Question

1. A bond has a coupon rate of 7% and has 5 years until maturity and the yield to maturity is 5%. (4 points) a. What is the price of the bond? ___________________ (2 points) b. How much annual interest is paid to the bondholder? _____________ (2 points) 2. A zero-coupon bond with a 20-year maturity, has a yield to maturity of 6% and a par value of $100,000? a. What is the price of the bond? ______________. (2 points) 3. If you paid $980 for a 10- year bond that pays $70 a year in interest. a. What is the bond’s yield to maturity? __________________________. (2 points) 4. A project has an initial investment of $100,000, an opportunity cost of capital of 6% and the following projected cash flows. Yr. 1 - $35,000 Yr. 2 - $40,000 Yr. 3 - $45,000 a. What is the NPV for this 3-year project? ________________ (2 points) 5. A stock is expected to pay a future annual dividend of $5, and has a growth rate of 2%. The required rate of return is 10%. a. What is the price of the stock? ________________. (2 points)

Answer 1

(1)

Annual Coupon Rate = 7% per annum, Time to Maturity = 5 years, Yield To Maturity = 5% per annum

Let the par value of the bond be $ 1000.

(a) Let the bond price be P(m)

Annual Coupon Payment = Annual Coupon Rate x Par Value = 0.07 x 1000 = $ 70

Therefore, P(m) = 70 x (1/0.05) x [1-{1/(1.05)^(5)}] + 1000 / (1.05)^(5)

P(m) = $ 1086.59

(b) Annual Interest Paid = Annual Coupon Payment = $ 70

(2) Yield to Maturity = 6%, Par Value = $ 100000 , Time to Maturity = 20 years

Let the ZCB's price be P0

Then, P0 = 100000 / (1.06)^(20) = $ 31180.47269 or $ 31180.473

(3) Market Price of Bond = $ 980, Time to Maturity = 10 years and Annual Coupon = $ 70

Let the par value be $ 1000 and yield to maturity be R

Then, 980 = 70 x (1/R) x [1-{1/(1+R)^(10)}] + 1000 / (1+R)^(10)

Using EXCEL Goal Seek Function to solve the above equation we get

R = 0.07288564 or 7.288 %

NOTE: Please raise separate queries for the solutions to the remaining parts and sub parts.