Answer:
a. Cost of debt = 5.03%.
b. Cost of equity = 11.47%
c. Cost of preferred stock = 4.90%
Explanation:
a. Calculation of cost of debt
The bond's Yield to Maturity is the before tax cost of debt and it can be calculated using the following RATE function in Excel:
YTM = RATE(nper,pmt,-pv,fv) * 2 .............(1)
Where;
YTM = yield to maturity = ?
nper = number of periods = number of semiannuals to maturity = Number of years * Number of semiannuals in a year = 21 * 2 = 42
r = semiannual coupon rate = Annual coupon rate / 2 = 7.4% / 2 = 0.074 / 2 = 0.037
pmt = semiannual coupon payment = semiannual coupon rate * Face value = 0.037 * $2,000 = $74 = 74
pv = present value = quoted bond price = 108.75% * fv = 108.75% * 2000 = 2,175 = 2175
fv = face value or par value of the bond = 2000
Substituting the values into equation (1), we have:
YTM = RATE(42,74,-2175,2000) * 2 ............ (2)
Inputting =RATE(42,74,-2175,2000)*2 into excel (Note: as done in the attached excel file), the YTM is obtained as 6.62%.
Therefore, we have:
After tax cost of debt = YTM * (100% - Tax rate) = 6.62% * (100% - 24%) = 5.03%
Therefore, cost of debt is 5.03%.
b. Calculation of cost of equity
Based on the information in the question, the return on equity can be calculated using the dividend discount model and capital asset pricing model (CAPM) formulae.
b-1. Using the dividend discount model formula, we have:
P = D1 / (r – g) ………………………. (3)
Where:
P = Common stock selling price per share = $66.40
D1 = Next year dividend = $4.60
r = return on equity = ?
g = dividend growth rate = 5.4%, or 0.054
Substituting the value into equation (3) and solve for r, we have:
66.40 = 4.60 / (r – 0.054)
66.40(r – 0.054) = 4.60
66.40r - 3.5856 = 4.60
66.40r = 4.60 + 3.5856
66.40r = 8.1856
r = 8.1856 / 66.40
r = 0.1233, or 12.33%
b-2. Using CAMP formula, cost of equity can be calculated as follows:
Return on equity = Risk free rate + Stock beta(Expected return – Risk free rate) = 4.55% + (1.09 * (10.1% - 4.55%)) = 10.60%
b-3. The cost of equity can therefore be calculated as the average of the returns of equity from the two formulae is as follows:
Cost of equity = (12.33% + 10.60%) / 2 = 11.47%
c. Calculation of cost preferred stock
Note that since the preferred stock selling price per share is $95.90, it indicates that it par value is $100 and is being sold at a discount. Therefore, we have:
Cost of preferred stock = (Preferred stock dividend rate * Preferred stock par value) / Preferred stock selling price per share = (4.70% * 100) / 95.90 = 0.0490, or 4.90%
