Question

# Arjen owns investment A and 1 bond B. The total value of his holdings is 1,157...

Arjen owns investment A and 1 bond B. The total value of his holdings is 1,157 dollars. Investment A is expected to pay annual cash flows to Arjen of 128.37 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 16.42 percent. Bond B pays semi-annual coupons, matures in 19 years, has a face value of \$1000, has a coupon rate of 7.6 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.

First let us find the value of bond B

investment A value=present value of future cash flows

=128.37+(128.37/(1+16.42%)^1)+(128.37/(1+16.42%)^2)+(128.37/(1+16.42%)^3)

=414.70

Value of B=total value-investment A

=1157-414.70=742.30

Use rate formulae in excel to find the yield to maturity of bond

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

nper=19*2(since semiannual)

pmt=face value*coupon rate=1000*(7.6%/2)=38

pv=-742.30

fv=1000

=rate(38,38,-742.30,1000,0,1)

=5.41%

annual YTM=5.41%*2=10.82%

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