Question

A ten-year Treasury note with a 5.000% coupon rate is sold at par value in the primary market (assume par value is $100). Bill purchases the Treasury note at a price of 103.000 when it has five years left to maturity and it has a 4.326% yield-to-maturity. Bill holds the Treasury note for three years and then sells it to George in the secondary market. George then holds the Treasury note to maturity. Assume three years from when Bill purchases the Treasury note, yield-to-maturities (interest rates) will be:

• 3.800% on T-notes with 1-year to maturity
• 4.000% on T-notes with 2-years to maturity
• 4.200% on T-notes with 3-years to maturity
• 4.400% on T-notes with 4-years to maturity
• 4.600% on T-notes with 5-years to maturity
• 5.2000% on T-notes with 10-years to maturity

1. Complete a time line for George’s Treasury note (while owned by George). You should include as much information as possible. You can let price be an unknown variable (i.e., Price = ? or PV = ?) as it will be calculated below.

0                           1     

|----------------------|-----------------      

2.         Enter the variables into the financial calculator box needed to solve for George’s purchase price.

Enter
	N	I/Y	PV	PMT	FV
Solve for

Answer 1

Bond Price = ∑(Cn x (1+YTM)n )+ P / (1+i)n

Here,

Cn =Coupon Rate / Amount of Interest

YTM = Yield to maturity

P = Face Value

N = Year(s) to maturity

I = Yield to maturity

Calculation of purchase price of bond

1-Year Maturity = ∑ (5 x (1+0.038) 1 + 100 / (1+0.038) 1

                             = 101.15

2-Year Maturity = ∑ (5 x (1+0.04) 2 + 100 / (1+0.04) 2

                             = 101.89

3-Year Maturity = ∑ (5 x (1+0.042) 3 + 100 / (1+0.042) 3

                             = 102.21

4-Year Maturity = ∑ (5 x (1+0.044) 4 + 100 / (1+0.044) 4

                             = 102.16

5-Year Maturity = ∑ (5 x (1+0.046) 5 + 100 / (1+0.046) 5

                             = 101.75

10-Year Maturity = ∑ (5 x (1+0.052) 10 + 100 / (1+0.052) 10

                             = 103.15

Years to maturity

0             1             2            3            4             5                      10

|-------------|------------|-----------|-----------|------------|-------------------|

100    101.15     101.89    102.21   102.16    101.75             103.15

N	I/Y	PV	PMT	FV
1	3.80%	101.15	5	100
2	4.00%	101.89	10	100
3	4.20%	102.21	15	100
4	4.40%	102.16	20	100
5	4.60%	101.75	25	100
10	5.20%	103.15	50	100