1a. Suppose you owned stock in a company for the last three years. You originall
ID: 2811758 • Letter: 1
Question
1a. Suppose you owned stock in a company for the last three years. You originally bought the stock three years ago for $30 and just sold it for $56. The stock paid an annual dividend of $1.35 on the last day of each of the past three years. What is your realized return on this investment?
1b. A $1,000 par value bond with Seven years left to maturity pays an interest payment semiannually with a 7 percent coupon rate and is priced to have a 6.2 percent yield to maturity. If interest rates surprisingly increase by 0.5 percent, by how much would the bond’s price change?(Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
1a. Realized Return = Total annual dividend for 3 years + stock appreciation * 100
Initial Investment
= ($1.35* 3 ) + ( $56 - $30) * 100
$30
= ($4.05 + $26) * 100 / $30
= $30.05 * 100 / $30
= 100.17%
1b. Interest to be received = 7% per annum
Semi annual interest = $1000 * 3.5% = $35
Years to maturity = 7 years
Yield to maturity semiannualy = 6.2 / 2 = 3.1%
>Price of the bond when interest is 7% and paid semiannualy
Price = Present value of interest received for 7 years semiannually + Present value of redeemable value at the end of 7th year
=Present value of $35 received for 7 years semiannually + Present value of $1000 at the end of 7th year
= ($35 * present value interest factor annuity @3.1% for 14 installments) + ($1000 * present value factor @ 3.1% for 14th installment)
=($35 * 11.219457) + ( $1000 * 0.6521968)
= $392.6809 + $652.1968
= $ 1044.88
> Price of the bond when interest is 7.5% and paid semiannualy
Interest payable semiannually = ($1000 * 7.5% ) / 2 = $37.5
Price = Present value of interest received for 7 years semiannually + Present value of redeemable value at the end of 7th year
=Present value of $37.5 received for 7 years semiannually + Present value of $1000 at the end of 7th year
= ($37.5 * present value interest factor annuity @3.1% for 14 installments) + ($1000 * present value factor @ 3.1% for 14th installment)
=($37.5 * 11.219457) + ( $1000 * 0.6521968)
= $420.7296 + $652.1968
= $ 1072.93
Therefore the bond's price would change by $ 28.05
Note : Here the present value interest factor annuity is the cummulative of all the present value factors for the given period ( that is the grand total of all the present value factors)
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