Question

A company just paid a dividend of $0.79 per share and you expect the dividend to grow at a constant rate of 5.2% per year indefinitely into the future. If the required rate of return is 12.4% per year, what would be a fair price for this stock today? (Answer to the nearest penny per share.)

A 6.4% coupon bearing bond pays interest semi-annually and has a maturity of 6 years. If the current price of the bond is $1,023.87, what is the yield to maturity of this bond? (Answer to the nearest tenth of a percent, e.g. 12.34%)

Answer 1

Ques-1)

Dividend just paid(D0)= $0.79 per share

Expected Growth rate of dividend(g) = 5.2% per year forever

Required rate of Return(Ke)= 12.40%

Calculating the Price of Stock:-

P0 = $11.54

Fair price of Stock = $11.54

Ques-2)

Face Value of Bond = $1000

Semi-annual Coupon payment = $1000*6.4%*1/2

= $32

No of years to maturity = 6

n = 6yrs*2 =12

Current Bond Price = $1023.87

As the price of Bond is higher than the face value of bond, the Yield to maturity(YTM) will be less than the Coupon Rate as Price and YTM have inverse relationship.

Taking YTM as 5%

Semi-annual YTM = 5%/2 = 2.5%

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Price = $ 328.25 + $743.56

Price = $1071.81

As at YTM@5%, Price is closer to Current price. Thus taking another YTM closer at 6%

Semi-annual YTM = 6%/2 =3%

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Price = $ 318.53+ $701.38

Price = $1019.91

Calculating YTM:-

YTM = 5.92%

So, YTM of Bond is 5.92%

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