Question

Callaghan Motor’s bonds have 7 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 5.5 percent. The bonds have a yield to maturity of 8 percent.

1. What is the current market price of these bonds?

2. What is the current yield?

3. What is the capital gain/loss yield?

Answer 1

(1)-The current market price of these 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

Annual Coupon Amount = $55 [$1,000 x 5.50%]

Annual Yield to Maturity = 8%

Maturity Period = 7 Years

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

= $55[PVIFA 8%, 7 Years] + $1,000[PVIF 8%, 7 Years]

= [$55 x 5.20637] + [$1,000 x 0.58349]

= $286.35 + $583.49

= $869.84

“The current market price of these bonds will be $869.84”

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.   

(2)-Current Yield of the Bond

Current Yield of the Bond = [Annual Coupon Amount / Intrinsic Value of the Bond] x 100

= [$55 / $869.84] x 100

= 6.32%

(3)-Capital Gain Yield

Yield to Maturity of the Bond = Current Yield + Capital Gain Yield

8.00% = 6.32% + Capital Gain Yield

Therefore, the Capital Gain Yield of the Bond = Yield to Maturity of the Bond - Current Yield

= 8.00% - 6.32%

= 1.68%