Question

XYZ Corp has bonds on the market with 7.5 years to maturity, a YTM of 6 percent, and a current price of $1,040. The face value is $1,000. The bonds make semiannual payments. What must be the dollar coupons (dollar amount, not percentage) paid every six-months on XYZ’s bonds?

Hint: A YTM of 6% for a semiannual bond is a reporting convenience. It implies the actual 6 month return is 3%.

You need to use the annuity formula to solve this one.

Answer 1

Purchase Price	1040
Time	7.5
Redemption value	1000
YTM	6%
Compounding	semianual
Effective rate	=(((1+6%/2)^2)-1)	6.090%
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Price of Bond	=PV of coupon payments + PV of redemption price
PV of coupon payments	annual coupon payments * (((1-(1 + 6.09%) ^- 7.5)) / 6%)
PV of coupon payments	annual coupon payments * 5.969
PV of redemption amount=	Redemption value/(1+rate)^time
PV of redemption amount=	1000/(1+6.09%)^7.5
PV of redemption amount=	641.86
Price of Bond	=PV of coupon payments + PV of redemption price
1040	=Annual coupon payment * 5.969 + 641.86
=1040-641.86	=Annual coupon payment * 5.969
398.14	=Annual coupon payment * 5.969
Annual coupon payment	=398.14/5.969
Annual coupon payment	66.70129
Semi annual payments	33.35