Cost of capital
The cost of capital refers to the required rate of return that a company must achieve in order to attract investment and fund its operations. It is the cost of financing a company's activities through a mix of debt and equity. The cost of capital is a crucial concept in corporate finance and is used in various financial decision-making processes, such as evaluating potential investments, determining capital structure, and assessing overall corporate performance.
There are different components of the cost of capital:-
Cost of Debt:
This is the interest rate a company pays on its debt, such as bonds or loans. It represents the cost of borrowing money.
Cost of Equity:
This is the return that shareholders require for investing in the company's stock. It is often estimated using models like the Capital Asset Pricing Model (CAPM), which considers the risk-free rate, the company's beta (a measure of its volatility compared to the market), and the market risk premium.
Weighted Average Cost of Capital (WACC):
This is the weighted average of the cost of debt and the cost of equity, taking into account the company's capital structure (the proportion of debt and equity in its financing). It reflects the overall cost of funding the company's operations and projects.
The formula for calculating WACC is:
Where:
- = Market value of the company's equity
- = Market value of the company's debt
- = Total market value of the company's equity and debt
- = Cost of equity
- = Cost of debt
- = Corporate tax rate
It's important to note that the cost of capital can vary depending on factors such as the company's risk profile, the industry it operates in, prevailing interest rates, and overall economic conditions. Companies aim to invest in projects or activities that generate returns greater than their cost of capital, ensuring value creation for shareholders.
Calculating and understanding the cost of capital is essential for making informed financial decisions and evaluating the attractiveness of investment opportunities.
There are four sources for collect long term capital-
1. Cost of debt /Bond /debenture /Loan
2. Cost of preferred stock
3. Cost of common stock
4. Cost of retained earning
Abbreviation
Ki = Cost of debt before tax
Kd= Cost of debt after tax
Int= interest
Tr =Tax rate
NSV = Net sales value (sales-floatation cost)
RV =Redeemable value
SV = sales value
N = Numbers of years
Kp= Cost of preferred stock
PD =Preference dividend
Po =Sales price/Market price /Issue Price
Fc= Flotation cost
Ke=Cost of common stock/common share/Equity
Do=Current year dividend/ last year dividend/normal dividend
D1=Next year dividend/End of year dividend/ expected dividend/ coming year dividend
Po=Sales price/market price /issue price
G=Growth rate /Increase rate
Pt= personal tax
Kr=Cost of retained earning
Some important formulas of cost of capital
(01). (Part- cost of debt)
01.Ki = (Int/NSV)*100 [when, no mention
years & tax rate]
02.Kd = {(Int(1-tr)/NSV)}*100 [when, no mention years & But exist tax rate]
03.Kd = Ki(i-tr) [when, cost of debts % & exist tax rate]
04. Kd = Int(1-tr)+ RV-NSV/N /RV+NSV/2 *100 [when, years &Tax rate exist ]
(2).(Part-cost of preferred stock /preference share)
05.Kp = ( pd/po)*100 [when years & flotation cost not exist]
06.Kp = (pd/po-Fc)*100 [when no mention years but flotation cost exist]
07.Kp = (pd+RV-NSV/N/RV+NSV/2*100 [when exist years & flotation cost ]
08.Kp = pD(1+DT)/Po-Fc*100
09.kp = PD(1+DT)+RV-NSV/N /RV+NSV/2*100
(3).(Part- cost of common stock /common share / Equity)
10.Ke = Do/Po*100 [When exist dividend rate & sales price/ market price]
11. Ke = D1/Po-Fc+G)*100 [When exist dividend increase rate & sales price/ market price]
12.D1 = Do(1+G)
(4). (Part- cost of Retained Earning)
13.Kr = ke(1-Pt)
14.Kr = D1/Po+g*100
15.Ke = D1(1-Pt)/Po+g*100
Lets start with Practical Examples....
(01). (Part- cost of debt)
Practical Example (01)
A company has 15% perpetual debt of Tk.100,000. The tax rate is 50%. Determine the cost of capital before- tax as well after tax, assuming the debt is issued at (i)par (ii)10% discount(iii)10% premium.
