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Solnce55
1 month ago
12

Consider an 8% coupon bond selling for $953.10 with three years until maturity making annual coupon payments. the interest rates

in the next three years will be, with certainty, r1 = 8%, r2 = 10%, and r3 = 12%. calculate the bond's (a) yield to maturity and (b) realized compound yield
Business
1 answer:
arsen [2.9K]1 month ago
5 0

Answer:

a) YTM = 9.8%

b) realized compound yield = 9.9%

Explanation:

a) PMT is 80

par value FV = 1000

coupon rate = 8%

current price PV = 953.1

years to maturity n = 3

Yield to maturity (YTM) is calculated as \frac{PMT+(FV-PV)/n}{(FV+PV)/2} = \frac{80+(1000-953.1)/3}{(1000+953.1)/2}= 9.8%

b) r2 = 10% = 100%+10% = 1.1

r3 = 12% = 100%+12% = 1.12

To find the realized compound yield, we first need the future value (FV) of the principal and reinvested coupons.

FV = ($80 * 1.10 * 1.12) + ($80 * 1.12) + $1080 = $1268.16

Let a be the rate at which the future value equals $1268.16.

953.1(1+y)³ = $1268.16

(1+y)³ = 1.33

1+y = 1.099

y = 0.099 = 9.9%

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