Solutions - Midterm I Review

Solutions - Midterm I Review - UNIVERSITY OF NORTH CAROLINA...

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U NIVERSITY OF N ORTH C AROLINA A T C HAPEL H ILL K ENAN -F LAGLER B USINESS S CHOOL B USI 408: C ORPORATE F INANCE E XTRA R EVIEW P ROBLEMS P ROF . A RZU O ZOGUZ F ALL 2008 1. You make a $2000 contribution every year to your IRA. You earn 8% compounded semiannually on your savings, and you would like to retire when you are 65. How much will you have saved when you retire if you start when you are: a. 35 years old: You need to find the future value of an annuity C = $2000, at 8% compounded semiannually, for T = 65 – 35 = 30 years. Note that the effective annual rate (EAR) is % 16 . 8 0816 . 0 1 2 08 . 0 1 2 = = + () [] () ( ) 324 , 233 1 0816 . 1 0816 . 0 2000 1 1 30 = = + = T r r C FV b. 25 years old: T now becomes T = 65 – 25 = 40 () [] () ( ) 436 , 540 1 0816 . 1 0816 . 0 2000 1 1 40 = = + = T r r C FV 2. What is the present value of a 4-year $200 annuity if the third payment is skipped (assume r = 8%) ? On a time-line, this would be like C 1 = $200, C 2 = $200, C 3 = $0, and C 4 = $200. You can find the present value by brute force: () () () () () () 658 . 503 08 . 1 200 0 08 . 1 200 08 . 1 200 1 1 1 1 4 2 4 4 3 3 2 2 1 = + + + = + + + + + + + = r C r C r C r C PV
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3. What is the value of a $50 perpetuity that starts in 3 years, and grows at 5% per year if the interest rate is 10%, compounded monthly? First, note that the interest rate is 10% compounded monthly. We need to, first, find the equivalent effective annual rate: % 47 . 10 1047 . 0 12 10 . 0 1 1 12 = = + = + EAR EAR Next, we need to find the present value of a growing perpetuity: 076 . 914 05 . 0 1047 . 0 50 $ 2 = = = g r C PV Note, however, that the perpetuity starts in year 3. Therefore, the present value is the present value one period before it starts, that is, in year 2. So, we need to discount it to time 0: () () () () 02 . 749 076 . 914 1047 . 1 1 05 . 0 1047 . 0 50 $ 1047 . 1 1 1 1 1 1 2 2 2 2 2 = = = + = + = g r C r PV r PV 4. Dirk Duncan, a first-round pick for the NBAs new expansion team, the Triangle Squirrels, says that he will not sign unless his new contract makes him the highest paid player in the league. Bob O'Neil, the leagues star center, recently signed a contract that included a $30M signing bonus (he got that amount immediately), $20M per year for 5 years (paid at year end) and a lump sum payment of $10M in 6 years (in case he lost all his money before that time). Jack Jones, the Squirrel's owner, is offering Duncan a contract that pays no signing bonus and $25M per year for 5 years (paid at year end) and a $20M bonus in 5 years. Jack Jones is telling Duncan that this contract will make him the highest paid player in the league. You are Duncan's agent, and you know that Jack Jones is lying. Duncan wants to make up the difference between the contract that Jack Jones is
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This document was uploaded on 11/04/2011 for the course BUSI 408 at UNC.

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Solutions - Midterm I Review - UNIVERSITY OF NORTH CAROLINA...

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