Question

1. Allied Corporation has just issued ten thousand $1,000 bonds, maturing in 2048, to establish a research and development fund for a new product. The goal is to develop and launch this new product by late 2020. The offering interest rate was 4.50% for the bonds. Identity the following values for each bond:

Face amount __________ Yield _____ Coupon payment _____ Amount paid _____ semiannually Periods to maturity _____ Present value __________ Yield to maturity _____

2. Using the Allied Corporation bond information from above, calculate the following: a. If the current market interest rate for new investors increases to 6.00%, what will be the present value for this bond? Show your work or your inputs. b. If the current bond market rates drop to 4.00%, what will be the present value for the Allied bond? Show your work or your inputs. c. What conclusion can you draw from this comparison? ____________________________________________________________________________________

3. Determine without the use of a calculator if the following bonds are trading at a premium, at a discount, or at face value: a. A 5% bond maturing in 2015 when current interest rates are 6%: _______________ b. A 4% bond paying monthly until 2042 when current interest rates are 2%: _______________ d. What general observation can you make about this? ________________________________________________________________________________

4. Calculate the answers for following questions. Show your work or your inputs. a. An IBM bond is selling today for $1,251.48 with a face amount of $1,000. There are 11 years until maturity and it has a coupon payment of $40 paid semiannually. What is the yield to maturity b. A Google bond with a face amount of $1,000 is paying a coupon payment of $100 semiannually. The yield to maturity is 4.75% and there are 15 years remaining for this bond. What is the current offering price? c. A Treasury bill has a current price of $1200 and face amount of $1,000. If there are 10 years remaining for this bond and the yield to maturity is 8%, what is the annual coupon payment? d. Nike has a bond that is selling today for $795 with a face amount of $1,000. There are 30 years until maturity and it has a coupon payment of $15, paid annually. What is the yield to maturity? e. A Pfizer bond with a face amount of $1,000 is paying a coupon payment of $70 semiannually. The yield to maturity is 4.78% and there are 20 years remaining for this bond. What is the current offering price? f. General Motors has a current price of $975 and face amount of $1,000. If there are 3 years remaining for this bond and the yield to maturity is 6.75%, what is the annual coupon payment?

Answer 1

1.)Answer

Face amount is $1000

Yield = $1000 (as the bond is issued and reddemed at par )

Coupon payment is $ 1000*4.5% = $45

Amount paid semiannually = 4.5/2 = 2.25% in 6 months = $1000*2.25% = 22.5$

Periods to maturity is 28 years (assumed issued at the end of 2020)

Present value = $1000 per dollar (as the bond issued and redeemed at par so the YTM is equal to the coupon rate therefore )

Yield to maturity = 4.5% ( as it is par value bond , the bond is issued and redeemed at par )

2(a) Answer

If current market interest rate for new investors increased to 6%, Present value of the bond, Po is calculated as:

Yield = 6%; As it is semi annual coupon payments, discount rate = YTM/2 = 6%/2 = 3%

Po = PV(Coupon payments) + PV(Maturity value)

Po = $20/(1+0.03) + $20/(1+0.03)^2 + $20/(1+0.03)^3 + .....$20/(1+0.03)^29 + $1020/(1+0.03)^30 = $804

2(b) Answer

If current market interest rate for new investors decreased to 2%, Present value of the bond, Po is calculated as:

Yield = 2%; As it is semi annual coupon payments, discount rate = YTM/2 = 4%/2 = 2%

Po = PV(Coupon payments) + PV(Maturity value)

Po = $20/(1+0.02) + $20/(1+0.02)^2 + $20/(1+0.02)^3 + .....$20/(1+0.02)^29 + $1020/(1+0.02)^30 = approximately$1,258.08

2(c) Answer

Price of the bond and the current market interest rate is inversely proportional. As new interest rate increase, demand for the old bonds decrease and the price falls.

3(a)Answer

. This will be trading at DISCOUNT. Current market rates are higher than the coupon rate on bond. This means when market is providing higher interest rates, this provides lower, which reduced the demand for this bond. Lower demand implies lower price and hence it trades at diacount.

3(b)Answer

This will be trading at PREMIUM. Market interest rates here are lower than the interest paid by bond. This implies there will be higher demand for this bond. Higher demand means higher price and hence a premium to par value.

3(d)Answer.

We can use the above options to formulate our general observations around market interest rates and interest rate on bond or coupon rate. These observations are,

If market rate > coupon rate, bond will trade at discount.

If market rate < coupon rate, bond will trade at premium.

If market rate = coupon rate, bond will trade at par (as demand and supply will be in equilibrium)