Question

A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $1,150. If the yield to maturity remains at its current rate, default risk is zero, and the bond is non-callable, what are the expected current and capital gains yields?A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $1,150. If the yield to maturity remains at its current rate, default risk is zero, and the bond is non-callable, what are the expected current and capital gains yields?

Answer 1

Before we get into these questions, let's understand couple of things:

• Total yield on the bond = Yield to maturity that can be calculated using the RATE function in excel.
• Total yield has two components:
  • Current yield = Annual coupon payment / Current price of the bond
  • Capital gains yield
• Total yield = Current Yield + Capital Gains Yield
• Hence, capital gains yield = Total Yield or YTM - Current Yield

Let's now solve the question.

A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $1,150. If the yield to maturity remains at its current rate, default risk is zero, and the bond is non-callable.

Yield to maturity can be calculated using the RATE function in excel. Inputs are:

Period = 25 years

PMT = Annual coupon = coupon rate x Par value = 8.5% x 1,000 = $ 85

PV = - Current price = -1,150

FV = Future value = Par value = 1,000

Hence, YTM = RATE (Period, PMT, PV, FV) = RATE (25, 85, -1150, 1000) = 7.19%

Current Yield = Annual coupon / Current Price = 85 / 1150 = 7.39%

Hence, Capital Gains Yield = Total Yield or YTM - Current Yield = 7.19% - 7.39% = - 0.20%

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