L2 example solution

L2 example solution - (1 r t => FV3 = \$445.89 Therefore...

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Example in Lecture 2 ! You have \$335 and you are offered two investment opportunities, A and B. A promises you \$400 in three year if you invest \$335 today. B promises you an annual return of 10%. Both investments are risk free. Which one should you choose?

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Method 1: Compare PV ! If you invest in project B, to get \$400 in year 3, how much do you need to invest today? What we know: FV3 = \$400, r=10%, t= 3 Plug the known variables in the formula: PV = FV t / (1+r) t => PV= \$300.53 ! To get the same payoff, we need less investment today in project B and you want to choose project B.
Method 2: Compare FV ! How much do you get if you invest \$335 in project B in 3 years? What we know: PV = \$335, r = 10%, t=3. Plug the known variables in the formula: FV t = PV

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Unformatted text preview: ! (1+r) t => FV3 = \$445.89 ! Therefore, we choose project B to get higher payoff. Method 3: Compare r ! What is return that project A offers? We know PV = \$335, FV3 = \$400, t = 3 Plug in the unknowns into the formula: r = (FV t /PV) 1/t – 1 => r= 6.09% ! Therefore, project A offers a lower return and you want to choose project B. Method 4: Compare t ! If you invest \$335 in project B, how long does the money grow into \$400? We know PV=\$335, FV3=\$400, r=10% Plug the known variables in the formula: t = [ln(FV t ) – ln(PV)] / ln(1+r) => r= 1.86 ! You can receive \$400 earlier if you invest in B. We know that cash flow in an earlier date is more valuable than the same cash flow in a later date. Therefore, you want to choose project B....
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