Question

Chapter 7 1. You are the CFO of Ford Motors Inc. The firm has decided to purchase new fixed assets that will allow them to more efficiently produce electric cars. To raise the funds needed to purchase these assets, you decide to issue bonds. You expect the new fixed assets to last about 15 years so you'd like to issue bonds with a maturity of 15 years and a face value of $1,000. To set the coupon payment, you ask Moody's what the credit rating is for bonds of this maturity and risk. They tell you they will rate your bonds AA which have a 7% return per year, so you set the coupon at $70 per year. 1a. What is the present value of the bond Ford is offering? 1b. One year later, market interest rates on bonds of similar maturity and risk fell to 5%. If you were an investor purchasing this Ford bond in the secondary market, what price should you pay?

Answer 1

Answer to 1a -

The present value of the bond is the total of:

1. The present value of the bond's interest payments that will occur every year, PLUS
2. The present value of the principal amount that occurs when the bond matures

The present value can be calculated using excel function "PV". To identify PV, we discount the future cash flows with the interest rate and identify what is it worth today. The formula for PV in excel is =PV(rate,nper,pmt,(FV)) where rate = the interest rate offered, nper = the number of payment periods (In our case 15 periods), pmt = the annual coupon payment made every year, FV= the amount of principal that is being paid back at the time of maturity. Please note while calculating the present value of the interest (As in point no 1), the FV value would be Zero since no principal payment is made at that time.

Rate	7%
nper	15
PMT	70
FV	1000	(Principal amount)
Present value of interest	=pv(7%,15,-70,0)
	$637.55
Present value of Principal Amount	=pv(7%,15,0,-1000)
	$362.45
Present value of bond	=637.55+362.45
	$1,000.00

The present value of interest payment is $637.55 and the present value of bond is $362.45. Sum total of both the present values amount to $1000 which is the issue price today.

Answer to 1b, When the interest rates fall in the market the discount rate in the above example i.e rate column gets changed but the annual coupon payment doesn't change. It remains at $70 annually. Similarly, since the investor is considering purchase of the bond one year later, the nper (Payment period) will have to be changed from 15 years to 14 years (Since 1 year has already elapsed). The cash flows for 14 years and the principal amount at the end of 14th year shall have to be discounted by 5% to arrive at the present value and price of the bond. The calculation is as below

Rate	5%
nper	14
PMT	70
FV	1000	(Principal amount)
Present value of interest	=pv(5%,14,-70,0)
	$692.90
Present value of Principal Amount	=pv(5%,14,0,-1000)
	$505.07
Present value of bond	=692.90+505.07
	$1,197.97

Price of the bond in secondary market would be $1197.97 after 1 year.

Answer to 3a -

Whenever you see the chart providing the details of the price of a bond or a stock, there are always two quotes/price provided. The bid price and the ask price. The bid price is what buyers are willing to pay for it. The ask price is what sellers are willing to take for it. If you are selling a stock, you are going to get the bid price, if you are buying a stock you are going to get the ask price. The ask price of a bond/stock will generally be higher than the bid price since it is inferred that a seller will always want to sell or quote his price higher than what the buyer is wanting to pay for it.

Answer to 3b-

Current price of the bond - $955.14. To calculate the YTM, we need the face value, current market price, maturity and the annual coupon payments. Based on the data provide, the calculations are as under.

Face Value	$1,000
Current price	$955.14
nper (Payment period left)	6
Coupon Payment	80
Yield to maturity Formula	=rate(nper,pmt,-pv,fv)
	=rate(6,80,-955.14,1000)
Yield to maturity of the bond is	9.00%