Corporate Finance - Problems to be solved in excel

Problem 1: What is the cost of new AND existing debt if the current price of the bonds is $1,050? The bonds pay a

semiannual coupon of $80 ($40 every six months), mature in 12 years, and have a face value of $1,000.

The floatation cost for debt is 5%. Check the number of periods per year on your calculator.

Answer:

(1). The cost of existing debt is without flotation or issuance cost:

C=$80, FV=$1,000, PV=$1,050, t=12 years, is Years to Maturity ,

rd = yield to maturity on the firm’s bonds (YTM)

=[C+(FV-PV)/t]/[(FV+PV)/2]

=[80+(1000-1050)/12]/[(1000+1050)/2]

=(80-5)/(2050/2)

≈7.398%

We get a yield to maturity of 7.398%. This represents the cost of existing

debt.

(2). The cost of new debt :

YTM=7.398%, fd =5%

Rd=yield tomaturity

(1−f d)

=YTM

(1−f d)

=7.398%/(1-5%)

≈7.79%

The cost of new debt is 7.79%

Problem2: Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each

six months (Total of $140 per year) and has 10 years to go before it matures. If you buy this bond, you

expect to hold it for 5 years and then to sell it in the market. You (and other investors) currently require a

nominal annual rate of return of 16%, but you expect the market to require a nominal rate of return of

only 12% when you sell the bond due to a general decline in interest rates. How much should you be

willing to pay for this bond today? Check the number of periods per year on your calculator.

Answer:

From the text we know : The price and the YTM move in opposite directions. As the YTM increases the

price decreases. When the required nominal annual rate of return is 16% and 12%,

the price of the bond will be lower at rate of 16% than at the rate of 12%. Therefore, the price of bond at

the rate of 12% is my top-line to pay for it.

The price of this bond with the return rate of 12%:

PVA=PMT*[1-1/(1+r)n]/r

=70*[1-1/(1+12%)(2*5)]/12%

=70*(1-1/1.1210)/12%

≈ $ 395.52

The price of this bond with the return rate of 16%:

PVA=PMT*[1-1/(1+r)n]/r

=70*[1-1/(1+16%)(2*5)]/16%

=70*(1-1/1.1610)/16%

≈ $ 338.33< $395.52

Therefore, I will be willing to pay this bond less than $ 395.52 .