# Price per $100 face value of a two-year, zero-coupon bond

1. What is the price per $100 face value of a two-year, zero-coupon, risk-free bond?

$79.63

$98.85

$79.36

$89.85

0.0605

2. What is the price per $100 face value of a four-year, zero-coupon, risk-free bond?

$79.63

$98.85

$79.36

$89.85

0.0605

3. What is the risk-free interest rate for a five-year maturity?

$79.63

$98.85

$79.36

$89.85

0.0605

4. Suppose that General Motors Acceptance Corporation issued a bond with ten years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.

What was the price of the bond when it was issued?

$1,122.87

$1,073.60

$950.75

$1,138.02

$1,032.09

5. Suppose that General Motors Acceptance Corporation issued a bond with ten years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.

Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment?

$1,122.87

$1,073.60

$875.38

$1,138.02

$1,143.60

6. Suppose that General Motors Acceptance Corporation issued a bond with ten years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.

Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?

$1,068.02

$1,073.60

$875.38

$1,138.02

$1,143.60

7. Suppose you purchase a ten-year bond with 6% annual coupons. You hold the bond for four years, and sell it immediately after receiving the fourth coupon. If the bond's yield to maturity was 5% when you purchase and sold the bond,

What cash flows will you pay and receive from your investment in the bond per $100 face value?

Ans. ______________

Bond Sold for:

Cash flows:

8.Suppose you purchase a ten-year bond with 6% annual coupons. You hold the bond for four years, and sell it immediately after receiving the fourth coupon. If the bond's yield to maturity was 5% when you purchase and sold the bond,

What is the interest rate of return of your investment?

4.90%

5.00%

6.00%

7.00%

11.00%

12. Complete Chapter 9, problem 5-a on page 275. Enter your answer for the following:

Dorpac corporation has a divident of 1.5%. Dorpac's equity cost of capital is 8%, and its dividends are expected to grow at a constant rate.

a. what is the expected growth rate of dorpac's dividends?

What is the expected growth rate of Dorpac's share dividends? (Points: 2)

4.5%

8.0%

6.5%

7.0%

8.0%

13.

What is the expected growth rate of Dorpac's share price?

4.5%

8.0%

6.5%

7.0%

8.0%

14.

Colgate-Palmolive Company has just paid an annual dividend of $0.96. Analysts are predicting an 11% per year growth rate in earnings over the next five years. After then, Colgate's earnings are expected to grow at the current industry average of 5.2% per year. If Colgate's equity cost of capital is 8.5% per year and its dividend payout ratio remains constant, what price does the dividend-discount model predict Colgate stock should sell for?

$51.56

$34.29

$39.78

$15.07

$39.44

https://brainmass.com/business/bond-valuation/price-per-100-face-value-of-a-two-year-zero-coupon-bond-248872

#### Solution Preview

1. What is the price per $100 face value of a two-year, zero-coupon, risk-free bond?

$79.63

$98.85

$79.36

$89.85

0.0605

Taking nterest rate as 5.5% . We will apply following formulae to find out the price

Price = Face value/(1+rate of interest)^duration

$89.85 =Answer

2. What is the price per $100 face value of a four-year, zero-coupon, risk-free bond?

$79.63

$98.85

$79.36

$89.85

0.0605

Taking nterest rate as 5.95% . We will apply following formulae to find out the price

Price = Face value/(1+rate of interest)^duration

$79.36 =Answer

3. What is the risk-free interest rate for a five-year maturity?

$79.63

$98.85

$79.36

$89.85

0.0605

Risk -free interest rate for a five-year maturity will be:

.0605=Answer

4. Suppose that General Motors Acceptance Corporation issued a bond with ten years until maturity, a face value of

$1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.

What was the price of the bond when it was issued?

$1,122.87

$1,073.60

$950.75

$1,138.02

$1,032.09

Price of Bond= Present Value of Inflows= 1073.60

Present value of inflows = Present value of annualcoupons Interest received + Pv of Principal repayment

PV of coupons= $515.21

Here we have to find out the present value of annuity

P=A*((1/r)-((1/(r*((1+r)^n)))

P=present value, A= Annuity r= rate of interest n=duration

A=70, r =6% n=10

PV of Principal Repayment= 558

P=present value, F= Future value r= rate of interest n=duration

P=F/(1+r)^n

Hence ...

#### Solution Summary

Response provides guidance to compute the price of a two-year, zero-coupon, risk-free bond

Price per Face Value of Two Year Zero Coupon, Risk Free Bond

Suppose the current zero-coupon yield curve for risk-free bonds is as follows:

Maturity (years) 1 2 3 4 5

_________________________

YTM 5.00 5.50 5.75 5.95 6.05

a)What is the price per$100 face value of a two year,zero-coupon,risk-free bond?

b) What is the price per $100 face value of a four year,zero coupon,risk free bond?

c) What is the risk-free interest for a five year maturity?