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Pharoah, Inc., has four-year bonds outstanding that pay a coupon rate of 7.10 percent and make...

Pharoah, Inc., has four-year bonds outstanding that pay a coupon rate of 7.10 percent and make coupon payments semiannually. If these bonds are currently selling at $917.89.

What is the yield to maturity that an investor can expect to earn on these bonds? (Round answer to 1 decimal place, e.g. 15.2%.)

What is the effective annual yield? (Round answer to 1 decimal place, e.g. 15.2%.)

Expert Solution

Yield to maturity of (YTM) of the Bond

The Yield to maturity of (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value
The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.
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

Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 7.10% x ½]	PMT	35.50
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [4 Years x 2]	N	8
Bond Price/Current Market Price of the Bond [-$917.89]	PV	-917.89

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 semi-annual yield to maturity on the bond (1/Y) = 4.8%

The semi-annual Yield to maturity = 4.8%

Therefore, the annual Yield to Maturity of the Bond = 9.6% [4.8% x 2]

“Hence, the Yield to maturity of (YTM) of the Bond will be 9.6%

Effective Annual Yield

Number of Compounding per year = 2 (Since, the compounding is done semi-annually)

Therefore, the Effective Annual Yield = [(1 + (YTM/2)]² – 1

= [(1 + (0.096/2)] ² – 1

= [1 + 0.048]² – 1

= [1.048] ² – 1

= 1.098304 – 1

= 0.098304 or

= 9.8% (Rounded to 1 decimal place)

“Hence, the Effective Annual Yield on the Bond will be 9.8%”

jeff jeffy answered 2 hours ago

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