Gabriele Enterprises has bonds on the market making annual payments, with eleven years to maturity, a par value of $1,000, and selling for $958. At this price, the bonds yield 6.4 percent.

Problem 7-5 Coupon Rates [LO2]

Gabriele Enterprises has bonds on the market making annual payments, with eleven years to maturity, a par value of $1,000, and selling for $958. At this price, the bonds yield 6.4 percent.

What must the coupon rate be on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Coupon rate 5.86% Explanation Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.   Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:   P = $958 = C(PVIFA6.40%,11) + $1,000(PVIF6.40%,11)   Solving for the coupon payment, we get:   C = $58.57   The coupon payment is the coupon rate times par value. Using this relationship, we get:   Coupon rate = $58.57/$1,000 Coupon rate = .0586, or 5.86%   Calculator Solution: Enter 11 6.4% ±$958 $1,000   N I/Y PV PMT FV Solve for $58.57 Coupon rate = $58.57/$1,000 Coupon rate = .0586, or 5.86%

Thanks

A Japanese company has a bond outstanding that sells for 95 percent of its ¥100,000 par value. The bond has a coupon rate of 5.4 percent paid annually and matures in 16 years.

Problem 7-4 Bond Yields [LO2]

A Japanese company has a bond outstanding that sells for 95 percent of its ¥100,000 par value. The bond has a coupon rate of 5.4 percent paid annually and matures in 16 years.

What is the yield to maturity of this bond (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer

yield to maturity 5.89%

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Here we need to find the YTM of a bond. The equation for the bond price is:

P = ¥95,000 = ¥5,400(PVIFAR%,16) + ¥100,000(PVIFR%,16)

Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find:

R = YTM = 5.89%

Calculator Solution:

Enter

16

±¥95,000

¥5,400

¥100,000

N

I/Y

PV

PMT

FV

Solve for

5.89%

Treasury bills are currently paying 7 percent and the inflation rate is 3.2 percent.

Problem 7-12 Calculating Real Rates of Return [LO4]
Treasury bills are currently paying 7 percent and the inflation rate is 3.2 percent.



a.
What is the approximate real rate of interest? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer
3.80%

b. What is the exact real rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Answer
3.68%

Explanation
Explanation
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.



The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h) is:



R ≈ r + h



Approximate r = .07 – .032
Approximate r = .038, or 3.80%



The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:



(1 + R) = (1 + r)(1 + h)

(1 + .07) = (1 + r)(1 + .032)
r = (1 + .07)/(1 + .032) – 1
r = .0368, or 3.68%

An investment offers a total return of 10 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 5 percent.

Problem 7-14 Nominal and Real Returns [LO4]
An investment offers a total return of 10 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 5 percent.



What does Janice believe the inflation rate will be over the next year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:



(1 + R) = (1 + r)(1 + h)



h = (1 + .10)/(1 + .05) – 1
h = .0476, or 4.76%