Question

I hope that you can explain step by step, I am not very clear about some calculation formula, thank you!

Maggie's Magazines (MM) has straight nonconvertible bond that currently yield 7%. MM's stock sells for $22 per share, has an expected constant growth rate of 7%, and has a dividend yield of 4%. MM plans on issuing convertible bonds that will have a $1,000 par value, a coupon rate of 6%, a 20-year maturity, and a conversion ratio of 32 (i.e., each bond could be convertible into 32 shares of stock). Coupon payments will be made annually. The bonds will be noncallable for 5 years, after which they will be callable at a price of $1,090; this call price would decline by $6 per year in Year 6 and each year thereafter. For simplicity, assume that the bonds may be called or converted only at the end of a year, immediately after the coupon and dividend payments. Management will call the bonds when the bonds' conversion value exceeds 25% of the bonds' par value (not their call price). 7% 15 16 Inputs: 17 Straight bond yield 18 Current stock price 19 Expected growth rate in stock price 20 Dividend yield 21 Par value (and issue price) of convertible bond 22 Coupon rate on convertible bond 23 Maturity of convertible bond (years) 24 Conversion ratio 25 Call protection period (years) 26 Call price when call protection ends 27 Call price decline per year after protection period Policy for call: Call when conversion value exceeds 28 this percent over bond's par value. $22.00 7% 4% $1,000.00 6.00% 20 32 $1,090.00 $6.00 25% 30 31 a. For each year, calculate: (1) the anticipated stock price; (2) the anticipated conversion value; (3) the anticipated straight- 32 bond price; and (4) the cash flow to the investor assuming conversion occurs. At what year do you expect the bonds will be 33 forced into conversion with a call? What is the bond's value in conversion when it is converted at this time? What is the cash 34 flow to the bondholder when it is converted at this time (Hint: the cash flow includes the conversion value and the coupon 35 payment, because the conversion is immediately after the coupon is paid.)

Answer 1

	.(1)&(2)	Anticipated stock Price & Conversion Value
		Current stock Price=P0	$22
		Growth Rateof stock price=7%	0.07
		Stock Price in Year 1=22*(1+0.07)	$23.54
		Stock Price in Year (N+1)=1.07*(Stock Price in Year (N)
			A	B=A*32
		Year	Stock Price	Conversion Value
		0	$22	$704.00
		1	$23.54	$753.28
		2	$25.19	$806.01
		3	$26.95	$862.43
		4	$28.84	$922.80
		5	$30.86	$987.40
		6	$33.02	$1,056.51
		7	$35.33	$1,130.47
		8	$37.80	$1,209.60
		9	$40.45	$1,294.28
		10	$43.28	$1,384.87
		11	$46.31	$1,481.82
		12	$49.55	$1,585.54
		13	$53.02	$1,696.53
		14	$56.73	$1,815.29
		15	$60.70	$1,942.36
		16	$64.95	$2,078.32
		17	$69.49	$2,223.81
		18	$74.36	$2,379.47
		19	$79.56	$2,546.04
		20	$85.13	$2,724.26
		Bonds par value	$1,000
		Conversion value at the time of convesrion	$1,250.00	(1+0.25)*1000
		YEAR OF CONVERSION	9
		Conversion value at conversion	$1,294.28
		Share Value at conversion	$40.45
	.(3)and (4)	STRAIGHT BOND PRICE and CASH Flow if Converted
		Straight Bond Price =Present Value of future Cash Flow
		Current Bond Price:
	Pmt	Coupon Payment per year	$60.00	(6%*1000)
	Nper	Number of years of payment left	20
	Rate	Yield	7%
	Fv	Terminal Cash Flow	$1,000
	P0	Straight Bond Price in year 0	$894.06	(Using PV function of excel with Rate=7%,Nper=20, Pmt=-60, Fv=-1000)
										Pn T(20-N) Number of years to maturity Straight Bond Price (Using PV function of excel with Rate=796, Nper=T, Pmt=-60, Fv=-1000) Terminal Cash Flow if converted(Conversion Value+60) NA NA $894.06 PO $896.64 P1 $899.41 P2 $902.37 P3 $905.53 P4 $908.92 PS $912.55 P6 $916.42 P7 $920.57 P8 $925.01 P9 $929.76 P10 $934.85 P11 $940.29 P12 $946.11 P13 $952.33 P14 $959.00 P15 $966.13 P16 $973.76 P17 $981.92 P18 $990.65 P19 $1,000.00 P20 13 14 $1,116.51 $1,190.47 $1,269.60 $1,354.28 $1,444.87 $1,541.82 $1,645.54 $1,756.53 $1,875.29 $2,002.36 $2,138.32 $2,283.81 $2,439.47 $2,606.04 $2,784.26 b Pv Nper Pmt Fv RATE EXPECTED RETURN WITH ANTICIPATED CONVERSION IN YEAR 9 Investment $894.06 (Note, the investment of investor is $894.06, NOT $1000) Number of years to conversion Annual Coupon Payment $60 Terminal Cash Flow on conversion $1,354.28 Expected Return of Investor 10.43% (Using RATE function of excel with Nper=9, Pv=-894.06, Pmt=60, Fv=1294.28) H45 X fic A B C K L M N O P =PV(H43,442,-H41,-444) D E I J Conversion value at the time of convesrion $1,250.00 (1+0.25)*1000 YEAR OF CONVERSION Conversion value at conversion $1,294.28 Share Value at conversion $40.45 .(3) STRAIGHT BOND PRICE Straight Bond Price =Present Value of future Cash Flow Pmt Nper Rate Current Bond Price: Coupon Payment per year Number of years of payment left Yield Terminal Cash Flow Straight Bond Price in year 0 $60.00 (6%*1000) 20 7% $1,000 $894.06 ( Using PV function of excel with Rate=7%,Nper=20, Pmt=-60, FV=-1000) PO Clipboard Font Allghment Number Styles Lells Edith 152 x fc =PV(7%,H52,-60,-1000) E F A B C D I J K L M N O P Pmt Nper Current Bond Price: Coupon Payment per year Number of years of payment left Yield Terminal Cash Flow Straight Bond Price in year 0 Rate N $60.00 (6%*1000) 20 7% $1,000 $894.06 (Using PV function of excel with Rate=7%,Nper=20, Pmt=-60, Fv=-1000) T(20-N) Pn Number of Straight years to Bond maturity Price (Using PV function of excel with Rate=7%,Nper=T, Pmt=-60, Fv=-1000) 20 $894.06 PO 19 $896.64 P1 18 $899.41 P2 17 $902.37 P3 16 $905.53 |P4 Year 1 Connons H76 * fic : IB =RATE(H73,474,-H72,H75) D E F C L M N O P HT 8 $940.29 P12 7 $946.11 P13 6 $952.33 P14 5 $959.00 P15 4 $966.13 P16 3 $973.76 P17 2 $981.92 P18 1 $990.65 P19 O $1,000.00 P20 $1,585.54 $1,696.53 $1,815.29 $1,942.36 $2,078.32 $2,223.81 $2,379.47 $2,546.04 $2,724.26 b Pv Nper Pmt FV RATE EXPECTED RETURN WITH ANTICIPATED CONVERSION IN YEAR 9 Investment $894.06 (Note, the investment of investor is $894.06, NOT $1000) Number of years to conversion Annual Coupon Payment $60 Terminal Cash Flow on conversion $1,294.28 Expected Return of Investor | 10.01% (Using RATE function of excel with Nper=9, Pv=-894.06, Pmt=60, Fv=1294.28)