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.

-->(I looked the sample but didn't get it very well), Please explain it clearly, Thank you

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

It can be calculated as below

coupon ratre=6.8 ; par value=100 ; 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

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

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

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