Solution (i) at par
Here,Debt=1,00,000,Interest=1,00,000*15%=15,000,NSV=1,00,000, Tr=50%,
Before tax cost of debt
Ki=(Int/NSV)*100 [when, no mention years & tax rate]
=(15,000/1,00,000)*100
=15%
After tax cost of debt
Kd ={(Int(1-tr)/NSV)}*100 [when, no mention years & But exist tax rate]
={(15,000(1-0.50)/1,00,000)}*100
=7.50%
Solution (ii) at 10% discount
Here, debt=100000, Interest=(1,00,000*15%)=15,000,,NSV={1,00,000-(1,00,000*10%)}=Tk.90,000
Tr=50%
Before tax cost of debt
Ki=(Int/NSV)*100 [when, no mention years & tax rate]
=(15,000/90,000)*100
=16.67%
After tax cost of debt
Kd ={(Int(1-tr)/NSV)}*100 [when, no mention years & But exist tax rate]
={(15,000(1-0.50)/90,000)}*100
=8.34%
Solution (iii) at 10% premium
Here,NSV=1,00,000*.110=Tk.1,10,000,Tr=50%
Before tax cost of debt
Ki=(Int/NSV)*100 [when, no mention years & tax rate]
=(15,000/1,10,000)*100
=13.64%
After tax cost of debt
Kd ={(Int(1-tr)/NSV)}*100 [when, no mention years & But exist tax rate]
={(15,000(1-0.50)/1,10,000}*100
=6.82%
Practical Example -02
Calculate the explicit cost of debt for each of the following situation.
(a). Interest rate 10%
(b) Corporate tax rate 40%
(c)Flotation cost 5% of issue price
(d) Face value Tk.1,00,000
Requirement
(i) Sold at par
(ii) Sold at 10% premium
(iii) sold at 10% discount
Solution(i) at par
Kd ={(Int(1-tr)/NSV)}*100
={10000(1-0.40)/95000}*100
=6.32%
(ii) Sold at 10% premium
Kd ={(Int(1-tr)/NSV)}*100
={10000(1-0.40)/104500}*100
=5.74%
(iii) sold at 10% discount
Kd ={(Int(1-tr)/NSV)}*100
={10,000(1-0.40)/85,500*100
=7.02%(Ans)
Practical Example -03
Calculate the explicit cost of debt if 10% debenture Tk.1,00,000 and corporate tax rate 40%
We know that,
Kd =Ki(1-tr) [when, cost of debts % & exist tax rate]
=10%(1-0.40)
=10*0.60
=6%(Ans)
Practical Example -04
Calculate the explicit cost of debt for each of the following situation.
(a). Interest rate 15%
(b) Corporate tax rate 40%
(c)Flotation cost 5% of issue price
(d) Face value Tk.1000
(e). Date of maturity 10 Years
Requirement
(i) Sold at par and flotation costs are 5% of issue price
(ii) Sold at 10% premium and flotation costs are 5% of issue price
(iii) Sold at 10% discount and flotation costs are 5% of issue price
(i) Sold at par
Kd =Int(1-tr)+ RV-NSV/N/RV+NSV/n*100 [when, years &Tax rate exist ]
=150(1-0.40)+ 1000-950/10/1000+950/2 *100
=90+5/975 *100
=9.74%
(ii) Sold at 10% premium
Kd =Int(1-tr)+ RV-NSV/N/RV+NSV/n*100 [when, years &Tax rate exist ]
=150(1-0.40)+ 1000-1045/10/1000+1045/2 *100
=90+(-)4.5/1022.50*100
=8.54%
(iii) Sold at 10% discount
Kd =Int(1-tr)+ RV-NSV/N/RV+NSV/n*100 [when, years &Tax rate exist ]
=150(1-0.40)+ 1000-855/10/1000+855/2 *100
=90+14.50/927.50*100
=10.64%
Practical Example -05
Face value of a 12% debenture is Tk.2500 .maturity period 10 years. After 10 years it is Redeemable at 12% premium but recently sales at 5% discount. The flotation cost 2% of its sales value. Corporate tax rate 40%. Calculate the cost of debenture.
Kd =Int(1-tr)+ RV-NSV/N/RV+NSV/n*100 [when, years &Tax rate exist ]
=300(1-0.40)+ 2800-2327.50/10/2800+2327.50/2 *100
=1840+47.25/2563.75*100
=220.25/2563.75
=8.86%
(2).(Part-cost of preferred stock /preference share)
Practical Example -06
A company sells an issue of Tk.100 per value preferred stock with a Tk .6 dividends and nets Tk. 95 a share after under writing commission. Compute the cost of preferred stock for the company.
Solutions
Kp=(pd/po)*100 [when years & flotation cost not exist]
=6/95*100
=6.32%
Practical Example -07
A company issues 10 % irredeemable preference share. The face value per share is Tk.1,000 but the issue price is Tk.950. What is the cost of preference share? What is the cost if the issue price is Tk.1050?
