Question

Calculate the value of a bond that matures in 16 years and has a $1,000 par value. The annual coupon interest rate is 12 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 16 percent.

Answer 1

Method 1:

The value of a bond can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, Yield to Maturity), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 16%, Nper = 16, PMT = 1,000*12% = $120 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Value of Bond = PV(16%,16,120,1000) = $773.26

Answer is $773.26.

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Method 2:

The value of bond can also be calculated with the use of formula given below:

Value of Bond = Coupon Payment Year 1/(1+YTM)^1 + Coupon Payment Year 2/(1+YTM)^2 + Coupon Payment Year 3/(1+YTM)^3 + Coupon Payment Year 4/(1+YTM)^4 + Coupon Payment Year 5/(1+YTM)^5 + Coupon Payment Year 6/(1+YTM)^6 + Coupon Payment Year 7/(1+YTM)^7 + Coupon Payment Year 8/(1+YTM)^8 + Coupon Payment Year 9/(1+YTM)^9 + Coupon Payment Year 10/(1+YTM)^10 + Coupon Payment Year 11/(1+YTM)^11 + Coupon Payment Year 12/(1+YTM)^12 + Coupon Payment Year 13/(1+YTM)^13 + Coupon Payment Year 14/(1+YTM)^14 + Coupon Payment Year 15/(1+YTM)^15 + (Coupon Payment Year 16 + Face Value of Bond)/(1+YTM)^16

Substituting values in the above formula, we get,

Value of Bond = 120/(1+16%)^1 + 120/(1+16%)^2 + 120/(1+16%)^3 + 120/(1+16%)^4 + 120/(1+16%)^5 + 120/(1+16%)^6 + 120/(1+16%)^7 + 120/(1+16%)^8 + 120/(1+16%)^9 + 120/(1+16%)^10 + 120/(1+16%)^11 + 120/(1+16%)^12 + 120/(1+16%)^13 + 120/(1+16%)^14 + 120/(1+16%)^15 + (120 + 1,000)/(1+16%)^16 = $773.26

Answer is same as $773.26.