When Alex Rodriguez moved to the Texas Rangers in$2001,$ he received a lot of attention for his $"$$$252$million$"$ contract$($the total of the payments promised was $$$$252$million$).$ He later moved to the$$ Yankees, but assume the following in order to determine the value of his contract when he signed$$ it:

Rodriguez earns $$$$16$ million in the first$$ year, $$$$17$ million in years $2$ through$4,$$$19$ million in years $5$ and$6,$$$23$ million in year$7,$ and $$$$27$ million in years $8$ through $10.$ He also receives his $$$$10$ million signing bonus spread equally over the first $5$ years $($$$2$ million per$$ year$).$ His deferred payments begin in $2011.$ The deferred payment amounts total $$$$33$ million and are $ $5$million$,$ then $$$$4$million$,$ then eight amounts of $$$$3$ million$($ending in$2020).$ However, the actual payouts will be different. All of the deferred payments will earn $3\%$ per year until they are paid. For$$ example, the $$$$5$ million is deferred from $2001$ to$2011,$ or $10$ years, meaning that it will actually be $$$$6\mathrm{.}7196$ million when paid. Assume that the $$$$4$ million payment deferred to $2012$ is deferred from $2002($each payment is deferred $10$ years$).$

The contract is a$10-$year contract, but each year has a deferred component so that cash flows are paid out over a total of $20$ years. The contractual$$ payments, signing$$ bonus, and deferred components are given in the following$$ table: LOADING.... Note$$ that, by$$ contract, the deferred components are not paid in the year they are$$ earned, but instead are paid$($plus interest$)10$ years later.

$$

Assume that an appropriate discount rate for Rodriguez to apply to the contract payments is $7\%$ per year.

a$.$ Calculate the true promised payments under this$$ contract, including the deferred payments with interest.

b$.$ Draw a timeline of all of the payments.

c$.$ Calculate the present value of the contract.

d$.$ Compare the present value of the contract to the quoted value of $$$$252$ million. What explains the$$ difference?

Question content area bottom

Part $1$

a$.$ Calculate the true promised payments under this$$ contract, including the deferred payments with interest.

The true promised payments under this contract for years $1$ through $5$ are:$($Round all values to the nearest$$ integer.$)$

Year$1$: $$$

$$

$18$ million.

Year$2$: $$$

$$

$19$ million.

Year$3$: $$$

$$

$19$ million.$$

Year$4$: $$$

$$

$19$ million.$$

Year$5$: $$$

$$

$21$ million.$$

Part $2$

The true promised payments under this contract for years $6$ through $10$ are:$($Round all values to the nearest$$ million.$)$

Year$6$: $$$

$$

$19$ million.

Year$7$: $$$

$$

$23$ million.$$

Year$8$: $$$

$$

$27$ million.$$

Year$9$: $$$

$$

$27$ million.$$

Year$10$: $$$

$$

$27$ million.

Part $3$

The true promised payments under this contract for years $11$ through $20$ are:$($Round all values to four decimal$$ places.$)$

Year$11$: $$$

$$

$6\mathrm{.}72$ million.

Year$12$: $$$

$$

$5\mathrm{.}38$ million.

Years $13$ to$20$: $$$

$$

$4\mathrm{.}03$ million.

Part $4$

b$.$ Draw a timeline of all of the payments.$($Select the best choice$$ below.$)$

A$.$

The timeline starts at Year $1$ and ends at Year $20.$ The cash flows are $$18$ in Year $1,$ $$19$ from Year $2$ to Year $4,$ $$21$ in Year $5,$ $$19$ in Year $6,$ $$23$ in Year $7,$ $$27$ from Year $8$ to Year $10,$ $$6\mathrm{.}72$ in Year $11,$ $$5\mathrm{.}38$ in Year $12,$ and $$4\mathrm{.}03$ from Year $13$ to Year $20$

Year$12345678910111213$nothing$20$

Cash Flows$ $18$$ $18$$ $19$$ $19$$ $21$$ $19$$ $23$$ $27$$ $27$$ $27$$ $6\mathrm{.}72$$ $5\mathrm{.}38$$ $4\mathrm{.}03$nothing$ $4\mathrm{.}03$

B$.$

The timeline starts at Year $1$ and ends at Year $20.$ The cash flows are $$18$ in Year $1,$ $$19$ from Year $2$ to Year $4,$ $$21$ in Year $5,$ $$19$ in Year $6,$ $$23$ in Year $7,$ $$27$ from Year $8$ to Year $10,$ $$6\mathrm{.}72$ in Year $11,$ $$5\mathrm{.}38$ in Year $12,$ and $$4\mathrm{.}03$ from Year $13$ to Year $20$

Year$12345678910111213$nothing$20$

Cash Flows$ $18$$ $19$$ $19$$ $19$$ $21$$ $19$$ $23$$ $23$$ $27$$ $27$$ $6\mathrm{.}72$$ $5\mathrm{.}38$$ $4\mathrm{.}03$nothing$ $4\mathrm{.}03$

C$.$

The timeline starts at Year $1$ and ends at Year $20.$ The cash flows are $$18$ in Year $1,$ $$19$ from Year $2$ to Year $4,$ $$21$ in Year $5,$ $$19$ in Year $6,$ $$23$ in Year $7,$ $$27$ from Year $8$ to Year $10,$ $$6\mathrm{.}72$ in Year $11,$ $$5\mathrm{.}38$ in Year $12,$ and $$4\mathrm{.}03$ from Year $13$ to Year $20.$

Year$12345678910111213$nothing$20$

Cash Flows$ $18$$ $19$$ $19$$ $19$$ $21$$ $19$$ $23$$ $27$$ $27$$ $27$$ $6\mathrm{.}72$$ $5\mathrm{.}38$$ $4\mathrm{.}03$nothing$ $4\mathrm{.}03$

D$.$

The timeline starts at Year $1$ and ends at Year $20.$ The cash flows are $$18$ in Year $1,$ $$19$ from Year $2$ to Year $4,$ $$21$ in Year $5,$ $$19$ in Year $6,$ $$23$ in Year $7,$ $$27$ from Year $8$ to Year $10,$ $$6\mathrm{.}72$ in Year $11,$ $$5\mathrm{.}38$ in Year $12,$ and $$4\mathrm{.}03$ from Year $13$ to Year $20$

Year$12345678910111213$nothing$20$

Cash Flows$ $18$$ $19$$ $19$$ $19$$ $19$$ $21$$ $23$$ $27$$ $27$$ $27$$ $6\mathrm{.}72$$ $5\mathrm{.}38$$ $4\mathrm{.}03$nothing$ $4\mathrm{.}03$

Part $5$

c$.$ Calculate the present value of the contract.

The present value of the contract is $$$

$$

$149\mathrm{.}5$ million.$($Round to the nearest$$ million.$)$

Part $6$

d$.$ Compare the present value of the contract to the quoted value of $$$$252$ million. What explains the$$ difference?$($Select the best choice$$ below.$)$

A$.$

The reason for the difference is that the contract was quoted incorrectly.

B$.$

The reason for the difference is although the $$$$252$ million quoted value