Question

AT&T issued $10,000,000 worth of bonds on April 13, 1999. The bonds had a 6% coupon rate with coupon payments every October and April 13th. Their maturity date is April 13, 2029. At the time of issuance, each $1,000 bond sold for $1,245.62. All rates are APR’s with semiannual compounding.

a. What was the original yield-to-maturity (YTM) when the bonds were issued?

b. If the market rate of interest for such bonds was 9% on April 13, 2020, at what price would a $1,000 bond sell on that date?

c. If you had purchased one, or more, of these bonds when they were issued and received all of the intervening coupon payments through April 13, 2020 what was your holding-period-yield (HPY)?

no excel please! thank you

Answer 1

a. We can use financial calculator for calculation of original YTM with below key strokes:

N = no. of semi-annual periods = 30*2 = 60; PV = selling price = -1,245.62; FV = par value = 1,000; PMT = semi-annual coupon = 1,000*6%/2 = 30 > CPT = compute > I/Y = semi-annual YTM = 2.25%

Annual YTM = 2.25%*2 = 4.5‬%

bond maturity is 30 years (2029 - 1999). PV needs to be entered as negative value because it's a cash outflow.

b. N = no. of semi-annual periods = 9*2 = 18; I/Y = semi-annual YTM = 9%/2 = 4.5%; FV = par value = 1,000; PMT = semi-annual coupon = 1,000*6%/2 = 30 > CPT = compute > PV = selling price = 817.60

Bond will sell at $817.60 on April 13,2020.

remaining maturity is 9 years (2029 - 2020).

c. If bond was purchased on April 13,1999 at $1,245.62 then holding period would be 21 years (2020 - 1999). in 21 years, 21*2 = 42 coupons of $30 each would have been received.

Holding period yield = [(ending value + income)/beginning value] - 1

ending value is price of bond on April 13,2020 which is $817.60. income is 42*$30 = $1,260 and beginning value is purchase price which is $1,245.62.

Holding period yield = [($817.60 + $1,260)/$1,245.62] - 1 = ($2,077.6‬/$1,245.62) - 1 = 1.6679 - 1 = 0.6679 or 66.79%