Question

A rs 5000 par value bond bearing a coupon rate of 10% will mature after 10 years. What is the price to buy the bond at today , if discounted rate is 12%

Answer 1

Bond Price = ∑(C_n / (1+YTM)ⁿ )+ P / (1+i)ⁿ

Where

• n = Period which takes values from 0 to the nth period till the cash flows ending period
• C_n = Coupon payment in the nth period
• YTM or i= interest rate or required yield
• P = Par Value of the bond

$n=10years$

Cn=10% of 5000 = 500

YTM or i = 12%= 0.12

P= 5000

$1+Interest = 1+\frac{12}{100}= 1.12$

$Bond Price =\frac{500}{(1.12)} +\frac{500}{(1.12)^{2}}+\frac{500}{(1.12)^{3}}+ \frac{500}{(1.12)^{4}}+ + \frac{500}{(1.12)^{5}} + \frac{500}{(1.12)^{6}} + \frac{500}{(1.12)^{7}} + \frac{500}{(1.12)^{8}}+ + \frac{500}{(1.12)^{9}}+ \frac{500}{(1.12)^{10}}+\frac{5000}{(1.12)^{10}}$

$BondPrice = 446.43+398.60+ 345.90+317.76+283.71+253.32+226.17+201.94+170.31+160.99 + 1609.87=4415$