TVM extra Apps Solutions - Time Value of Money(More Fun...

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1 Time Value of Money (More Fun Applications) 1. First City Bank pays 4% simple interest on its savings account balances. Second City Bank pays 4% interest, compounded quarterly. If you deposit $10,000 in each account, how much will you have in each after 10 years? First City Bank – simple interest $10,000 x .04 = $400 interest per year. Interest is paid only on the original amount deposited, so over 10 years the interest earned is $400 per year times 10 years = $4,000. After 10 years you have $10,000 deposit + $4,000 interest = $14,000. Second City Bank – compound interest, with quarterly compounding P/Y = 4 for quarterly compounding I = 4 N = 40 PV = -10,000 Solve: FV = $14,888.64 Or, try this – you earn 4% per year, or 1% per quarter. So you would have: 10,000 (1.01)(1.01)(1.01) (do this 40 times) or 10,000 (1.01) 40 = $14,888.64 2. Near the end of 2005, baseball player A. J. Burnett signed what was reported to be a $55 million contract with the Toronto Blue Jays. It consisted of a $6 million signing bonus, a $1 million salary for 2006, and a $12 million salary for years 2007 through 2010. Did he really get $55 million? Estimate the value of his contract. Since the payoffs are not considered high risk, use a discount rate of 5 percent. Timeline: 0 6,000,000 1 1,000,000 2 12,000,000 3 12,000,000 4 12,000,000 5 12,000,000
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2 Discount $1,000,000 back 1 year to time 0: P/Y = 1 FV = 1,000,000 N = 1 I = 5 Solve: PV = $952,381 Discount 4-year deferred annuity of 12,000,000 back to year 1 and then back to 0: N=4 I=5 PMT = 12,000,000 PV = 42,551,406 (this PV is at year 1) FV = 42,551,406 N = 1 I = 5 Solve: PV = $40,525,149 Add the 2 present values above to the $6,000,000
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