QUESTION THREE a) Consider the following zero-coupon rates: Zero-coupon rate (%)
ID: 2806633 • Letter: Q
Question
QUESTION THREE a) Consider the following zero-coupon rates: Zero-coupon rate (%) 4.00 4.50 4.75 4.90 5.00 Maturity (years) 4 Required: i) What is the price of a 5-year bond with a US$ 100 face value which delivers a 5% annual coupon rate? (5 marks) i) What is the yield to maturity of this bond? (5 marks) ii) Suppose that the zero-coupon rates increase instantaneously, and uniformly by 0.5%. What is the new price and the new yield to maturing of the bond? What is the impact of this rate increase for the bondholder? (7 marks) iv) Suppose now that the zero-coupon rates remain stable over time. You hold the bond until maturity. What is the annual return rate of your investment? Why is this rate different from the yield to maturity? --(8 marksrExplanation / Answer
Part a :
Price of a 5 year bond (P)
Face value = $100 , Annual coupon rates = 5%= $5
Year coupon/ Redemption PVF DCF
1 5 1/1.04 4.81
2 5 1/ (1.045)2 4.58
3 5 1/ (1.0475)3 4.35
4 5 1/ (1.049)4 4.13
5 105 1/ (1.05)5 82.27
Price of bond $ 100.14
Part b : YTM
Bond Price = cash flow * {1- [1/(1+i)n]} / i + [ Maturity Value * {1+i}n]
n = total number of coupon payments
i= Interest rate
100.14 = 5* {1- [1/(1+i)5]} / i + [ 100 /(1+i)5]
YTM = 4.969%
Part c : Coupon rate increases by 0 .5%
Price of bond = 5/1.045 + 5/ (1.05)2 + 5/ (1.0525)3 + 5/(1.054)4 + 105/ (1.055)5
= $97.999 or $ 98
Part d : Yield remains constant over time and bond held to maturity
F = 5* (1+4.9%)4 + 5 * (1+4.75%)3 + 5 * (1+4.5%)2 + 5* (1+4% )1 + 105
= $ 127.46
Let annual rate of return be x
100.14 * (1+x)5 = 127.46
X= 4.944% p.a.
If the coupon interest rate had been at FLAT 4.969% p.a. , the rate of return over 5 years would have been 4.944% p.a.
Coupon Rate Cash flow 0 5 1 4% 5 2 4.50% 5 3 4.75% 5 4 4.90% 105Related Questions
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