Question

Question 12 (5 points) 12. Compute the price of a 3.25 percent coupon bond with 5 years left to maturity and a market interest rate of 5.75 percent. (Assume interest payments are semi-annual) (just type the number without $ and round up to second decimal places. For example, if your answer is $750.84, enter 750.84). Question 13 (5 points) 13. A bond has a coupon rate of 7.5 %, pays semiannual interest, and has 12 years left to maturity. The bond's current price is $1,375. What is the yield to maturity (YTM)? (just type the number without % and round up to second decimal places. For example, if your answer is 5.498%, enter 5.50). AV

Answer 1

Solution to Question-12

The price of the bonds

The Price 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 = $16.25 [$1,000 x 3.25% x ½]

Semi-annual Yield to Maturity = 2.875% [5.75% x ½]

Maturity Period = 10 Years [5 Years x 2]

Therefore, the Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $16.25[PVIFA 2.875%, 10 Years] + $1,000[PVIF 2.875%, 10 Years]

= [$16.25 x 8.58488] + [$1,000 x 0.75318]

= $139.51 + $753.18

= $892.69

“Hence, the price of the bond will be $892.69”

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-13

Yield to Maturity 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 7.50% x ½]	PMT	37.50
Yield to Maturity [YTM]	1/Y	?
Time to Maturity [12 Years x 2]	N	24
Bond Price [-$1,375]	PV	-1,375

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 = 3.62%

“Hence, the Yield to Maturity of the Bond will be 3.62%”