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#1 Solutions - TVM

#1 Solutions - TVM - UNIVERSITY OF NORTH CAROLINA AT CHAPEL...

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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 S OLUTIONS TO P RACTICE P ROBLEM SET #1: T IME V ALUE OF M ONEY P ROF . A RZU O ZOGUZ 1. Bob and Jane Loveboat are saving to buy a boat at the end of 5 years. If the boat costs $25,000, and they can earn 8 percent a year on their savings, how much do they need to put aside at the end of every year 1 through 5? You need to find the amount they need to set aside every year such that the annual savings, invested at 8 percent a year, accumulate to $25,000. That is, you have an annuity of $C with FV = $25,000. Recall that the formula for the future value of an annuity is given by: ( ) [ ] r r C FV t 1 1 + × = where C is the annual payment, r is the annual year interest rate, FV is the future value of the annuity. Therefore we have: ( ) 08 . 1 08 . 1 000 , 25 5 × = C . Solving for C gives, C = $4,261.41 2. Leeds Autos has just announced its new promotional deal on the new $45,000 Z4 Roadster. You pay $5,000 down, and then $1000 for the next 40 months. Its next door competitor, Chatham Hill Autos will give you a $3000 off the list price straight away. If the interest rate is 6% a year, which company is giving a better deal? You need to compare the present value of the two streams of payments, paying $42,000 today, vs. paying $5000 today, plus $1000 for the next 40 months. Note that the payments are monthly, so we need to use the monthly rate of 6%/12 = 0.5%. The present value of Leeds Autos offer: $5000 + PV(annuity($1000,T=40,r=0.5%)) = = ( ) 23 . 172 , 41 $ 005 . 1 1 1 005 . 0 1000 $ 5000 $ 40 = × + The present value of Chatham Hill Autos offer: $45,000 - $3000 = $42,000.
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