Back Matter
Appendix B: Key Equations
© The McGraw−Hill
Companies, 2010
B
KEY EQUATIONS
CHAPTER 2
4. The ratio of net working capital to total assets:
1. The balance sheet identity or equation:
Assets Liabilities
Shareholders’ equity
[2.1]
[2.2]
3. The cash flow identity:
Cash flow from assets Cash flow to creditors Cash flow to stockholders
[2.3]
where
a. Cash flow from assets Operating cash
flow (OCF) Net capital spending Change in net working capital (NWC)
(1) Operating cash flow Earnings
before interest and taxes (EBIT) Depreciation Taxes
(2) Net capital spending Ending net
fixed assets Beginning net fixed
assets Depreciation
(3) Change in net working capital Ending NWC Beginning NWC
b. Cash flow to creditors Interest paid Net new borrowing
c. Cash flow to stockholders Dividends
paid Net new equity raised
1. The current ratio:
[3.5]
6. The total debt ratio:
Total debt ratio
Total assets Total equity
______________________
Total assets
[3.6]
7. The debt-equity ratio:
Debt-equity ratio
Total debtTotal equity
[3.7]
8. The equity multiplier:
Equity multiplier
Total assetsTotal equity
[3.8]
9. The long-term debt ratio:
Long-term debt ratio
Long-term debt
_________________________
Long-term debt Total equity
[3.9]
10. The times interest earned (TIE) ratio:
11. The cash coverage ratio:
[3.1]
2. The quick or acid-test ratio:
Current assets Inventory
Quick ratio ______________________ [3.2]
Current liabilities
3. The cash ratio:
Cash
Cash ratio _______________
Current liabilities
Interval measure
Current assets
________________________
Average daily operating costs
EBIT [3.10]
Times interest earned ratio _______
Interest
CHAPTER 3
Current assets
Current ratio _______________
Current liabilities
[3.4]
5. The interval measure:
2. The income statement equation:
Revenues Expenses Income
Net working capital to total assets
Net working capital
_________________
Total assets
APPENDIX
Ross−Westerfield−Jordan:
Fundamentals of Corporate
Finance, Ninth Edition,
Alternate
[3.3]
Cash coverage ratio
EBIT Depreciation
__________________
Interest
12. The inventory turnover ratio:
[3.11]
Inventory turnover
Cost of goods sold
________________
Inventory
13. The average days’ sales in inventory:
[3.12]
Days’ sales in inventory
365 days
________________
Inventory turnover
[3.13]
B-1
Ross−Westerfield−Jordan:
Fundamentals of Corporate
Finance, Ninth Edition,
Alternate
B-2
Back Matter
APPENDIX B
© The McGraw−Hill
Companies, 2010
Appendix B: Key Equations
Key Equations
14. The receivables turnover ratio:
Receivables turnover
Sales
_________________
Accounts receivable
15. The days’ sales in receivables:
2. The internal growth rate:
[3.14]
ROA b
Internal growth rate ____________
1 ROA b
[4.2]
3. The sustainable growth rate:
ROE b
Sustainable growth rate ____________
1 ROE b
Days’ sales in receivables
365 days
__________________
Receivables turnover
[3.15]
[3.16]
17. The fixed asset turnover ratio:
Sales
Fixed asset turnover _____________
Net fixed assets
Total assets
Sales
[3.18]
[3.19]
[3.20]
21. Return on equity (ROE):
Net income
Return on equity __________
Total equity
22. The price-earnings (PE) ratio:
Price per share
PE ratio ________________
Earnings per share
PV (1 r)t FVt
PV FVt (1 r)t FVt [1(1 r)t]
Annuity present value
[3.22]
1 Present value factor
C ____________________
r
(
{
[3.23]
[3.24]
Return on assets
t
)
}
[6.1]
2. The future value factor for an annuity:
Annuity FV factor
(Future value factor 1)r
[(1 r)t 1]r
3. Annuity due value Ordinary annuity value
(1 r)
[6.2]
[6.3]
4. Present value for a perpetuity:
ROE Profit margin
Total asset turnover
Equity multiplier
PV for a perpetuity Cr C (1r)
1. The dividend payout ratio:
[4.1]
[6.4]
5. Growing annuity present value
1g t
1 _____
1r
C ___________
rg
[6.5]
6. Growing perpetuity present value
C
_____
rg
[6.6]
CHAPTER 4
Dividend payout ratio
Cash dividendsNet income
[5.3]
