Question

Q1. Moerdyk Corporation's bonds have a 15-year maturity, a 5.25% coupon rate with interest paid semiannually, and a par value of $1,000. The nominal required rate of return on these bonds is 7.50%. What is the bond’s intrinsic value?

Q2.Niendorf Corporation's 25-year maturity bonds have an 8.75% coupon rate with interest paid semiannually, and a par value of $1,000. The bonds are currently selling at a premium price of $1,150 in the bond market. What is their yield to maturity (YTM)

Answer 1

Solution to Question-1

Intrinsic Value of the Bond

The Intrinsic 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 = $1,000

Semi-annual Coupon Amount = $26.25 [$1,000 x 5.25% x ½]

Semi-annual Yield to Maturity = 3.75% [7.50% x ½]

Maturity Period = 30 Years [15 Years x 2]

The Intrinsic Value of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $26.25[PVIFA 3.75%, 30 Years] + $1,000[PVIF 3.75%, 30 Years]

= [$26.25 x 17.82925] + [$1,000 x 0.33140]

= $468.02 + $331.40

= $799.42

“Intrinsic Value of the Bond = $799.42”

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.   

Solution to Question-2

Yield to Maturity (YTM) of the Bond

The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Face Value [$1,000]	FV	1,000
Coupon Amount [$1,000 x 8.75% x ½]	PMT	43.75
Yield to Maturity [YTM]	1/Y	?
Time to Maturity [25 Years x 2]	N	50
Bond Price [-$1,150]	PV	-1,150

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the yield to maturity (YTM) on the bond = 7.42%

“Therefore, the Yield to Maturity (YTM) of the Bond would be 7.42%”