Question

Following are the securities and projections for Mogul Corp:

Stock A: REQUIRED RATE OF RETURN = 5% Constant-growth - growth rate of 3% D0 = $3.00

Stock B: REQUIRED RATE OF RETURN = 7% D0 = $4.00, growth at 5% per year for 2 years, followed by 4% forever

Stock C: REQUIRED RATE OF RETURN = 9% D0 = $2.00, growth at 25% for next 4 years, followed by 5% forever

Mogul has a 3.5% Treasury bond, semi-annual interest, with 4 years left to maturity and a quoted price of $962.81.

1) Calculate the bond’s current yield and yield to maturity.

2) Calculate the value per share today for stock A.

3) Calculate the value per share 4 years from today for stock B.

4) Calculate the value per share today for stock C.

Answer 1

(1) Current Bond Price = P(m) = $ 962.81, Time to Maturity = 4 years or 8 half years, Annual Coupon Rate =3.5% per annum or 1.75% per half year.

Let the bond's yield to maturity be denoted by 2R and face value be $ 1000

Semi-Annual Coupon = Annual Coupon Rate x 0.5 x Face Value of Bond = 0.035 x 0.5 x 1000 = $ 17.5

Therefore, 962.81 = 17.5 x (1/r) x [1-{1/(1+R)^(8)}] + [1000/(1+R)^(8)]

Solving the above equation using the EXCEL Goals Seek Function we get

R = 0.02263 or 2.263% per half year

Therefore, YTM = 2 R = 4.526% per annum

Current Yield = Annual Coupon / Market Price = (17.5 x 2) / 962.81 = 0.0363 or 3.63% per annum

(2) Stock's Required Rate of Return =r(a) = 5%, Constant Growth Rate = g = 3% and D0= $ 3 per share

Therefore, Current Stock Price = P0 = [D0 x (1+g)] / [r(a) - g] = / (0.05 - 0.03) = $154.5

(3) Stock's Required Rate of Return = r(b) = 7% , Initial Growth Rate of 5% per year followed by a flat growth rate of 4% to perpetuity.

D0= $ 4

Therefore, D1 = D0 x 1.05 = 4 x 1.05 = $ 4.2 and D2 = 4.2 x (1.05) = $ 4.41, D3 = 4.41 x 1.04 = $ 4.5864

D4 = D3 x 1.04 = 4.5864 x 1.04 = $ 4.769856 and D5 = D4 x 1.04 = 4.769856 x 1.04 = $ 4.96065024

Hence, share price 4 years from now = D5 / (r(b) - g) = = 4.96065024 / (0.07 - 0.04) = $ 165.355

(4) Required Rate of Return =r(c) = 9%, D0 = $ 2 and initial growth rate =g1 =25% per year and flat growth rate =g2 =5% per year

D0 =$2 , D1 = D0 x (1+g1) = 2 x 1.25 = $2.5 , D2 = D1 x (1+g1) = 2.5 x 1.25 = $ 3.125, D3 =D2 x (1+g1) = 3.125 x (1.25) = $ 3.90625, D4 = D3 x (1+g1) = 3.90625 x (1.25) = $ 4.8828125

Therefore, current stock price = D1 / [1+r(c)] + D2 / [1+r(c)]^(2) + D3 / [1+r(c)]^(3) +D4 / [1+r(c)]^(4) + [D4 x (1+g2)] / [r(c) -g2]

= $ 139.573 per share