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