Question

3. A $1,000 par bond has a 5% semi-annual coupon and 12 years to maturity. Bonds of similar risk are currently yielding 6.5%. a. What should be the current price of the bond? b. If the bond’s price five years from now is $1,105, what would be the yield to maturity for the bond at that time? c. What will the price of this bond be 1 year prior to maturity if its yield to maturity is the same as that computed in part b?

Answer 1

3a. Current price of the bond will be the present value of all future coupon payments and maturity amount that will be discounted using a rate of 6.5%.

Semi-annual coupon payment = 5%*1000*1/2 = $25. No. of coupon payments = 12*2 = 24

The 1st coupon payment will be made 0.5 years from now (i.e after 6 months), 2nd after 1 year, 3rd after 1.5 years and so on.

Year	Cash flow	1+r	PVIF	PV
0.50	25.00	1.065	0.9690	24.23
1.00	25.00		0.9390	23.47
1.50	25.00		0.9099	22.75
2.00	25.00		0.8817	22.04
2.50	25.00		0.8543	21.36
3.00	25.00		0.8278	20.70
3.50	25.00		0.8022	20.05
4.00	25.00		0.7773	19.43
4.50	25.00		0.7532	18.83
5.00	25.00		0.7299	18.25
5.50	25.00		0.7073	17.68
6.00	25.00		0.6853	17.13
6.50	25.00		0.6641	16.60
7.00	25.00		0.6435	16.09
7.50	25.00		0.6236	15.59
8.00	25.00		0.6042	15.11
8.50	25.00		0.5855	14.64
9.00	25.00		0.5674	14.18
9.50	25.00		0.5498	13.74
10.00	25.00		0.5327	13.32
10.50	25.00		0.5162	12.91
11.00	25.00		0.5002	12.51
11.50	25.00		0.4847	12.12
12.00	25.00		0.4697	11.74
12.00	1,000.00		0.4697	469.68
			NPV	884.14

Thus price = $884.14

b. Bond price at t = 5 (at the end of 5th year) is 1105.

Let the yield to maturity be x%. Thus no. of coupon payments left = (12-5)*2 = 14 coupon payments

No. of years left = 12-5 = 7 years

Thus 25/(1+x)^0.5+25/(1+x)^1+25/(1+x)^1.5........+25/(1+x)^7+1000/(1+x)^7 = 1105

Solving we get x = 3.33%

Thus YTM = 3.3347%

c. 1 year prior to maturity = 12-1 = 11th year

Thus at the end of 11th year the present value of cash flow receivables = 25/(1+3.3347%)^0.5+25/(1+3.3347%)^1+1000/(1+3.3347%)^1

= $998.32