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Apple Inc. recently issued 15-year bonds at $950 per share. These bonds pay $25 coupons every...

Apple Inc. recently issued 15-year bonds at $950 per share. These bonds pay $25 coupons every six months. Their price has remained stable since they were issued, i.e., they still sell for $950 share today. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 15 years, a par value of $1,000, and it will pay $20 coupons every six months. If both bonds have the same yield to maturity, how many shares of new bonds must Apple Inc. issue today to raise $2,188,000 cash today?

Solutions

Expert Solution

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

M = value at maturity, or par value = $1000

P0 = the current market price of bond = $950

C = coupon payment = $25 in every six months

n = number of payments (time remaining to maturity) = 15 years; therefore number of payments n = 15 *2 = 30

YTM = interest rate, or yield to maturity =?

Now we have,

$950 = $25 * [1 – 1 / (1+YTM) ^30] /YTM+ 1000 / (1+YTM) ^30

By trial and error method we can calculate the value of YTM = 2.75% semiannual

Or annual YMT = 2 * 2.75% = 5.49% per year

[Or you can use excel function for YTM calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(30,-25,950,-1000)” = 2.75%]

Now calculate the price of second bond of Apple Inc. by assuming the same YTM as calculated above

The Bond’s price can be calculated the help of following formula

Bond price P = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

The par value or face value of the Bond = $1000

Price of the bond P =?

C = coupon payment on semi-annual basis = $20

n = number of payments = = 15 *2 = 30

i = yield to maturity or priced to yield (YTM) = 5.49% per annum or 5.49%/2 = 2.75% semiannual

Therefore,

P = $20 * [1 – 1 / (1+2.75%) ^30] /2.75% + $1000 / (1+2.75%) ^30

= $405.16 + $443.56

= $848.71

The bond price of second bond of Apple Inc. is $848.71

Number of shares of new bonds must Apple Inc. issue today to raise $2,188,000 cash today

= Cash required / bond price

= $2,188,000/ $848.71

= 2578.03 shares of new bonds or 2578 shares (rounding off to nearest whole number)

jeff jeffy answered 1 year ago

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