Question

Suppose your firm has the following bond information.

Years to maturity: 10

Coupon Rate: 5%, semi-annual payments

Par Value: $1,000

Price: 112% of par value

Part A & B: Calculate the yield to maturity on the bond and also calculate the current yield on the bond.

Answer 1

(A). Calculation of Yield to Maturity of Bond:

Time to maturity = 10 years or 20 semi-annual periods

Coupon rate = 5% or 2.5% semi-annual

Par value = $1,000

Price of Bond = 112% of Par value = 1.12 * $1,000 = $1,120

Now, formula to calculate YTM = { [Coupon + (FV - PV) / t] / (FV + PV) / 2 }

Coupon = 2.5% semi-annual or 0.025 * $1,000 = $25

where, FV = face value or Par value of the bond = $1,000

PV = Present value or Price of the Bond = $1,120

t = time period until maturity = 20 semi-annual

Therefore, YTM = {$25 + ($1,000 - $1,120) / 20] / ($1,000 + $1,120) / 2}

YTM = {[$25 + $6] / 1,060} = 0.029 or 2.9% semi-annual or 2.9 % * 2 = 5.8% annual

(B). Calculation of Current yield:

Formula : Current Yield =  Annual Coupon / Current market price

Annual Coupon = 5% of Par value = 0.05 * $1,000 = $50

Current Market price = $1,120

Therefore, Current Yield = $50 / $1,120 = 0.0446 or 4.46%