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1. What is the present value of \$1,250 due in 10 years at a 7% discount rate?

2. Suppose an index of small firm stocks started in 1946 at 10, and the index level was 1890.59 in 2001. What is the capital gains yield of the small firm stocks for the period?

3. Suppose the following relationships for the Dawn Corporation:
Sales/total assets= 10x
Return on assets= 15%
Return on equity= 25%

What is their profit margin?

4. Suppose the following data on yields from holds:

3-month T-Bill=5.0%
30-year T-Bond=6.5%
30-year AAA Corporate=7.3%
30-year Municipal=5.475%

Assume the same risk for 30-year AAA Corporate bonds and 30-year Municipal Bonds. If you are indifferent between the two bonds what is your implied marginal tax rate?

## SOLUTION This solution is FREE courtesy of BrainMass!

1. We are to find the PV of a lump sum
PV = FV/(1+rate)^n = 1,250/(1+7%)^10 = \$635.44

2. The capital gains yield is the growth rate of the index. The initial value = 10 and the final value is 1890.59 and the time period is 2001-1946 = 55 years
Using the compound interest formula
1,890.59 = 10 X (1+rate)^55
(1+rate) = (1,890.59/10)^(1/55) = 1.1
Capital gains yield = 1.1-1 = 10%

3. Profit margin = Net Income/Sales
We can write
Return on Assets = Net Income/Sales X Sales/Assets
Return on Assets = Profit Margin X Sales/Assets
15% = Profit Margin X 10
Profit Margin = 15%/10 = 1.5%

4. The municipal bond is tax free while the corporate bond is taxed. The after tax yield on the corporate bond should be equal to the municipal bond to be indifferent.
After tax yield = Before tax yield X (1-tax rate)
We get
5.475% = 7.3% X (1-tax rate)
(1-tax rate) = 5.475%/7.3% = 0.75
Tax rate = 25%.

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