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Solution
Examples: A company issues $100,000 of 5 year bonds with a stated rate of 8%. Interest payments are
made semiannually.
Draw a timeline for each of the two cash flows:
_______|_______|_______|_______|_______|_______|_______|_______|_______|_______| $100,000
_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
$4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000
Par Example (market rate = stated rate)
A company issues $100,000 of 5 year bonds with a stated rate of 8% when the market rate of interest is
8%. Interest payments are made semiannually. What is the selling price (proceeds) of the bond issue?
Market rate = 8%; Stated rate = 8%
Selling price(proceeds):
Present value of the principal
+Present value of the interest payments per compound period
Selling price of the bonds
n = 5 years X 2 = 10
i = 8% ÷ 2 = 4%
Interest payment per compound period:
Face value X stated rate X time
$100,000 X 8% X 6/12 = $4,000
OR
$100,000 X 4% = $4,000
PV = FV(PVFSSn,i) = $100,000(PVFSS10,4%) = $100,000(.67556) = $67,556
+PV = R(PVFOAn,i) = $4,000(PVFOA10,4%) = $4,000(8.1109) =
32,444 (rounded)
Selling price $100,000
Cash
Bonds Payable
100,000
100,000
Solution 10-2 Par
Premium example (market rate < stated rate)
A company issues $100,000 of 5 year bonds with a stated rate of 8% when the market rate of interest is
6%. Interest payments are made semiannually. What is the selling price (proceeds) of the bond issue?
Market rate = 6%; Stated rate = 8%
Selling price(proceeds):
Present value of the principal
+Present value of the interest payments per compound period
Selling price of the bonds
n = 5 years X 2 = 10
i = 6% ÷ 2 = 3%
Interest payment per compound period:
Face value X stated rate X time
$100,000 X 8% X 6/12 = $4,000
OR
$100,000 X 4% = $4,000
PV = FV(PVFSSn,i) = $100,000(PVFSS10,3%) = $100,000(.74409) = $74,409
+PV = R(PVFOAn,i) = $4,000(PVFOA10,3%) = $4,000(8.5302) =
34,121(rounded)
Selling price $108,530
Cash
Bonds Payable
Premium on Bonds Payable
108,530
100,000
8,530
Discount example (market rate > stated rate)
A company issues $100,000 of 5 year bonds with a stated rate of 8% when the market rate of interest is
10%. Interest payments are made semiannually. What is the selling price (proceeds) of the bond issue?
Market rate = 10%; Stated rate = 8%
Selling price(proceeds):
Present value of the principal
+Present value of the interest payments per compound period
Selling price of the bonds
n = 5 years X 2 = 10
i = 10% ÷ 2 = 5%
Interest payment per compound period:
Face value X stated rate X time
$100,000 X 8% X 6/12 = $4,000
OR
$100,000 X 4% = $4,000
PV = FV(PVFSSn,i) = $100,000(PVFSS10,5%) = $100,000(.61391) = $61,391
+PV = R(PVFOAn,i) = $4,000(PVFOA10,5%) = $4,000(7.72173) =
30,887 (rounded)
Selling price $92,278
Cash
92,278
Discount on Bonds Payable 7,722
Bonds Payable
100,000
Solution 10-3 Premium
Solution 10-4 Discount
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