Time Value of Money Concepts

Time Value of Money Concepts - Time Value of Money Concepts...

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Time Value of Money Concepts Business 4099

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2 K. Hartviksen Topics Holding period returns reinvestment rate assumption arithmetic vs. geometric rates nominal rates vs. effective annual rates risk inflation income taxes opportunity cost Annual percentage rate (APR) Effective annual rate (EFR)
Concepts and Terms Simple interest Compound interest Compounding Annuity Discounting a single cash flow Discounting an annuity Discounting a growing annuity Loan amortization tables More frequent compounding Calculating Time Rate Present value Ex ante Ex post

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Mathematics of Finance Central to the work of the financial planner You must become proficient in estimating future values, discounting cash flows, and in using judgment in the selection of appropriate discount rates
Interest Time Value of Money Skills…

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Interest The charge for the privilege of borrowing money Usually expressed as an annual percentage rate. Lenders charge interest for the use of their money…borrowers pay the lend for the privilege.
Interest Invest \$10,000 @ 8% for one year: Interest earned by the lender by the end of one year = = \$1,000 × .08 = \$80

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Simple Interest Invest \$10,000 @ 8% for one year: Interest and principal forecast at end of one year = = (\$1,000 × .08) + \$1,000 = \$1,080 = \$1,000 × (1 +.08) = \$1,080
Simple Interest A General Formula (one year): Future Value = (\$1,000 × .08) + \$1,000 FV = \$1,080 FV = \$1,000 × (1+r) FV = C × (1+r)

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Simple Interest Simple interest assumes that when interest is received at the end of the investment period, the interest is removed from the investment…and only the original principal is invested in the next period.
Compounding Time Value of Money Skills

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Compound Interest Compound interest assumes that when interest is received at the end of the investment period, the interest is reinvested together with the original principal. This means that in each successive period, interest is earned on both the original principal as well as the accumulated interest of prior periods.
Compound Interest How much will you have in (at the end of) two years?: Future Value 2 = \$1,000 × (1+r 1 ) × (1+r 2 ) FV 2 = \$1,000 (1.08)(1.08) FV 2 = \$1,000 (1.08) 2 FV 2 =C×(1+r) t

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Compound Interest Notice the compound interest assumptions that are embodied in the basic formula: Future Value 2 = \$1,000 × (1+r 1 ) × (1+r 2 ) FV t = C × (1+r) t Assumptions: The rate of interest does not change over the periods of compound interest Interest is earned and reinvested at the end of each period The principal remains invested over the life of the investment The investment is started at time 0 (now) and we are determining the compound value of the whole investment at the end of some time period (t= 1, 2, 3, 4,…)
Compound Interest Time = 0 Time = 1 Time = 2 Time of Investment

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Compound Interest Formula (For a single cash flow) FV t =C(1+r)
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This document was uploaded on 03/14/2011.

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Time Value of Money Concepts - Time Value of Money Concepts...

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