1 0 1 2 3 4 5 periods 400 100 100 200 300 cash flows

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-1 0 1 2 3 4 5 Periods -|--------|--------|--------|--------|--------|--------|--- $400 -$100 $100 $200 -$300 Cash Flows I What is PV 0 of all of these cash flows? I Long way: I Short way: PV 0 = $400*1.03 ! $100*1.03 ! 1 + $100*1.03 ! 2 + $200*1.03 ! 4 ! $300*1.03 ! 5 = $412 ! $97.0874 + $94.2596 + $177.6974 ! $258.7826 = $328.0870 PV 0 = FV 3 *1.03 ! 3 = $358.5095*1.03 ! 3 = $328.0870
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Example: Moving along the Timeline (3) 5 I Assume the effective interest rate per period is 3%. -1 0 1 2 3 4 5 Periods -|--------|--------|--------|--------|--------|--------|--- $400 -$100 $100 $200 -$300 Cash Flows I What is the value of these cash flows at t = -1? I Short way: PV ! 1 = $400 ! $100*1.03 ! 2 + $100*1.03 ! 3 + $200*1.03 ! 5 ! $300*1.03 ! 6 = $318.5311 PV ! 1 = FV 3 *1.03 ! 4 = PV 0 *(1.03) ! 1 = = $358.5095*1.03 ! 4 = $318.5310
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iClicker Example: Moving along the Timeline I Using the following timeline, what is the value at t=K of $1,000 to be received at the beginning of period D and another $1,000 at the beginning of period Q? I The per period interest rate is 5%? N A K R P D V Q Periods -|-------|-------|-------|-------|-------|-------|-------|- PV k $1,000 $1,000 Cash Flows a. $1,690.56 b. $1,816.22 c. $1,647.74 d. $1,729.73 e. None of the above. Correct answer is d) since the beginning of period D is at P and beginning of period Q is at V 6 PV k = $1,000 (1.05) 2 + $1,000 (1.05) 4 = $1,729.73
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Solving for other Things using the FV Formula I Recall our FV Formula I One equation with four variable => If we know three out of the four variables, we can solve for the 4 th => So far we only solved for FV or PV => Now we solve for n and r FV n = PV 0 *(1 + r ) n 7
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Example: Solving for the Interest Rate r I A company has the option of buying a machine for $355,000 today. The government promises to buy all the output of the machine in four years for $400,000.
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