This paper presents worked solutions to a series of financial accounting and valuation problems. It demonstrates the present value (PV) formula and applies it at multiple interest rates to a $10,000 bond, illustrating the inverse relationship between interest rates and present value. The paper also examines McDonald Corporation's GAAP versus economic balance sheet values, explaining why a large gap exists between book and market value due to brand equity and liability omissions. Finally, it analyzes three loan repayment options for Dover Bank, equating them to financial instruments such as zero-coupon bonds, mortgages, and par-value bonds, and evaluates their relative risk profiles.
This paper uses the following formula to solve the present value problems.
Original equation: FV = PV × (1 + i)n
Dividing both sides by (1 + i)n yields the final equation:
Final equation: PV = FV / (1 + i)n or equivalently PV = FV × (1 + i)−n
Where:
PV = Present Value
FV = Future Value
i = Interest rate
n = Number of years
Using this formula, the paper calculates the present value of a $10,000 bond with a 6% annual coupon at the end of a five-year term. Calculations were performed using Excel 2007.
PV = $10,000 / (1 + 0.06)5
PV = $7,472.58
Excel formula: =B1/(1+B2)^5
PV = $10,000 / (1 + 0.08)5
PV = $6,805.83
"GAAP vs. economic balance sheet and valuation gap"
"Three loan options mapped to bond instruments with PV"
"Riskiest and safest repayment options for Dover Bank"
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