Question

Kyan owns investment A and 1 bond B. The total value of his holdings is $6,600. Investment A is expected to pay annual cash flows to Kyan forever with the first annual cash flow expected in 1 year from today. Investment A has an expected return of 11.49 percent. The first cash flow is expected to be $515 in 1 year and annual cash flows are expected to increase by 2.21 percent each year forever. Bond B pays semi-annual coupons, matures in 9 years, has a face value of $1000, has a coupon rate of 12.66 percent, and pays its next coupon in 6 months. What is the yield-to-maturity for bond B? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Answer:

YTM on bond B:  11.80%

Explanation:

Investmetn A is a perpetuity with a grow rate of 2.21% and required return of 11.49%

the present value is:

$\frac{515}{.1149 - .0221} = Investment_A$

A=5549.568966

if Kyan holding value is 6,600 then the bond present value is:

6,600 - 5,549.57 = 1,050.43

Now we need to calcualte the YTM for bond B:

$YTM_s = \frac{C + \frac{F-P}{n }}{\frac{F+P}{2}}$

Coupon payment =1,000 x 12.66%/2 payment per year = $ 63.3

Face Value    = 1000

Present value= 1050.43

n= 9 years x 2 payment per year = 18

$YTM_s = \frac{63.3 + \frac{1,000-1,050.43}{18 }}{\frac{1,000+1,050.43}{2}}$

$YTM_s = \frac{63.3 + \frac{60.49833333}{1025.215}$

YTMs = 5.9010386%

This is a semiannual rate, as we were working with semiannual payment

to get the YTM we multiply by 2 and get:

YTM: 0.118020773 = 11.80%