Comm298-Week3-Time_value_of_money-wit

# Comm298-Week3-Time_value_of_money-wit - Com298 Week 3 Time...

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Com298: Week 3 Time Value of Money Learning Objectives: Focus on the following: Rationale for time value of money. Simple interest and compound interest. FV and PV in multiple periods. Compute the discount rate and the number of periods. PV and FV of unequal multiple cash flows. Rationale for Time Value of Money Time value of money: A dollar today is worth more than a dollar in the 1

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future. A dollar today can be invested to earn interest so that it will increase overtime. Reasons for money to have a time value: Time preference: Investors must be compensated (with interest) to part with their money. Risk: Investors must be compensated for bearing risks. Inflation: Lenders must be compensated for loss in purchasing power. Four Key Equations Four key equations for time value of money: FV and PV equations: FV(r,t) = PV(r,t) x FVIF(r,t) PV(r,t) = FV(r,t) x PVIF(r,t) 2
FVA and PVA (annuity) equations: FVA(r,t) = C x FVIFA(r,t) PVA(r,t) = C x PVIFA(r,t) Notations: FVIF(r,t) = (1 + r) t PVIF(r,t) = 1 / (1 + r) t FVIFA(r,t) = [ (1 + r) t - 1]/r PVIFA(r,t) = [ 1 – 1/(1 + r) t ]/r C = annuity or cash flows of fixed amount Solving the FV and PV Equations Four elements in the time value of money equation: FV(r,t) = future value PV(r,t) = present value r = interest rate (or discount rate) t = number of time periods If you know 3 of them, you can solve for the 4 th 3

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unknown: Given PV, r and t, solve for FV: FV = PV(1 + r) t Given FV, r and t, solve for PV: PV = FV/(1 + r) t Given FV, PV and t, solve for r: r = (FV / PV) 1/t – 1 Given FV, PV and r, solve for t: t = ln(FV / PV) / ln(1 + r) Using the Sharp EL-738 Business Calculator Financial Calculator Keys: FV = future value PV = present value I/Y = period interest rate Interest is entered as a percent, not a decimal N = number of periods The financial calculator views cash inflows (FV) as positive numbers and cash outflows (PV) as negative numbers. 4
When typing in any cash outflow (e.g. PV or PMT), you must type the (+/-) key before the cash outflow. Remember to clear the register (2ndF CA) after each problem. Another way to clear the register (2ndF M-CLR) and then type 0 0. Future Value: Multiple Periods Example: FV in multiple periods Suppose you invest \$100 at 10% for 5 years. How much will the \$100 be worth after 5 years?

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Comm298-Week3-Time_value_of_money-wit - Com298 Week 3 Time...

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