
Non-Gift/Term Loans
· deemed transferred on the date the loan was made (7872b1)
o not 12/31
· Compensation-Related:
o Lender/Employer: interest = paid compensation/salary and deductible unless excessive (162) à wash
§ OID accrual over yr = gross income
o Borrower/Employee: interest = compensation/salary and potentially deductible (could be a wash)
§ interest = OID accruing daily portions summed over yr (potentially deductible)
· Corporate-Shareholder:
o Lender/Corporation: interest = paid dividend so NO deduction and income from interest
o Borrower/Shareholder: interest = dividend/gross income and possibly DRD