,INV3702 Assignment 2 (COMPLETE ANSWERS) Semester
2 2024 - DUE September 2024 ; 100% TRUSTED Complete,
trusted solutions and explanations.
Question 1 You observe the following sovereign bonds. Time to
maturity Coupon Yield to maturity Bond A 1 year 6% 2.342%
Bond B 1 year 0% 2.350% Bond C 2 years 6% 2.496% Bond D
2 years 0% 2.500% Bond E 3 years 6% 2.711% Bond F 3 years
0% 2.725% Determine whether Bond C is overvalued,
undervalued or fairly valued. All coupons are paid annually. (3)
To determine whether Bond C is overvalued, undervalued, or
fairly valued, we need to compare its price with its theoretical
value based on its coupon rate, yield to maturity (YTM), and
time to maturity. Let's break this down step-by-step:
1. Bond Pricing Formula
The price of a bond can be calculated using the present value of
its future cash flows, which includes the annual coupon
payments and the face value (which is usually paid at maturity).
The formula for the price of a bond is:
P=∑C(1+r)t+F(1+r)nP = \sum \frac{C}{(1 + r)^t} + \frac{F}{(1
+ r)^n}P=∑(1+r)tC+(1+r)nF
where:
• PPP = Price of the bond
• CCC = Annual coupon payment
• rrr = Yield to maturity (YTM)
, • ttt = Year in which the coupon is paid
• FFF = Face value of the bond (assumed to be 100 for
simplicity)
• nnn = Time to maturity
2. Given Data for Bond C
• Time to Maturity (n): 2 years
• Coupon Rate: 6%
• Yield to Maturity (YTM): 2.496%
• Annual Coupon Payment (C): 6%×100=66\% \times 100
= 66%×100=6 (assuming a face value of 100)
3. Calculate the Price of Bond C
Using the given data, we calculate the price of Bond C using the
present value formula:
P=6(1+0.02496)1+6(1+0.02496)2+100(1+0.02496)2P =
\frac{6}{(1 + 0.02496)^1} + \frac{6}{(1 + 0.02496)^2} +
\frac{100}{(1 + 0.02496)^2}P=(1+0.02496)16+(1+0.02496)26
+(1+0.02496)2100
Breaking it down:
• Year 1 Coupon Payment:
6(1+0.02496)1=61.02496≈5.857\frac{6}{(1 + 0.02496)^1} =
\frac{6}{1.02496} \approx 5.857(1+0.02496)16=1.024966
≈5.857
• Year 2 Coupon Payment:
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