Bond Valuation: How to Calculate Bond Value and YTM
Learn how to value bonds, calculate yields, and understand the relationship between market price and bond value. Get insights on prices, yields, and key formulas for bond investing.
Bond Valuation: How to Calculate Bond Value and YTM
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Bond Valuation Bond Contract Issuer (Seller) Investors (Buyers) $ $ $
Bond Contract How much should you pay ? Bond Value = ? Buy the bond today 1 2 3 4 n C C C C C 1 Par 2
Value of Bond today C = Coupon Payment = coupon rate x par Par value or Face Value = $1,000 Bond Value = C (PVIFA i, n) + Par (PVIF i, n) 1 2 3 4 n C C C C C 1 Par 2
An example You buy bond with $1,000 par value, Coupon rate 9% paid once per year, 5 years until maturity. Assume interest rate is 3%. What is the value of this bond? 90 90 90 90 90 1,000 Vb = C x PVIFA i, n + PAR x PVIF i, n 90 x PVIFA 3%,5 + 1,000 x PVIF 3%,5 1,274.77
Find value of bond with $1,000 par value, Coupon rate 15% paid once per year, 4 years until maturity Vb = C (PVIFA i,n) + Par (PVIF i,n) If interest Bond Price • Bond sold at Premium = 10% $ 1,158.49 • Bond is sold at Par = 15% $ 1,000 • Bond sold at Discount = 20% $ 870.61 • Price-Yield relationship
Semiannual coupon payment Coupon per period = coupon per year ÷ 2 Find value of bond with 10% coupon rate paid semiannually, 10 years maturity. Interest rate is 6% Bond Value = C (PVIFA i/2,nx2) + Par (PVIF i/2,nx2) Coupon per period = 10% x 1,000 ÷ 2 = 50 Vb = 50 (PVIFA 3% , 20 ) + 1,000 (PVIF 3% , 20 ) Vb = 50 (14.8775) + 1,000 (0.5537) Vb = 1,297.57
Finding the interest rate (YTM) = coupon per year + [(par – price) ÷ n] (par + price) ÷ 2 ***coupon per year = coupon rate x par ***par = $1,000 ***price = market price ***n = number of years
Finding the interest rate (YTM) = coupon per year + [(par – price) ÷ n] (par + price) ÷ 2 ***coupon per year = 10% x 1000 = $ 100 ***par = $1,000 ***price = $ 850 ***n = 5 years
Finding the interest rate (YTM) = $ 100 + [(1,000 – 850) ÷ 5] (1,000 + 850) ÷ 2 ***coupon per year = 10% x 1000 = $ 100 ***par = $1,000 ***price = $ 850 ***n = 5 years
Finding the interest rate (YTM) = $ 100 + [(1,000 – 850) ÷ 5] (1,000 + 850) ÷ 2 = $ 100 + 30 925 = 0.1405 = 14.05 %
Finding the interest rate (YTM) = $ 160 + [(1,000 – 1,100) ÷ 10] (1,000 + 1,100) ÷ 2 ***coupon per year = 16% x 1000 = $ 160 ***par = $1,000 ***price = $ 1,100 ***n = 10 years
Finding the interest rate (YTM) = $ 160 + [(1,000 – 1,100) ÷ 10] (1,000 + 1,100) ÷ 2 = $ 160 - 10 1,050 = 14.29 % = 0.1429
Exercise 1. A corporate bond with a coupon rate of 7% matures in 4 years. Its price is currently $1,150. - Calculate the current yield on this bond - Calculate the yield to maturity on this bond
Current Yield Formula The current yield refers simply to the annual payment (coupon) divided by the price. Yc = R/P where Yc is the current yield, R is the annual coupon payment in dollars, P is the market price.
Current Yield Example Market price of 5-years treasury bond is $1,020. the bond is paying a coupon of $50 per year. Find the current yield. Yc = 50 1020 Yc = 0.049 or 4.9%
Comparing bond value & market price If the marketprice of Bond < Bond Value Then the Bond is “Cheap” Bond is Undervalued (Underpriced) Investors will buy the Bond Demand > Supply Price will increase
Comparing bond value & market price If the marketprice of Bond > Bond Value Then the Bond is “Expensive” Bond is Overvalued (Overpriced) Investors will sell the Bond Demand < Supply Price will decrease
A bond will have a higher price if: Interest rate (yield) is …………….(higher/lower) Coupon rate, payment is …………….(higher/lower) Maturity is ……….(longer/shorter)
