Question

In: Finance

21) BrightHouse bonds currently sell for $960 each, have a par value of $1,000, 12% coupon...

21) BrightHouse bonds currently sell for $960 each, have a par value of $1,000, 12% coupon rate paid annually, and 5 years left to maturity (10 points total).

(a) Illustrate the bond’s time value of money timeline (2.5 points)

(b) Calculate the bond’s yield to maturity (2.5 points)

(c) Explain why the bond’s yield to maturity is different from its coupon rate (2.5 points)

(d) If the bond paid interest semi-annually, what would be the bond’s yield to maturity? (2.5 points)

Expert Solution

a) The bonds time value of money is as follows:

Year	Cash flow	Present Value Factor @ 12 %	Present Value
1	120	.893	107.16
2	120	.797	95.64
3	120	.712	85.44
4	120	.636	76.32
5	1120	.567	635.04

Till fourth year the cash flow is calculated as 12% on 1000 i.e 120, which is the amount paid as interest. For 5th year amount is 1120 i.e annual interest of 120 and 1000 ( par value)to be paid on maturity.

Total Present Value of the bond = 107.16+95.64+85.44+76.32+635.04 = 999.6 i.e. 1000

b) YTM = I +[MV-C]/n / [MV+C]/2

I = Amount of annual interest = $120

MV = Maturity value at the end of holding period = $1000

C = Current market price of the bond = $960

n = Holding period till maturity = 5

YTM = 120+[1000-960]/5 / [1000+960]/2

= .1306 i.e 13.06%

Hence YTM is 13.06%

c) A bond's YTM (Yield to Maturity) is different from Coupon rate. Because the YTM is the estimated annual rate of return for the bond which further states that the investor holds the asset until its maturity date and reinvests the payment at the same rate. Whereas an interest rate or coupon rate is the annual income, which an investor expect to receive for holding the bond for a period of time.

d) The bond with a par value of $1,000 whose current price is $960. Its coupon rate is 12% and it matures five years from now. To calculate the semi-annual bond payment, take 12% of the par value of $1,000, or $120, and divide it by two. The bond therefore pays $60 semiannually.

By dividing the $40 gain($1000-$960) by 60 gives $.67 in gain per payment. Add that to the $60 in interest, which would come around $60.67 i.e $61 and that works out to a yield of 6.35%, or $61 divided by $960.

Hence YTM of the bond for semi annually paid interest is 6.35%

jeff jeffy answered 1 year ago

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