Intro to Finance: Valuation Bond Valuation Coupon Bonds ZeroCoupon Yield to Maturity Current Yield

What This Is

Bond valuation is the process of determining the present value of a bond's future cash flows. This is crucial in finance as it helps investors and analysts assess the bond's value, determine its yield to maturity, and make informed investment decisions. For example, consider a $1,000 face value bond with a 5% annual coupon rate and 10 years to maturity. If the market discount rate is 8%, we can use bond valuation techniques to determine the bond's current price.

Key Formulas & Symbols

• PV = FV / (1 + r)^n where PV = present value, FV = future value, r = periodic interest rate, n = number of periods.
• FV = PV × (1 + r)^n where FV = future value, PV = present value, r = periodic interest rate, n = number of periods.
• YTM = (C + (FV - PV) / N) / PV where YTM = yield to maturity, C = annual coupon payment, FV = face value, PV = present value, N = number of years to maturity.
• Current Yield = C / PV where Current Yield = current yield, C = annual coupon payment, PV = present value.
• Zero-Coupon Bond Value = FV / (1 + r)^n where Zero-Coupon Bond Value = value of zero-coupon bond, FV = face value, r = periodic interest rate, n = number of periods.
• Accrued Interest = C × (N - T) / 365 where Accrued Interest = accrued interest, C = annual coupon payment, N = number of days to maturity, T = number of days since last coupon payment.
• Dirty Price = PV + Accrued Interest where Dirty Price = dirty price, PV = present value, Accrued Interest = accrued interest.

Step-by-Step Calculation

1. Determine the bond's cash flows: coupon payments and face value at maturity.
2. Calculate the present value of each cash flow using the formula PV = FV / (1 + r)^n.
3. Sum the present values of all cash flows to determine the bond's current price.
4. Determine the yield to maturity (YTM) using the formula YTM = (C + (FV - PV) / N) / PV.
5. Calculate the current yield using the formula Current Yield = C / PV.

Common Mistakes

• Mistake: Confusing yield to maturity (YTM) with current yield.
• Correction: YTM is the total return an investor can expect to earn from a bond, while current yield is the annual coupon payment divided by the bond's current price.
• Mistake: Not considering accrued interest when calculating the dirty price.
• Correction: Accrued interest is the interest that has accrued on the bond since the last coupon payment, and it must be added to the present value to determine the dirty price.
• Mistake: Using the wrong discount rate when valuing a bond.
• Correction: The discount rate used to value a bond should be the market rate of return for a bond with similar credit risk and maturity.

Exam / CFA Tips

• Tip: Be careful when using the formula YTM = (C + (FV - PV) / N) / PV to calculate the yield to maturity, as it assumes that the bond's cash flows are paid at the end of each period.
• Tip: When valuing a zero-coupon bond, use the formula Zero-Coupon Bond Value = FV / (1 + r)^n, where FV is the face value, r is the periodic interest rate, and n is the number of periods.
• Tip: When calculating the current yield, use the formula Current Yield = C / PV, where C is the annual coupon payment and PV is the present value.

Quick Practice Problem

A $1,000 face value bond with a 5% annual coupon rate and 10 years to maturity is trading at a price of $900. What is the bond's yield to maturity?

Answer: 6.17% Explanation: Using the formula YTM = (C + (FV - PV) / N) / PV, we can calculate the bond's yield to maturity.

Last-Minute Cram Sheet

• ⚠️ The yield to maturity (YTM) is not the same as the current yield.
• The dirty price is the sum of the present value and accrued interest.
• Accrued interest is calculated using the formula Accrued Interest = C × (N - T) / 365.
• The present value of a bond's cash flows is calculated using the formula PV = FV / (1 + r)^n.
• The yield to maturity (YTM) is calculated using the formula YTM = (C + (FV - PV) / N) / PV.
• The current yield is calculated using the formula Current Yield = C / PV.
• ⚠️ Zero-coupon bonds have no coupon payments, but their value is determined using the formula Zero-Coupon Bond Value = FV / (1 + r)^n.
• ⚠️ The discount rate used to value a bond should be the market rate of return for a bond with similar credit risk and maturity.