Yesterday Dexter’s Laboratory paid a dividend of $2.00 a share on its common sto

Question

Yesterday Dexter’s Laboratory paid a dividend of $2.00 a share on its common stock. The firm’s earnings and dividends are expected to grow indefinitely at 5%, and the market requires a 15% rate of return on Dexter’s common stock.

Ten years ago you purchased a convertible debenture of Dexter’s Lab. At that time, the bond had 15 years left to maturity and its yield to maturity was 14% a year, compounded semi-annually. The $1,000 par value bond pays an annual coupon of 12%, compounded semi-annually. The bond is convertible into Dexter’s common stock at a conversion price of $20 a share.

{a} What price did you pay for the bond?

{b} What annual internal rate of return did you earn over the last 10 years if you convert the bond today?

{c} What annual rate of return did you earn over the last 10 years if, instead of converting, you surrender the bond when it is called today at $1,090?

Explanation / Answer

Part A)

The price of the bond can be calculated with the use of PV function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Yield to Maturity, Nper = Maturity Period, PMT = Interest Payment and FV = Face Value

___________

Here, Rate = 14%/2 = 7%, Nper = 15*2 = 30, PMT = 1,000*12%/100*1/2 = $60 and FV = $1,000 [we use 2, since the bond is semi-annual]

Using these values in the above function/formula for PV, we get,

Price of the Bond = PV(7%,30,60,1000) = $875.91

___________________

Part B)

The annual internal rate of return can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,PV,FV) where Nper = Period, PMT = Interest Payment, PV = Present Value and FV = Face/Conversion Value

We will also have to find the conversion ratio and conversion value today. For that, we will have to determine the stock price. It can be calculated with the use of following formula:

Stock Price = D1/(ke - g) where D1 = Expected Dividend, ke = Required Return and g = Growth Rate

_____

The formulas for conversion ratio and conversion value are:

Conversion Ratio = Bond's Face Value/Conversion Price

Conversion Value = Number of Shares as Conversion Ratio*Stock Price

___________

Stock Price = 2*(1+.05)/(15% - 5%) = $21 per share

___

Conversion Ratio = $1,000/20 = 50 shares per bond

Conversion Value = 50*21 = $1,050

___________

Here, Nper = 10*2 = 20, PMT = 1,000*12%*1/2 = $60, PV = $875.91 and FV = $1,050 (same as conversion value)

Using these values in the function/formula for Rate, we get,

Annual Internal Rate of Return = Rate(20,60,-875.91,1050)*2 = 14.64% (we multiply by 2 to get the annual rate)

___________________

Part C)

The annual internal rate of return can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,PV,FV) where Nper = Period, PMT = Interest Payment, PV = Present Value and FV = Face/Callable Value

___________

Here, Nper = 10*2 = 20, PMT = 1,000*12%*1/2 = $60, PV = $875.91 and FV = $1,090 (given)

Using these values in the function/formula for Rate, we get,

Annual Internal Rate of Return = Rate(20,60,-875.91,1090)*2 = 14.84% (we multiply by 2 to get the annual rate)

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.