Question

An issue of Australian treasury bonds with par of $1,000 matures in 15 years and pays 8% coupon interest annually. The market price of the bonds is $1,085 and your required rate of return is 10% p.a. Determine the value of the bond to you, given your required rate of return.

A. $103.00

B. $108.00

C. $847.88

D. $1,085.00

Answer 1

Given the required rate of return of 10%, value of the bond is $847.88.

Correct option is C.

-------------------------------------------------------------------------------------------------------------------------

Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ n]

Where,

Face value = $1000

Coupon rate = 8%

YTM or Required rate = 10%

Time to maturity (n) = 15 years

Annual coupon C = $80

Let's put all the values in the formula to find the bond current value

P = 80* [{1 - (1 + 0.1) ^ -15}/ (0.1)] + [1000/ (1 + 0.1) ^15]

P = 80* [{1 - (1.1) ^ -15}/ (0.1)] + [1000/ (1.1) ^15]

P = 80* [{1 - 0.23939}/ 0.1] + [1000/ 4.17725]

P = 80* [0.76061/ 0.1] + [239.39194]

P = 80* 7.6061 + 239.39194

P = 608.488 + 239.39194

P = 847.87994

So price of the bond is $847.88

-------------------------------------------------------------------------------------------------------------------------

Hope that answers your query.

Pls rate this answer if you found it useful.