Question

Evergreen Sports, Inc., has 9 percent annual coupon payment bonds on the market that will mature in 13 years. They have a par value of $1,000. If the YTM on these bonds is 9.4 percent, what is the current bond price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Gievn that Coupon Rate - 9% (Annual Coupon Payment)

Annual Coupon Amount = Coupon Rate x Par Value

Annual Coupon Amount = 9 % x $ 1000 = $ 90

Maturity Years = 13 Years

Given that YTM or Yoeld to Maturity of the bond = 9.2%

now to compute the Current Bond Price = Present Values of Coupons of the bond + Present Value of Par Value to be received at the end of 13 years.

where the discount rate is YTM of the Bond. Therefore we have the following:-

Years	Coupons (A)	Discount Factors @ 9.4 % (B)	Derivation of Discount Factors @ 9.2 % (B)	Present Values            (C= A x B)
Year 1	90	0.9140768	=1/1.094^1	82.27
Year 2	90	0.8355364	=1/1.094^2	75.20
Year 3	90	0.7637444	=1/1.094^3	68.74
Year 4	90	0.698121	=1/1.094^4	62.83
Year 5	90	0.6381362	=1/1.094^5	57.43
Year 6	90	0.5833055	=1/1.094^6	52.50
Year 7	90	0.533186	=1/1.094^7	47.99
Year 8	90	0.487373	=1/1.094^8	43.86
Year 9	90	0.4454963	=1/1.094^9	40.09
Year 10	90	0.4072178	=1/1.094^10	36.65
Year 11	90	0.3722284	=1/1.094^11	33.50
Year 12	90	0.3402453	=1/1.094^12	30.62
Year 13	90	0.3110103	=1/1.094^13	27.99
Total of Present Values of Coupons	659.67

Now the par value of the bond would be realized at the time of redemption of the bond which is 13 years. therefore we need to discount the par value.

Current Bond Price = $ 659.67 + $1000 / (1+YTM)^13

Current Bond Price = $ 659.67 + $311.01

Current Bond Price = $ 970.68