Question

Question 1 Suppose you enter into a forward contract for a 15-year coupon paying corporate bond. The bond has a face value of $10,000 and pays six-monthly coupons of 8% per annum. The forward contract specifies that in 5.5 years, immediately after the coupon then due, you will sell the bond to the other party (Investor A) for a certain forward price, K₀.

(a) Assuming a risk-free effective rate of interest of 5% per annum (i.e., i = 5%), and an agreed forward price of $10,400, calculate the current price of the bond. [4 marks]

(b) Suppose it is now exactly 3.75 years since you entered into the forward contract and you have decided to sell the forward contract to another investor (Investor B, who will therefore also hold the short position in the contract). Assuming the same risk-free rate of interest as in (b) above, and that the current price (i.e., at 3.75 years after entering the forward contract) of the corporate bond is $10,900, and that no arbitrage opportunities exist, what price will Investor B be willing to pay for the existing forward contract?

(Step-by-step solution is preferred, please not solve by using an excel spreadsheet. Thanks in advance)

Answer 1

(a)

Current price of the bond= PV of the interest to be received in 5.5 years + PV of 10400 ( to be received at end of 5.5 years)

Interest on bond = 8% pa, 4% for every 6 months.

PV shall be found out using risk free rate of 5% pa, which will be discounted at half yearly basis @2.5%

current price of bond=

Period of Interest	Interest at PV		bond value @PV
1	=400/1.025^A2	390.243902439024
2	=400/1.025^A3	380.725758477097
3	=400/1.025^A4	371.439764367899
4	=400/1.025^A5	362.380257919902
5	=400/1.025^A6	353.541715043807
6	=400/1.025^A7	344.918746384202
7	=400/1.025^A8	336.506094033368
8	=400/1.025^A9	328.298628325237
9	=400/1.025^A10	320.291344707548
10	=400/1.025^A11	312.479360690291
11	=400/1.025^A12	304.857912868576	=10400/1.025^A12	7926.30573458299
	=SUM(B2:B12)	3805.68348525695	=SUM(D12)	11731.98

(b)

After 3.75 years, bond is sold to B with the existing forward contract to sell it to A at end of 5.5 years.

So B will hold it for 1.25 years and after that sell it to A @10400

B will receive 3 interest instalments

interest	due date of interest	due date of interest in yrs	pv of interest @5%	PV of interest
400	3 month	0.25	=400/1.0125	395.06
400	9 month	0.75	=400/(1.0125*1.025)	385.43
400	15 months	1.25	=400/(1.0125*1.025*1.025)	376.02
				1156.51
		PV of 10400	=10400/(1.0125*1.025*1.025)	9776.67
			Max amount B will be willing to pay	10933.18