Present value calculations involve the discounting of future cash amounts to a present value. To discount means to remove the interest or to remove the time value of money.
The rate used to discount the future cash amounts is referred to as the discount rate, the effective interest rate, the yield, the yield-to-maturity, the market interest rate, the required rate, the target rate, the time value of money, the time-adjusted rate of return, the internal rate of return, and perhaps others.
To assist in calculating the present value of the future amounts, one can use mathematical formulas, the present value factors contained in present value tables, a financial calculator or computer software.
The two most common present value tables are (1) the present value of 1 table, and (2) the present value of an ordinary annuity table. The present value of 1 table shows the present value of receiving a single payment of $1 sometime in the future. For example, if the time value of money is 10% per year, receiving $1 at the end of one year has a present value of 0.90909 [1/(1 + 10%)1] or [1/(1.10)]1. The present value of receiving a single $1 at the end of two years is 0.82645 calculated as [1/(1 + .10)2] or [1/1.21].
A series of equal cash amounts occurring at the end of equal time intervals is known as an ordinary annuity or an annuity in arrears. When the amount occurs at the beginning of each equal time interval, it is an annuity due or an annuity in advance.
A bond is both an ordinary annuity and a single amount. The bond's interest payments at the end of each six-month period form an ordinary annuity. The bond's maturity amount or face amount is a single amount that occurs when the bond matures. To determine the present value of a bond, both (1) the series of interest payments and (2) the maturity amount must be discounted by the market interest rate. The market interest rate is also referred to as the yield or yield-to-maturity.
Accountants may need to calculate the present value of some future amounts in order to comply with the cost principle.
Sample Present Value and Bonds Questions
1) The effective interest rate method provides perfect correlation between a bond's interest expense on the corporation's income statement and the bond's ____________ value on the corporation's balance sheet.
2) A bond maturing in three years will be reported as a long-term _____________on the issuing corporation's balance sheet.
3) The difference between each year's bond interest expense and the cash paid for interest is the amount of _________________ of a bond's discount or premium.
4) The amortization of the premium on bonds payable will result in bond interest expense being ________ (less, more) than the cash payment for interest.
5) The __________ interest rate is used to discount a bond's interest payments and the bond's maturity amount to their present values.
6) An advantage for issuing bonds instead of common _______ is that the interest is deductible on the corporation's income tax return.
7) A bond's interest payments form an _____________ annuity.
8) A bond's _________-to-maturity is also the effective interest rate.
9) An increase in the market interest rates will cause the market value of a bond to __________ (decrease, increase).
10) A 20-year bond has a stated interest rate of eight percent per year with the interest paid semiannually. If the market interest rate is ten percent, the present value factor to be used will be based on 'i' equal to _________ percent.