Valuation – corporate bond

Now that I have done the first one you can copy the technique and do the second one yourself.   

A U.S. Government bond with a face amount of $10,000 with 8 years to maturity is yielding 3.5%. What is the current selling price?

What is the value of a share of preferred stock that pays a $4.50 dividend, assume k is 10%.

A $1,000 corporate bond with 10 years to maturity pays a coupon of 8% (semi-annual) and the market required rate of return is a) 7.2% 

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First lets think about this a bit.

You will be happy with at return of 7.2%.  This is less than the coupon rate of 8% so that means you will be prepared to pay more than $1000 for the bond.  You will use this logic when you check the reasonableness of the answer that we will get.  

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r=0.08/2=0.04 every 6 months

i=0.072/2=0.036 every 6 months

C=1000

$$P=C+[(I-Ci)a_{n|i}]$$

Where 

n=20 (lots fo 6 months) and

$$a_{n|i}\\\\ =\frac{1-(1+i)^{-n}}{i}\\ =\frac{1-(1+0.036)^{-20}}{0.036}\\ =\frac{1-(1.036)^{-20}}{0.036}\\$$

$$\left({\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{1.036}}}^{\left(-{\mathtt{20}}\right)}\right)}{{\mathtt{0.036}}}}\right) = {\mathtt{14.084\: \!658\: \!505\: \!338\: \!905\: \!8}}$$

near enough to 14.08466

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$$\\P=C+[(I-Ci)a_{n|i}]\\\\ P=1000+[(40-1000*0.036)*14.08466]\\ P=1000+[(40-36)*14.08466]\\ P=1000+[4*14.08466]\\$$

$${\mathtt{1\,000}}{\mathtt{\,\small\textbf+\,}}\left[{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{14.084\: \!66}}\right] = {\mathtt{1\,056.338\: \!64}}$$

The price you wil pay to get a return of 7.2% is   $1056.34

this is more than $1000 so it fits with the reasonableness check