Dewey Cheetham & Howe accounting firm is considering the purchase of a $1000 New
ID: 2714115 • Letter: D
Question
Dewey Cheetham & Howe accounting firm is considering the purchase of a $1000 New Haven Municipal Bond. The stated coupon rate is 5% paid quarterly. The bond will mature in 22 years. The YTM for similar bonds is 4%.
1) What should the market price of the bond be?
2) What is the effective rate?
3) What should the market price be if the coupon were paid annually?
4) If the current market price of the ond is $1080, find the YTM with the original coupon.
5) Explain why an investor would buy a bond at a premium or at a discount.
7) What is the yield to call if the bond is callable in 10 years at a 12 premium with the original coupon?
Explanation / Answer
1..Price of bond = PV OF INTEREST + PV OF REDEMTION VALUE
PV OF INTEREST = C X F X [ 1-(1+r)^-t / r ]
C= COUPON RATE = 0.05/4=0.0125 , F = FACE VALUE = 1000, T= TIME PERIOD OCCURING OVER BOND = 22 x 4 = 88 , r = yield = 0.04/4 = 0.01 , PV = PRESENT VALUE.
= 0.0125 x 1000 x [ 1 – (1 + 0.01)^-88 / 0.01 ]
=729.25
PV OF REDEMPTION = FACE VALUE /(1+r)^t
= 1000 / (1+0.01)^88
= 416.60
Hence Price of Bond = 729.25 + 416.60 = 1145.85
2..Effective rate = (1+r)^t – 1
= (1+0.0125)^4 – 1
=1.05095 -1
=5.10%
3..Price of bond = PV OF INTEREST + PV OF REDEMTION VALUE
PV OF INTEREST = C X F X [ 1-(1+r)^-t / r ]
C= COUPON RATE = 0.05 , F = FACE VALUE = 1000, T= TIME PERIOD OCCURING OVER BOND = 22 , r = yield = 0.04 , PV = PRESENT VALUE.
= 0.05 x 1000 x [ 1 – (1 + 0.04)^-22 / 0.04 ]
=722.56
PV OF REDEMPTION = FACE VALUE /(1+r)^t
= 1000 / (1+0.04)^22
= 421.96
Hence Price of Bond = 722.56 + 421.96 = 1144.51
4.. YTM = Annual interest +( par value – market value)/years to maturity
( Par value + market price)/2
= 1000 x .05 +(1000 – 1080)22
(1000+1080)/2
=4.46%
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