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**Unformatted text preview: **Problem Set I Solutions Time Value of Money and Stock and Bond Valuation Problem 1 The cash flows can be broken into three separate cash flows patterns: 1. a single cash flow at the end of three years Discount Rate = 10% Present Value (PV at t=0) is $gGGG (gG.g) = $751 2. an annuity beginning at the end of fourth year and continuing for next ten years Discount Rate = 8% Present Value (PV at t=3) is $gGGG G.G x1 g (gG.G) = $6,710 Present Value (PV at t=0) is $gG (gG.g) = $5,041 3. and a perpetuity beginning at the end of fourteenth year Discount Rate = 6% Present Value (PV at t=13) is $gGGG G.G = $16,666 Present Value (PV at t=3) is $g, (gG.) = $7,719 Present Value (PV at t=0) is $,g (gG.g) = $5,800 Therefore, Present Value (PV) is $751 + $5,041 + $ 5,800 = $11,592 Problem 2 This represents a growing annuity with: Interest Rate r = 0.7% per month Growth Rate g = 0.3% per month Number of withdrawals t = 48 Present Value (PV) = $30,000 C represents the amount of first withdrawal Therefore, Hence, you can withdraw $690.03 after the first month of college. 03 . 690 $ 007 . 1 003 . 1 1 003 . 007 . 000 , 30 $ 1 1 1 48 = + + = + + = C C r g g r C PV t Problem 3 Bank pays an annual interest rate of 10% compounded semi-annually. The EAR (Effective Annual Rate) = (1 + g G ) G 1 = (1 + . ) 1 = 10.25 % Part a The cash flow represents a $100,000 annuity with ten periods (n=10) Present Value (PV at t = -1) of this annuity is g x 1 () = $, . x1 (.) = $607,912 Future Value (FV at t = 25) of this annuity is $607,912 x (1 + 0.1025) = $7,685,724 Therefore, you will have $7,685,724 in the bank account after 25 years. Part b Let each deposit be C Present Value (PV at t = -1) of this annuity is g x 1 () = $, . x1 (.) = C x 6.079 Present Value (PV at t = -1) of $5 million to be received after 25 years is $,, (.) = $395,482 Therefore, C x 6.079 = $395,482 i.e. C = $65,056 Hence, each deposit should be equal to $65,056 Problem 4 The cash flows can be broken into two separate cash flows patterns: 1. an annuity beginning at the end of first year and continuing for next ten years Discount Rate = 8% Present Value (PV at t=0) is $ . x1 (.) = $10,065 2. and a perpetuity beginning at the end of tenth year Discount Rate = 6%...

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