1. The present value of an annuity of C dollars per period
for t periods when the rate of return or interest rate is r:
1 [1(1 r) ]
C ______________
r
24. The Du Pont identity:
Sales ______
Net income ______
Assets
ROE __________
Assets
Sales
Equity
[5.2]
3. The relationship between future value and present
value (the basic present value equation):
CHAPTER 6
[3.21]
23. The market-to-book ratio:
Market-to-book ratio
Market value per share
___________________
Book value per share
[5.1]
2. The present value of $1 to be received t periods in
the future at a discount rate of r:
PV $1 [1(1 r)t] $1(1 r)t
20. Return on assets (ROA):
Net income
Return on assets __________
Total assets
1. The future value of $1 invested for t periods at rate
of r per period:
Future value $1 (1 r)t
19. Profit margin:
Net income
Profit margin __________
1
________________
Total asset turnover
CHAPTER 5
[3.17]
18. The total asset turnover ratio:
Sales
Total asset turnover __________
4. The capital intensity ratio:
Total assets
Capital intensity ratio __________
Sales
16. The net working capital (NWC) turnover ratio:
Sales
NWC turnover _____
NWC
[4.3]
(
)
Ross−Westerfield−Jordan:
Fundamentals of Corporate
Finance, Ninth Edition,
Alternate
Back Matter
© The McGraw−Hill
Companies, 2010
Appendix B: Key Equations
APPENDIX B
PV of cash flows
Profitability index ________________
Cost of investment
EAR [1 (Quoted ratem)]m 1
8. Effective annual rate (EAR), where q stands for the
continuously compounded quoted rate:
CHAPTER 10
1. Bottom-up approach to operating cash flow (OCF):
EAR e q 1
OCF Net income Depreciation
CHAPTER 7
[7.1]
[7.2]
[7.3]
[7.4]
[10.3]
[11.1]
2. Relationship between operating cash flow (OCF)
and sales volume:
Q (FC OCF)(P v)
[11.3]
Q FC(P v)
4. Financial break-even level:
[8.3]
Q (FC OCF*)(P v)
where
[8.7]
NPV Present value of future cash flows
Investment cost
2. Payback period:
Payback period Number of years that pass before
the sum of an investment’s cash flows equals the cost
of the investment
3. Discounted payback period:
Discounted payback period Number of years that
pass before the sum of an investment’s discounted
cash flows equals the cost of the investment
IRR Discount rate of required return such that
the net present value of an investment is zero
OCF (Sales Costs) (1 T)
Depreciation T
3. Cash break-even level:
1. Net present value (NPV):
5. Internal rate of return (IRR):
3. Tax shield approach to operating cash flow (OCF):
Q (FC D)(P v)
CHAPTER 9
4. The average accounting return (AAR):
Average net income
AAR _________________
Average book value
[10.2]
1. Accounting break-even level:
2. Required return:
R D1P0 g
OCF Sales Costs Taxes
CHAPTER 11
CHAPTER 8
1. The dividend growth model:
D0 (1 g) ______
D1
P0 ___________
Rg
Rg
[10.1]
2. Top-down approach to operating cash flow (OCF):
1. Bond value if bond has (1) a face value of F paid at
maturity, (2) a coupon of C paid per period, (3) t periods
to maturity, and (4) a yield of r per period:
1 R (1 r) (1 h)
Rrhrh
Rrh
B-3
6. Profitability index:
7. Effective annual rate (EAR), where m is the number
of times the interest is compounded during the year:
Bond value
C [1 1(1 r)t]r F(1 r)t
Bond value
Present value
Present value
of the coupons
of the face amount
2. The Fisher effect:
Key Equations
OCF* Zero NPV cash flow
5. Degree of operating leverage (DOL):
DOL 1 FCOCF
[11.4]
CHAPTER 12
1. Variance of returns, Var(R) or ␴2:
1 [(R __
R )2 · · ·
Var(R) _____
T 1 __1
(RT R )2]
[12.3]
2. Standard deviation of returns, SD(R) or ␴:
Var(R)
SD(R) CHAPTER 13
1. Risk premium:
Risk premium Expected return
– Risk-free rate
[13.1]
2. Expected return on a portfolio:
E(RP) x1 E(R1) x 2 E(R2) · · ·
xn E(R n)
[13.2]
Appendix A: Formula Sheet
The following are useful formulae
1. Simple Interest Formula
SI = P0 × r × n
2. Compound Interest (Single deposit)/ Future Value
a. Single compounding
FVn = PV0 (1 + r )
n
b. Compounding more than once
r

