Question

Consider a bond with a par value of £1,000, a coupon rate of 8%, a maturity of 20 years and one coupon instalment per year. The market interest rate is currently 10%. Suppose you buy the bond today with the view to sell it in a year’s time. What would be your return on the bond if interest rate were to rise to 15% in a year’s time? 

Answer 1

Solutions:

Derive the annual interest rate:

Annual interest rate =$Par \;value\times coupon \;rate$

                                = $\pounds1000\times 8\% = \pounds80$

Yield To Maturity (YTM) interest rate = 15%

Return on the bond = $\frac{C}{N}[\frac{1 - ((1+\frac{R}{N}))^{2} (-N\times T))) ]}{\frac{R}{N}}]+[\frac{F}{((1+\frac{R}{N}))^{2}(-N\times T)))} ]$

Where:

C = Annual interest = £80

N = Number of payments per year = 1

R = YTM = 0.15

F = Par value = £1000

T = Number of years until maturity = 20 years

Plug the figures into the formula:

$\frac{80}{1}[\frac{1 - ((1+\frac{0.15}{1}))^{2} (-1\times 20))) ]}{\frac{0.15}{1}}]+[\frac{1000}{((1+\frac{0.15}{1}))^{2}(-1\times 20)))} ]$

$\frac{80}{1}[1-(\frac{(1.15^{2} -20)}{0.15}]+[\frac{1000}{1.15^{2} 20)}]$

$(80) (\frac{1-0.0611}{0.15} )+(\frac{1000}{16.3665} )$

$(80) (\frac{0.9389}{0.15} )+(61 )$

$500.75+61 = \pounds561.75$

Return on the bond = £561.75