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Return to Table 10.1 and calculate both the real and nominal rates of return on the TIPS bond in the second and third years.

Time

Inflation in Year just ended

Par Value

Coupon Payment

Coupon Payment + Principal payment

Total Payment

0


\( 1000 .00




1

2

\) 1020.00

\( 40.80

0

\) 40.80

2

3

\( 1050. 60

\) 42.02

0

\( 42.02

3

1

\) 1061.11

\( 42.44

\) 1061.11

1103.54

Short Answer

Expert verified

Second year = 7.12% and 4.00%

Third year = 5.04% and 4.00 %

Step by step solution

01

Calculation of Nominal return and real return in the second year

The formulae for Nominal Return = Interest + Price Appreciation / Initial Price

= $ 42.20 + $ 30.60 / $ 1020.00

= 0.071196

= 7.12%

The formula for real return = 1 + Nominal return / 1 + Inflation rate – 1

= (1 + 0.071196) / (1 + 0.03) – 1

= 1.071196 / 1. 03 – 1

= 1.0400 – 1

= 4.00 %

02

Calculation of Nominal return and real return in the third year

The formulae for Nominal Return = Interest + Price Appreciation / Initial Price

= $ 42.44 + $ 10.51 / $ 1050.60

= 0.050400

= 5.04%

The formula for real return = 1 + Nominal return / 1 + Inflation rate – 1

= (1 + 0.050400) / (1 + 0.01) – 1

= 1.050400 / 1. 01 – 1

= 1.0400 – 1

= 4.00 %

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Most popular questions from this chapter

The stated yield to maturity and realized compound yield to maturity of a (default-free) zero-coupon bond will always be equal. Why?

Question: A large corporation issued both fixed- and floating-rate notes five years ago, with terms given in the following table:


9% Coupon Notes

Floating Rate note

Issue size

250 million

280 Million

Maturity

20 Years

15 Years

Current Price (% of par

93

98

Current Coupon

9%

8%

Coupon Adjusts

Fixed coupon

Every year

Coupon reset rule

-----

1 Year T bill rate + 2%

Callable

10 Years after issue

10 Years after issue

Call Price

106

102

Sinking fund

None

None

Yield to Maturity

9.9%

---------

Price range since issued

\(85 - \)112

\(97 - \)102


a. Why is the price range greater for the 9% coupon bond than the floating-rate note?

b. What factors could explain why the floating-rate note is not always sold at par value?

c. Why is the call price for the floating-rate note not of great importance to investors?

d. Is the probability of call for the fixed-rate note high or low?

e. If the firm were to issue a fixed-rate note with a 15-year maturity, callable after five years at 106, what coupon rate would it need to offer to issue the bond at par value?

f. Why is an entry for yield to maturity for the floating-rate note not appropriate?

The following multiple-choice problems are based on questions that appeared in past CFA examinations.

a. A bond with a call feature:

(1) Is attractive because the immediate receipt of principal plus premium produces a high return.

(2) Is more apt to be called when interest rates are high because the interest saving will be greater.

(3) Will usually have a higher yield to maturity than a similar non-callable bond.

(4) None of the above.

b. In which one of the following cases is the bond selling at a discount?

(1) Coupon rate is greater than current yield, which is greater than yield to maturity.

(2) Coupon rate, current yield, and yield to maturity are all the same.

(3) Coupon rate is less than current yield, which is less than yield to maturity.

(4) Coupon rate is less than current yield, which is greater than yield to maturity.

c. Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be:

(1) Higher

(2) Lower

(3) The same

(4) Par

d. Which of the following statements is true?

(1) The expectations hypothesis indicates a flat yield curve if anticipated future short term rates exceed current short-term rates.

(2) The basic conclusion of the expectations hypothesis is that the long-term rate is equal to the anticipated short-term rate.

(3) The liquidity hypothesis indicates that, all other things being equal, longer maturities will have higher yields.

(4) The liquidity preference theory states that a rising yield curve necessarily implies that the market anticipates increases in interest rates

If the plan in the previous problem wants to fund and immunize its position fully, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets? Funding the plan?.

“A pension plan is obligated to make disbursements of \(1 million, \)2 million, and $1 million at the end of the next three years, respectively.”

Long-term Treasury bonds currently sell at yields to maturity of nearly 8%. You expect interest rates to fall. The rest of the market thinks that they will remain unchanged over the coming year.

Choose the bond that will provide the higher capital gain in each question if you are correct. Briefly explain your answer.

a. (1) A Baa-rated bond with a coupon rate of 8% and a time to maturity of 20 years.

(2) An Aaa-rated bond with a coupon rate of 8% and a time to maturity of 20 years.

b. (1) An A-rated bond with a coupon rate of 4% and maturity of 20 years, callable at

105.

(2) An A-rated bond with a coupon rate of 8% and maturity of 20 years, callable at

105.

c. (1) A 6% coupon noncallable T-bond with a maturity of 20 years and YTM 5 8%.

(2) A 9% coupon noncallable T-bond with a maturity of 20 years and YTM 5 8%.

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