Question

A $35,000 bond has a payable interest of 6% per year compounded quarterly. The bond is expected to mature in fifteen years. If the market interest rate is 8% per year compounded quarterly, the present value of the bond closest to which of the following values?

	a.	$37,570
	b.	$22,700
	c.	$28,900
	d.	$33,400

Answer 1

Correct answer is option C. 28900

Present Value of the Bond

The Present Value of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $35,000

Quarterly Coupon Amount = $525 [$35,000 x 6.00% x ¼]

Quarterly Yield to Maturity = 2.00% [8.00% x ¼]

Maturity Period = 60 Years [15 Years x 4 Quarters]

Present Value of the Bond = Present Value of the Coupon payments + Present Value of Face Value

= $525[PVIFA 2.00%, 60 Years] + $35,000[PVIF 2.00%, 60 Years]

= [$525 x 34.76089] + [$35,000 x 0.30478]

= $18,250 + $10,667

= $28,917

“Hence, the Present Value of the Bond is closest to (c). $28,900”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)n} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.