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Time Value of Money

Time Value of Money. Interest Market price of money Supply – lending rate Demand – borrow rate Difference – margin for lender Makes values at different points in time equivalent Holder indifferent between payment now and payment in future. Compound Interest Formulas.

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Time Value of Money

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  1. Time Value of Money • Interest • Market price of money • Supply – lending rate • Demand – borrow rate • Difference – margin for lender • Makes values at different points in time equivalent • Holder indifferent between payment now and payment in future

  2. Compound Interest Formulas • Classification of formulas • Time direction (time is relative) • Forward (compound) • Backward (discount) • Frequency of payment • Single • Annual • Periodic

  3. Nomenclature • Vn = value at time n • Vo = value at time zero • n = number of years • i = interest rate as a decimal • a = payment made at the end of a regular interval, e.g. an annuity • t = number of interest periods between payments when interest period and payment period differ • nt = total number of interest periods

  4. Nomenclature • Single payment – discounting. • Payment made at point n and discounted back to point 0 • Single payment – compounding. • Payment made at point 0 and compounded for n years n-2 n-1 n 0 1 2 3 4

  5. V20 = $60 x (1.09)20 V20 = $60 x 5.60 V20 = $336.26 Tree is worth $60 now. If it increases in value by 9% annually, what’s its estimated value in 20 years? Final (future) value of a single payment (compounding) Vn = V0 x (1+i)n

  6. If a tree is expected to be worth $120 in 10 years, and you want to earn 5% interest, what’s it worth to you now? V0 = $120 x (1/(1.05)10) V0 = $120 x 0.6139 V0 = $73.67 Present value of a single payment in the future (discounting) V0 = Vn x (1/(1+i)n)

  7. A high quality tree is worth $320 today and is expected to be worth $600 in 10 years. If I want to earn 6% on my investment should I cut it now or in 10 years? i = (600/320)1/10-1 i = 1.88 0.1 –1 i = 1.065 –1 i = 0.065 or 6.5% 6.5% > 6% so cut in 10 years, not today Rate earned (1+i)n= Vn/V0 i = (Vn/V0)1/n -1

  8. Assumptions for multiple payment formulas Annuity payments – annual payments of an equal amount 1st payment 2nd payment . . . . . . nth payment n-2 n-1 n 0 1 2 3 4

  9. Assumptions for multiple payment formulas • Compounding • First annuity payment compounded for n periods. • Last annuity payment not compounded • Discounting • First annuity payment discounted for 1 year • Last annuity payment discounted for n years • Year zero payments must be handled separately n-2 n-1 n 0 1 2 3 4

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