Question

A bond was issued by Ranyah Corporation 13 years ago and pays interest annually. The bond has a coupon rate of 5% and a face value of SAR 5,000. The bond will mature in 17 years. What is the closest value to an investor with a required return of 7%?

Answer 1

Given

Face value of a Bond = SAR 5000

Coupon rate = 5%

Coupon Amount = Face value * Coupon rate

= SAR 5000*5%

=SAR 250

Reqired rate of return = 7%

Remaining time to maturity =17 Years

We know that Bond market price is equal to the Present value of future Cash flows at a required rate of return

Bond Price = Present value of interest accruing for 17 Years+PV of Redemption amount.

Computation of Present value of interest

We know that PV of Ordinary Annuity = C [ { 1-( 1+i)^-n } /i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

PV of interest = SAR 250[ { 1-( 1+0.07)^-17} /0.07]

= SAR 250[ { 1- ( 1.07)^-17} /0.07]]

= SAR 250[ { 1-0.31657439} /0.07]

= SAR250[ { 0.68342561/0.07}]

= SAR 250*9.7632

= SAR 2440.80

Hence Present value of interest is $ 2240.80

Computation of Present value of Redemption amount

We know that Present Value = Future Value / ( 1+i)^n

= SAR 5000/ ( 1+0.07)^17

= SAR 5000/ ( 1.07)^17

= SAR 5000/ 3.1588

= SAR 1582.8719

Computation of Market price of a Bond

Market price of a bond = PV of interest + PV of redemption amount

= SAR 2440.80+SAR 1582.8719

= SAR 4023.671952

Hence the Price of a Bond is Close to SAR 4023.671952.