NO EXCEL A local newspaper headline blared Jim Smith signed

NO EXCEL: A local newspaper headline blared: “Jim Smith signed for $10 Million.” A reading of the article revealed that on April 1, 1997, Jim Smith, a junior hockey scoring sensation, signed a $10 million package with the Toronto Maple Leafs. The terms of the contract were $1 million immediately, $800,000 per year for the first 5 years (first payment after 1 year) and $1 million per year for the next 5 years (first payment at year 6). If Jim’s interest rate is 8 % per year, how much is his contract worth at the time of the signing?

Solution

Contract at the time of signing

At the time of Signing the contract =$1,000,000

For first five years : Future Value = 5*$800,000 = $4,000,000

Present Value @8% interest rate = $4,000,000*(1/(1+8%)⁵)

= $4,000,000*(1/(1+0.08)⁵)

= $4,000,000*(1/(1.08)5)

= $4,000,000*(1/1.469328)

= $4,000,000*0.680583 = $2,722,333

For last five years : Future Value = 5*$1,000,000 = $5,000,000

Present Value @8% interest rate = $5,000,000*(1/(1+8%)⁵)

= $5,000,000*(1/(1+0.08)⁵)

= $5,000,000*(1/(1.08)⁵)

= $5,000,000*(1/1.469328)

= $5,000,000*0.680583 = $3,402,916

Thus at the time of signing the Contract the Contract Worth is = $1.000,000+ $2,722,333+ $3,402,916

= $ 7,125,249