Question

Arjen owns investment A and 1 bond B. The total value of his holdings is 2,607 dollars. Investment A is expected to pay annual cash flows to Arjen of 342.76 dollars per year with the first annual cash flow expected later today and the last annual cash flow expected in 7 years from today. Investment A has an expected return of 14.48 percent. Bond B pays semi-annual coupons, matures in 20 years, has a face value of $1000, has a coupon rate of 5.98 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:

0.0782

Explanation:

First and foremost we need to determine the price of investment A in order to ascertain the price of Bond B as well:

The price of investment A is the present value of its cash flows.

price of investment A=$342.76+$342.76/(1+14.48%)^1+$342.76/(1+14.48%)^2+$342.76/(1+14.48%)^3+$342.76/(1+14.48%)^4+$342.76/(1+14.48%)^5+$342.76/(1+14.48%)^6+$342.76/(1+14.48%)^7=$ 1,791.31  

Price of Bond=total value of holdings-price of investment A=$2,607-$1,791.31=$ 815.69  

The yield to maturity on Bond can be determined using rate formula in excel:

=rate(nper,pmt,-pv,fv)

nper is the number of coupon payments which 20*2=40

pmt is the semiannual coupon=$1000*5.98%*6/12 =$29.9

pv is the current price of $815.69

fv is the face value of $1000

=rate(40,29.9,-815.69,1000)=3.91%

Annual yield=3.91% *2=7.82%