Question

Financial managers of BECN firm plan toissue a stock with a $5 annual year-end dividend. This firm’s earnings per share (EPS) is expected to be $10. This firm’s ROE is 8%. If BECN firm has a beta 2.0, T-bills rate (i.e., risk-free rate) is 2%, and the market return is 5%. What price should the stock be sold at?

If you purchase a five-year, 9% coupon bond for $950, how much could it be sold for four years later if interest rates have remained stable?.

Answer 1

Expected cost of capital or required rate of return by using CAPM

r = risk free rate + beta of company * (Market return – risk free rate)

r = 2% + 2 * (5% -2%) = 8%

Expected Dividend = Expected EPS * (1 - plowback ratio)

$5 = $10 * (1-plowback ratio)

Or Plowback ratio = 1 - $5/$10 = ½ or 50%

Growth rate g = (plowback ratio) * (ROE) = 50% * 8% = 4%

The current market price for this company using the constant growth model (the dividend growth model)

Current market price of stock = Expected Dividend /(r-g)

Where,

Expected Dividend = $5 per share

Required rate of return r = 8%

Constant dividend growth rate g = 4%

Therefore

Current market price of stock = $5 / (8% - 4%)

= $5 / (0.08 -0.04) = $125

Price of stock is $125

If you purchase a five-year, 9% coupon bond for $950, how much could it be sold for four years later if interest rates have remained stable?.

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,

P0 = the current market price of bond = $950

M = value at maturity, or par value = $ 1,000

C = coupon payment = 9% of $1,000 = $90

n = Time periods to maturity = 5 years

YTM = interest rate, or yield to maturity =?

Now we have,

$950 = $90 * [1 – 1 / (1+YTM) ^5] /YTM + 1,000 / (1+YTM) ^5

From above equation, we can calculate the value of YTM, which is 10.33% per year

Now price of the bond after four years can be calculated in following manner if interest rates have remained stable at 10.33%

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

Where,

P0 = the current market price of bond =?

M = value at maturity, or par value = $ 1,000

C = coupon payment = 9% of $1,000 = $90

n = Time periods to maturity = 5 – 4 =1 year

YTM = interest rate, or yield to maturity =10.33%

Now we have,

Price of Bond = $90 * [1 – 1 / (1+10.33%) ^1] /10.33% + 1,000 / (1+10.33%) ^1

= $987.94

Therefore price of the bond four years later will be $987.94