Question

An investor purchases a 10-year, 6% annual coupon payment bond at $90 per $100 of par value. The investor receives a series of 10 coupon payments of $6 (per 100 of par value) for a total of $60, plus the redemption of principal ($100) at maturity. In addition to collecting the coupon interest and the principal, the investor has the opportunity to reinvest the cash flows.

1) If the coupon payments are reinvested at 8%, per 100 of par value, what is the future value of the reinvested coupons at the end of the 10-year reinvestment period?

a) $79.085

b) $86.919

c) $82.899

29) Based on your answer from #28, and assuming you receive par back at maturity, the total return for this investment at the end of 10 years is:

a) $179.085

b) $186.919

c) $182.899

2) What would the realized rate of return (%) be on this investment?

a) 7.582%

b) 7.123%

c) 7.349%

3) What would the realized rate of return (%) be on this investment?

a) 7.582%

b) 7.123%

c) 7.349%

4) Let’s assume the investor in this security decided to sell the bond after 4 years. What would be the future value of reinvested coupons at this point again remembering that the investor is reinvesting the 6% coupons at an interest rate of 8%.

a) $26.248

b) $26.639

c) $27.037

5) If the investor sells the 10-year, 6% annual coupon bond after 4-years, assuming the coupons payments can be reinvested at 8% for its 10-year life, what would they realize in sale proceeds in year 4?

a) $90.754

b) $100.000

c) $95.234

6) The total return from the sale of the bond after 4-years is:

a) $127.037

b) $117.393

c) $117.791

7) In this example where the investor purchased the bond at $90 (discount price) and 4 years later sold the bond, the resulting gain or loss they incurred on the security is determined by comparing the sale price to the:

a) Original purchase price

b) Carrying Value

c) Original purchase price plus the amortized amount of the premium

8) An investor buys a 6% annual payment bond with 10 years to maturity. The bond has a YTM of 8% and is currently priced at $86.580 per 100 of par. What is the bond’s Macaulay Duration?

a) 7.2469 years

b) 7.8017 years

c) 7.6151 years

Answer 1

At the outset I want you to know that I can only answer 4 parts of one question. I request you to ask separately the other questions. Also I see that two questions are absolutely identical regarding realised rate of return.

1. We can use excel function = FV to get future value of these cash flows

Basically what we are doing is 6*(1.08^9) + 6*(1.08^8)+...6*(1.08^0)

=Fv(.08,10,6) =$ 86.919.

Thus correct option is b. $86.919

29. Thus at the end of 10 years you get back 100+86.919 = $186.919

Correct option is b. $186.919

2. We can excel function =irr

First we will write down cash flows. Year 0 will have -90. Year 1 to 9 will have 0. And year 10 will have 186.919. We have taken into consideration the different reinvestment rate for coupons by taking their future value. =Irr(the 11 columns containing cashflows) = 7.582%

Basically the equation solved is npv= 0.

-90+186.919/(1+irr)^10 = 0.

We get irr = 7.582% option A ia correct.

4. Again we will use =fv function

=Fv(.08,4,6) = 27.037

Basically the equation will be

6*(1.08^3) + 6*(1.08^2) + 6*(1.08) + 6 = 27.037

Thus the correct option is c. $27.037