Solutions to the Present Value Problems

Solutions to the Present Value Problems

The study uses the formula below to solve the problems.

Formula:

Original Equation: FV = PV * (1+ i) n

Manipulation: Divide both sides by (1 +i) n

Final Equation: PV = FV / (1+ i) n or PV = FV * (1+i) -n

Where

PV = Present Value

FV =Future Value

i= interest rates n = Number of years.

Using the formula presented above, the paper calculates the PV of the $10,000 bond with the 6% of annual coupon at the end of the five-year. Using the Excel Software 2007 for the calculation, the answers to the problems are as follows:

At 6% interest rates, the PV is as follows:

PV = $10,000 / (1 + 0.06)

PV= $7,472.58

Using the excel formula, the solution is as follows:

Excel Formula

=B1 / (1+B2)^

A

B

FV

10000

Interest Rates

0,06

Number of Years

PV

7472,58173

b. At 8% interest rates

PV = $10,000 / (1 + 0.08)

PV = $6,805.83197

Using the Excel formula, the solution is as follows:

Excel Formula

=B1 / (1+B2)^5

A

B

FV

10000

Interest Rates

0,08

Number of Years

PV

c. At 4% interest rates

PV = $10,000 / (1 + 0.04)5

PV = $8,219.27107

Using the Excel formula, the solution is as follows:

Excel Formula

=B1/(1+B2)^5

A

B

FV

10000

Interest Rates

0,04

Number of Years

PV

8219,27107

d. The results of the (a), (b) and (c) reveal that increase in the interest rates decrease the present value of the investment. By January 1, 2000, investors will be willing to pay $8,219.27 if the interest rate is 4%, $6,805.83 if the interest rate is 8% and $7,472.58 if the interest rates are 8%. Thus, investors are advisable to choose the option (b), which the present value is $6,805 since investors will pay the lowest PV for the investment.

Answers to Problem 7-5

a. McDonald Corporation ($Million)

1999 Consolidated Balance Sheet

GAAP

Economic

Difference

Curent Assets

Cash and Equivalents

Account & Notes Receivable

Inventories at cost (not in excess of market)

82.7

Prepaid Expenses & other Current Assets

Total Current Assets

Other Assets

Investments in & advanced to affliates

Intangible Assets (net)

1985.42

Miscellaneous

Total Other Assets

Property & Equipment

Property and Equipment, at cost

22450.8

57776.85

35326.05

Accumulated Depreciation & Amortization

(6126.30)

(15765.95)

(9639.65)

Net Property & Equipment

16324.5

42010.89

25686.39

Total Assets

$20,983.20

$54,000

$33,016.80

b. Justification of Economic Value

The justification of the economic value is to estimate the maximum amount that the asset of McDonald worth in a free market economy. Sometimes, investor may be willing to purchase the company in the future; the economic value reveals the maximum amount of price that the company may be willing to offer its assets.

c. Major reason a large difference occurs between the McDonald's book value and market value is that the paper has not considered the total liabilities of the company in the calculation. If the paper subtracts the total liabilities from the total assets, the difference between the book value and market value will be small. Thus, a large difference occurs between the company book value and market value because the paper does not consider total liabilities in the calculation.

Other reason leading to a large difference between the book value and market is that McDonald is one of the largest companies in the world, and the company has one of the most valuable brands in the world. It is also one of the Fortune 500 lists. Thus, the company's market value will be the combination of the prices of the total assets, brands and goodwill. However, the McDonald book value will only consider the price of the assets and not price of the brands and goodwill.

Answers to Problem 12-11

a. The option 1 is equivalent to zero -coupon bond because the zero-coupon bond does not pay the interest until the end of the maturity. Thus, the option 1 is equivalent to the zero -coupon bond.

b. The Option 2 is equivalent of the mortgage because the mortgage loan allows borrowers to pay interest and principal at installment within the three years of the payment term.

c. The Option 3 is equivalent of the bond sold at par value.

d. The present value of each of the option is as follows:

Option 1: Present value is $86,383.73. The breakdown is revealed in the table below:

PV (Present Value)

$86,383.73

FV (Future Value)

$99,999.97

N (Number of Periods)

3.000

I/Y (Interest Rate)

5.000

PMT (Periodic Payment)

$5,000.00

Starting Investment

$72,767.49

Total Principle

$87,767.49

Total Interest

$12,232.48

Option 2: The present value at each of the year is 34,792.20 and the PV for the three-year is 34,792.20 x 3 = $104,916.6.

PV (Present Value)

$34,972.20

FV (Future Value)

$36,720.81

N (Number of Periods)

1.000

I/Y (Interest Rate)

5.000

PMT (Periodic Payment)

$0.00

Starting Investment

$34,972.20

Total Principle

$34,972.20

Total Interest

$1,748.61

Option 3: Present value is $86,383.78. The breakdown is revealed in the table below:

PV (Present Value)

$86,383.78

FV (Future Value)

$100,000.03

N (Number of Periods)

3.000

I/Y (Interest Rate)