Question

Assuming annual interest payments and a principal value of $100, what is the value of a 4-year 6.8% coupon bond when the discount rate is i) 4.8%, ii) 6.8%, and iii) 7.1%? Show that your results are consistent with the relationship between the coupon rate, discount rate, and price relative to par value.

Answer 1

Value or price of a bond is the sum of present value of its future cashflows. ie we need to calculate NPV at different discount rates.

Value of Bond = Present Value of Coupons + Present Value of Redemption Amount of Bond.

It can be calculated as below

coupon rate=6.8 ;

par value=100 ;

annual coupon = 100*6.8% = $6.8

term 4 years

i: 4.8% discount rate (using npv formula in excel)

Bond (Annual payment)
Years	0	1	2	3	4
Price
Coupon payment		6.8	6.8	6.8	6.8
Par value					100
Total cashflows	0	6.8	6.8	6.8	106.8
Price/NPV @4.8%	107.12

Working:

Cash Flows	DF @ 4.8%	Present Value
6.8	0.954198473	6.49
6.8	0.910494726	6.19
6.8	0.868792678	5.91
106.8	0.829000647	88.54
Present value of the Bond:	107.12

ii: 6.8%

Bond (Annual payment)
Years	0	1	2	3	4
Price
Coupon payment		6.8	6.8	6.8	6.8
Par value					100
Total cashflows	0	6.8	6.8	6.8	106.8
Price/NPV @6.8%	100.00

Working:

Cash Flows	DF @ 6.8%	Present Value
6.8	0.936329588	6.37
6.8	0.876713097	5.96
6.8	0.820892413	5.58
106.8	0.768625855	82.09
Present value of the Bond:	100.00

iii: 7.1%

Bond (Annual payment)
Years	0	1	2	3	4
Price
Coupon payment		6.8	6.8	6.8	6.8
Par value					100
Total cashflows	0	6.8	6.8	6.8	106.8
Price/NPV @7.1%	98.99

Working:

Cash Flows	DF @ 7.1%	Present Value
6.8	0.933706816	6.35
6.8	0.871808418	5.93
6.8	0.814013463	5.54
106.8	0.760049918	81.17
Present value of the Bond:	98.99

The results are consistent with the relation between coupon rate, discount rate and price

• If coupon rate and discount rate are same; the price=par value
• if coupon rate higher than discount rate; the price> par value
• if coupon rate lower than discount rate ; the price<par value