Question

XYZ owns investment A and 1 bond B. The total value of his holdings is $2,200. Investment A is expected to pay annual cash flows to XYZ of $200 per year with the first annual cash flow expected later today and the last annual cash flow expected in 6 years from today. Investment A has an expected return of 17.40 percent. Bond B pays semi-annual coupon, matures in 9 years , has a face value of $1000, has a coupon rate of 9.80 percent and pays its next coupon in 6 months. What is the yield-to-maturity for bond B?

Answer 1

XYZ owns investment A and 1 bond B

total value of his holdings is $2200

Investment A is expected to pay annual cash flows to XYZ of $200 per year with the first annual cash flow expected later today and the last annual cash flow expected in 6 years from today

Investment A has an expected return of 17.40 percent

So, it has total 7 annual payment with 1st payment starting today.

So, present value of this investment can be calculated using PV formula of an annuity due

PV = A*(1+r)*(1 - (1+r)^(-t))/r = 200*1.174*(1 - 1.174^(-7))/.174 = 910.42

total holding value = $2200

So Price of the bond B = 2200-910.42 = $1289.58

Bond B pays semi-annual coupon, matures in 9 years , has a face value of $1000, has a coupon rate of 9.80 percent and pays its next coupon in 6 months,

So, using financial calculator to compute yield to maturity, using following values

FV = 1000

PV = -1289.58

N = 2*9 = 18

PMT = (9.8%/2) of 1000 = 49

compute for I/Y, we get I/Y = 2.83%

So, annual yield to amturity = 2*2.83 = 5.65%