We know that,
Kp=(pd/po)*100 [when years & flotation cost not exist]
=100/950*100
=10.53%%
Again,
Kp=(pd/po)*100
=100/1050*100
=9.52%
Practical Example -08
A company issues 14 % irredeemable preference share. The face value per share is Tk.100 each .but the issue price is Tk.950. Flotation cost is estimated about 5% of expected sales price. What is the kp, if preference share are issued –
(i) At Par
(ii) 10% premium
(iii) 5% discount
We know that,
(i) At Par
=(pd/po-Fc)*100 [when no mention years but flotation cost exist]
=(14/100-5)*100
=14.74%
(ii) 10% premium
=(pd/po-Fc)*100 [when no mention years but flotation cost exist]
=(14/110-5.50)*100
=13.40%
(iii) 5% discount
= (pd/po-Fc)*100 [when no mention years but flotation cost exist]
= (14/95-4.50)*100
=15.51%
Practical Example -09
A company pays a dividend of Tk.15 per share of preferred stock which sells Tk.125. Flotation cost is 4% and dividend tax is 10%. Calculate cost of preferred stock.(KP)
We know that,
Kp=pD(1+DT)/Po-Fc*100
Kp=15(1+0.10)/125-5*100
Kp=16.50/120*100
=13.75%
Practical Example -10
ABC company currently issues 14% preference share of Tk.1,000 per share redeemable after 5 yers .issue price is Tk.960. per share flotation cost Tk.20.
1. Calculate cost of preferred stock.(KP
We know that,
Kp=(pd+RV-NSV/N/RV+NSV/2*100 [when exist years & flotation cost ]
=140+1000-9400/5/1000+940/2*100
=140+12/970*100
=15.05%
Practical Example -11
A 15% preference share of Tk.1,000 each is issued at a discount of 7.50% and redeemable at premium of 5% after 5 years. Flotation cost is 2% and dividend tax rate is 10%.
01. Calculate the cost of preference share(Kp).
Here,
FV = Tk.1000,
Pd =1,000*15%=Tk.150
RV = {1000+(1000*5%)}=Tk.1050,
SV = {(1000-(1000*7.50%)=Tk.925
FC =925*2%=Tk.18.50
NSV=(SV-FC)=(925-18.50 )=Tk.906.50
DT=10% or,0.10
N= 5 years
We know that,
Kp={PD(1+DT)+(RV-NSV/N )/ (RV+NSV/2)}*100 [when exist years & flotation cost ]
={150(1+0.10)+(1050-906.50/5)/(1050+906.50)/2}*100
={(165+28.70) /(978.25)*100}
=19.80%(Ans)
(3).(Part- cost of common stock /common share / Equity)
Practical Example -12.
Wimax company Ltd. currently paid dividend Tk.12 per share. Currently market price per share is Tk.140 .
01.Compute the coast of Equity capital
We know that,
Ke=Do/Po*100
=12/140-0*100
=8.57%(Ans)
Practical Example -13.
XYZ company currently market price of the share is Tk.120 and expected dividend is Tk.9 if expected growth rate =4%,
01. determined the cost of equity capital?
We know that,
Ke=(D1/Po-Fc)*(100)+g
=(9/120*100)+4%
=(7.50%+4%)
=11.50%(Ans)
Practical Example -14
The wimax company ltd. Currently paid dividend Tk.12 per share which is expected to increase at about 2% per year. The market price of the share is Tk.200. Flotation cost are estimated about 5% of market price.
01.What is the cost of equity capital?
We know that,
Ke=D1/Po-Fc=100+g
=12.24/200-10*100+2%
=6.44%+2%
=8.44% (Ans)
Practical Example -15
Current market price is Tk.300 per share, current dividend is Tk.12 per share. Dividend per share is expected to increase at about 2% per share.
01.Calculate the cost of equity share capital ?
We know that,
Ke = (D1/Po-Fc)=100+g
= (12.24/300-0*100)+2%
= 4.08%+2%
= 6.08 % (Ans)
(4). (Part- cost of Retained Earning)
Practical Example -16
The cost of equity share capital(Ke) is 12% and Parsonal tax rate is 40%. Compute cost of retained earnings.
We know that,
Kr=ke(1-Pt)
=12%(1-0.40)
=12%*0.60
=7.20%
Practical Example -17
ABC Company current dividend is Tk.12 per share, market price of share is Tk.105 and flotation cost is Tk.5. What is the cost of retained earning if the personal tax rate is 35%.
Kr=Do(1-Pt)/Po*100
= 12(1-.35)/105*100
=7.8/105*100
=7.43%
Practical Example -18
Market price of equity share of Moon Company is Tk.150 per share and flotation cost is 5%. The company pays dividend is Tk.15 and growth rate of dividend expected to 6%.
Calculate cost of retain earning if personal tax rate is 40%.
We know that,
Ke=Do(1-Pt)/Po+g*100
= 15.90(1-0.40)/150+6%*100
=6.36%+6%
=12.36%(Ans)