A local newspaper headline blared, \"Bo Smith Signed for $30 Million. A reading

Question

A local newspaper headline blared, "Bo Smith Signed for $30 Million. A reading of the article revealed that on April 1, 2014, Bo Smith, the former record-breaking running back from Football University, signed a $30 million package with the Dallas Rangers. The terms of the contract were $3 million immediately, $2.4 million per year for the first five years (with the first payment after one year) and S3 million per year for the next five years (with the first payment at year 6). If Bo's interest rate is 8% per year what would his contract be worth at the time he signs it? Click the icon to view the interest factors for discrete compounding when ,-8% per year More Info The contract will be worth S millions at the time Bo signs it. (Round to two decimal places.) Compound Present Compound Sinking Present Capital Amount Worth Recovery Factor (FIA, ?N) 1.0000 2.0800 Factor Factor (AF, i, N) 1.0000 0.4808 0.3080 0.2219 0.1705 (F/P i, N) (P/F, i, N) (P/A, i, N) 1.0800 1.1664 1.2597 1.3605 1.4693 0.9259 0.8573 0.7938 0.7350 0.6806 (AP, i, N) 1.0800 0.5608 0.3880 0.3019 0.2505 0.9259 2.5771 3.3121 3.9927 4.5061 1.5869 17138 1.8509 1.9990 2.1589 7.3359 8.9228 10.6366 12.4876 14.4866 0.1363 0.1121 0.0940 0.0801 0.0690 4.6229 5.2064 5.7466 6.2469 6.7101 0.2163 0.1921 0.1740 0.1601 0.1490 0.5835 0.5403 0.4632 PrintDone Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

We need to calculate the PV of the total cashflow series at time t=0.

Cash flow at year 1 is already at PV. So that one is sorted.

We have two 5 yr annuities - one that starts next year and is of $2.4 mil, other that starts from year 6 and is of $3 mil.

PV of the 2 annuities can be found from the table above,

For first annuity of $2.4 mil, that starts at year 1 and lasts till year 5, at 8%,

PV (for first annuity) = $2.4 * 3.9927 = $9.5825mil (where 3.9927 is the PV worth factor for 5 yr annuity in table above)

For second annuity of $3 mil, that starts at year 6 and lasts till year 10 (so is a 5 yr annuity again), at 8%,

PV (at year = 5) = $3 * 3.9927 = $11.9781 mil (where 3.9927 is the PV worth factor for 5 yr annuity in table above)

Now, in order to discount this value to t = 0,

PV (at t= 0) for 2nd annuity = 11.9781 * 0.6806 = $8.1523 mil

Hence, combined PV = $3 mil +  $9.5825mil + $8.1523 mil = $20.73 mil

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