Question

Arjen owns investment A and 1 bond B. The total value of his holdings is 1,529 dollars. Investment A is expected to pay annual cash flows to Arjen of 218.19 dollars per year with the first annual cash flow expected later today and the last annual cash flow expected in 3 years from today. Investment A has an expected return of 9.87 percent. Bond B pays semi-annual coupons, matures in 23 years, has a face value of $1000, has a coupon rate of 6.4 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:

In order to find the present value of the bond we have to calculate the present value of investment A and subtract is from 1529. We can find the present value of A by discounting all its cash flows.

As the first cash flow is received today and the last will be received 3 years form now there will be a total of 4 cash flows

1) 218.19 (Will not be discounted as we are receiving it today in the present)

2) 218.19/1.0987 (Discount by 1 year as cash will be received in 1 year)

3) 218.19/1.0987^2 (Discount by 2 years as cash will be received in 2 years)

4) 218.19/ 1.0987^3 (Discount by 3 years as cash will be received in 3 years)

= 218.19 + 198.58 + 180.74+ 164.51 = 762.02

PV of Bond = 1529-762.09= 766.91

Semi annual coupons mean 2 payments a year. Bond B matures in 23 years which means a total of 46 payments (23*2). N=46. A coupon rate of 6.4 percent means that the bond pays $64 (0.064*1000) each year. $64 divided by 2 is 32 which is the amount of each semi annual payment Arjen receives. Pv= 766.91 FV = 1000

In a financial calculator put

PV= -766.91

N= 46

FV=1000

PMT= 32

and compute I

I is 4.38 and we will multiply it by 2 because the payments are semi annual. So we will get an I of 8.76

YTM= 0.0876

Explanation: