Question

Part (a) It is said (S. Branch Walker) that the Indian who sold Manhattan for $29 was a sharp salesman. If he had put his $29 away at 4% compounded semiannually, it would now be worth over $8 billion, and he could buy most of the now-improved land back! Assume that this seller invested on January 1, 1701, the $29 he received. (Round your answers to the nearest whole dollar amount and not in millions.)

Required: 1. Use Excel to determine the balance of the investment as of December 31, 2018, assuming a 4% interest rate compounded semiannually. (Hint: Use the FV function in Excel.)

2. Use Excel to determine the balance of the investment as of December 31, 2018, assuming an 5% annual interest rate, compounded semiannually. (Hint: Use the FV function in Excel.)

3. What would be the balances for requirements 1 and 2 if interest is compounded quarterly?

4. Assume that the account consisting of this investment had a balance of $8.5 billion as of December 31, 2018. How much would the total amount be on December 31, 2024, if the annual interest rate is 5%, compounded semiannually?

Part (b) In 2000, a star major-league baseball player signed a 10-year, $257 million dollar contract with the Texas Rangers. Assume that equal payments would have been made each year to this individual and that the owner’s cost of capital (discount rate) was 11% at the time the contract was signed. What is the present value cost of the contract to the owners as of January 1, 2000, the date the contract was signed, in each of the following independent situations? (Round your answers to the nearest whole dollar amount and not in millions.)

Required: 1. The baseball player received the first payment on December 31, 2000.

2. The baseball player received the first payment on January 1, 2000, the date the contract was signed.

3. Assuming the owner is in the 43% income tax bracket, calculate your answer for requirement 1.

Answer 1

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As per Chegg policy I have solved first four questions. Thanks!

We know FV=P*(1+i)^n

Where FV= Future Value

P= Principle

i= interest rate

n=number of compounding for the period

Answer to part a_1
Here P=	$29
Rate of interest	4%
i=	4%/2= .02	as it is compounded semiannually.
Number of years from 1701 to 2018= 318
n=	636.00	as it is compounded semiannually so 318*2
FV=P*(1+i)^n
FV=29*(1+.02)^636
FV=	8,552,779.00
The balance of the investment as of December 31, 2018 is $ 8,552,779.
Answer to part a_2
Here P=	$29
Rate of interest	5%
i=	5%/2= .025	as it is compounded semiannually.
Number of years from 1701 to 2018= 318
n=	636.00	as it is compounded semiannually so 318*2
FV=P*(1+i)^n
FV=29*(1+.025)^636
FV=	191,768,110.00
The balance of the investment as of December 31, 2018 is $ 191,768,110.

Answer to part a_3
Here P=	$29					Here P=	$29
Rate of interest	4%					Rate of interest	5%
i=	4%/4= .01	as it is compounded quarterly.				i=	5%/4= .0125	as it is compounded quarterly.
Number of years from 1701 to 2018= 318						Number of years from 1701 to 2018= 318
n=	1,272.00	as it is compounded quarterly so 318*4				n=	1,272.00	as it is compounded quarterly so 318*4
FV=P*(1+i)^n						FV=P*(1+i)^n
FV=29*(1+.01)^1272						FV=29*(1+.0125)^1272
FV=	9,103,019.00					FV=	211,289,813.00
The balance of the investment as of December 31, 2018 is $ 9,103,019.						The balance of the investment as of December 31, 2018 is $ 211,289,813.

Answer to part a_4
Here P=	$8,500,000,000
Rate of interest	5%
i=	5%/2= .025	as it is compounded semiannually.
Number of years from 2018 to 2024= 6
n=	12.00	as it is compounded semiannually so 6*2
FV=P*(1+i)^n
FV=8500000000*(1+.025)^12
FV=	11,431,555,006.00
The balance of the investment as of December 31, 2024 is $ 11,431,555,006.