Question

El Sol Inc. is offering its bonds on the market at 8% annual interest but ensures that they are paid semi-annually for 7 years. The prevailing market interest rate is currently 10%. What is the value of the bonds?

Present value $ ____________ is sold with a premium or discount ______________

Please show the formula and how to calculate the Present value and premium or discoun!!
not do it in excel do it in paper

Answer 1

	Let us assume that the Face Value of the Bond be $1000,
	and it is matured at Face Value.
	Present Value of Bond
	= Present Value of all Coupons + Present Value of Maturity Value
	= Coupons*Present Value Annuity Factor @ 10% for 7 Years
	+ Maturity Value*Present Value Factor @ 10% for 7th Year
	= (Face Value*Coupon Rate)*[(1+Interest Rate)^No of Years - 1 / Interest Rate*(1+Interest Rate)^No of Years]
	+ Maturity Value / (1+Interest Rate)^No of Years
	= ($1000*8%)*[(1+10%)^7 - 1 / 10%*(1+10%)^7] + $1000 / (1+10%)^7
	= $80*[(1.10)^7 - 1 / 0.10*(1.10)^7] + $1000 / (1.10)^7
	= $80*[1.9487171 - 1 / 0.10*1.9487171] + $1000 / 1.9487171
	= $80*[0.9487171 / 0.19487171] + $513.16
	= $389.47 + $513.16
	= $902.63
	Present Value of Bond is less than Face Value, so it is sold at discount
	Discount = $1000 - $902.63 = $97.37
	Present Value $902.63 is sold with discount of $97.37.