Reading this question the first few thing that you should focus on to solve such questions are:
1. finding the market value of equity (value of common share). For value of common stock, it is given in the question that currently the number of common shares outstanding with the company is 1.2 million. Note that, 1.2 million is the number of shares outstanding with the company and it is not the value of those outstanding common stock. So, now your task is to find what is the current price at which this common stock is trading or price at which the investors are ready to buy. Keep think where in the given question this piece of information is shared.
2. Finding the market value of debt (bonds). Read carefully, the question shares the Face value of the bond, coupon %age and yield of the bond, which clearly indicates that we have to calculated market value of the bond to solve the question.
3. Weights of Debt (bond) and equity (common stock) in the capital structure of the company. Note, to calculate the weights you need to first calculated the market value of common stock equity and debt.
4. Once you know the weight, use the weight to calculate the new amount of bond that have to be raised. Total new capital to be raised is 7.5 million, therefore, the amount of new debt (bond) to be raised will be 7.5 million * weight of debt in the capital structure. Note, it is given that company will follow its existing capital structure.
5. Finding the after tax cost of debt. It is given in the question that If the company issues upto $2.5 million of new bond , the yield will be 13.65% and if it issues bonds beyond $2.5 million, the expected yield on the entire issuance will be 16%. Note, this is before tax cost of debt as nowhere in the question it is given that yiled is after tax yield or after tax cost of debt. Be careful while reading such questions.
6. finding the cost of equity. The question has provided all the information to calculate the cost of equity using CAPM model. Beta is 2.2 ; risk free rate is 3% ; expected market return in 10%. Note, the expected market return is not the premium that you get for investing in risky instrument like equity. So CAPM model need risk premium ( expected market return - risk free rate) to calculate the cost of equity.
Now you have all the information to calculate the WACC.
It goes like this!
1. Market value of equity (value of common share) = 1.2 * 1,000,000 * 10 = 12,000,000. 1.2 million shares are multiplied by 10 because it is given in the question that the company can issue new common stock at $10 per share. which means investors are ready to pay $10 per share.
2. Market value of debt (bonds): Use your financial calculator to get the present value of the bond.
FV of the bond is the face value of the bond, because it is the face value that bond investor will get at maturity.
FV = - 10,000,000
Bond is entitled to get semi annual coupons. Coupon rate is 8%.
Coupon in Calculator is PMT = Coupon rate of 8% / 2 * FV of 10,000,000 = 400,000
Number of years to mature is 5 and bond is a semi-annual bond. So, N = 5*2 = 10
Yield for this bond is given as 13.65%. I/Y = 13.65%
Compute for PV. PV = 7,999,688.
3. Weights of Debt (bond) and equity (common stock) in the capital structure:
Market Value of Debt = 7,999,688
Market Value of Equity = 12,000,000
Total Market Value (Debt + Equtiy) = 19,999,688
weight of debt = 7,999,688 / 19,999,688 = 40%
weight of equity = 1- 40% = 60%
4. New debt issuance: to raise 7.5 million in total, company would issue new debt (bond) worth of 40% * 7.5 million = 3 million in bonds
5. After tax cost of debt: Since company is issuing debt more than $2.5 million, the yield rate will be 16%.
After tax cost of debt: 16% *(1-30%) = 11.2%. Tax rate 30% is given.
6. Cost of equity:
CAPM = Rf + beta*(Expected Market Return - Rf)
= 3% + 2.2 * (10% - 3%) = 18.4%
Therefore WACC will be:
WACC = (40%*0.112) + (60%*0.184%) = 15.52%
Hope this help!!!