FVn = PV0  1 + 
m

mn
3. Future Value of an Annuity
a. Ordinary annuity
 (1 + r )n − 1 

FVOA = C 
r


© The Author(s) 2017
J.Y. Abor, Entrepreneurial Finance for MSMEs,
DOI 10.1007/978-3-319-34021-0
391
392
Appendix A: Formula Sheet
b. Annuity due
 (1 + r )n − 1 
 (1 + r )
FVAD = C 
r


4. Future Value of Perpetuity
Since a perpetuity is designed to live infinitely, it is not possible to
work its future value.
5. Present Value of a Single Deposit
PV0 =
FVn
(1 + r )
n
6. Present Value of an Annuity
a. Ordinary annuity
1

n
1 −
(1 + r )
PVOA = C 

r








b. Annuity due
1

n
1 −
(1 + r )

PVAD = C

r




 (1 + r )



7. Growing annuity
PV =
n
C  1+ g  
1 − 

r − g   1 + r  
Appendix A: Formula Sheet
8. Present Value of a Perpetuity
PV =
C
r
9. Rate Implicit on an Investment
1
 FV  t
r =
 −1
 PV 
10. Number of Years
 FV 
ln 

PV 
n= 
ln (1 + i )
11. Effective Annual Rate of Interest
m
r

EAR =  1 +  − 1
m


12. External Funds Needed
EFN =
L
A
( ∆S ) − ( ∆S ) − ( PM )( PS) (1 − d )
S
S
13. Break-Even Quantity
QB =
F
P −V
14. Economic Order Quantity
EOQ =
2DCo
HC
393
Appendix A: Formula Sheet
15. Market Capitalization
𝑀𝐶 = 𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 × 𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
16. Enterprise Value
𝐸𝑉 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 + 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 − 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑑𝑒𝑏𝑡 – 𝐶𝑎𝑠ℎ
17. EV Multiple
𝐸𝑉 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑒 =
𝐸𝑉
𝐸𝐵𝐼𝑇𝐷𝐴
𝑊ℎ𝑒𝑟𝑒 𝐸𝑉 = 𝐸𝑞𝑢𝑖𝑡𝑦 + 𝐷𝑒𝑏𝑡 − 𝐶𝑎𝑠ℎ & 𝐸𝐵𝐼𝑇𝐷𝐴 = 𝑆𝑎𝑙𝑒𝑠 − 𝐶𝑜𝑠𝑡𝑠
18. Payout Ratio
𝑑 =
𝐷𝑒𝑣𝑖𝑑𝑒𝑛𝑑
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
19. Plowback (Retention) Ratio
𝑏=
𝐴𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑡𝑜 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝑜𝑟
𝑏 = (1 − 𝑑)
20. FV with continuous compounding
𝐹𝑉𝐶 = 𝐶0 × 𝑒 𝑟𝑡
21. ROE
𝑅𝑂𝐸 = 𝑅𝑂𝐴 × 𝐸𝑞𝑢𝑖𝑡𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = 𝑅𝑂𝐴 × (1 + 𝐷𝑒𝑏𝑡 − 𝑒𝑞𝑢𝑖𝑡𝑦 𝑟𝑎𝑡𝑖𝑜)
22. Coupon Rate
𝐶𝑜𝑢𝑝𝑜𝑛 𝑟𝑎𝑡𝑒 =
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝑝𝑎𝑟 𝑣𝑎𝑙𝑢𝑒
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑖𝑒𝑙𝑑 =
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝑏𝑜𝑛𝑑 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒
23. Current Yield
24. Dirty Price (Invoice Price)
𝐷𝑖𝑟𝑡𝑦 𝑃𝑟𝑖𝑐𝑒 (𝐼𝑛𝑣𝑜𝑖𝑐𝑒 𝑃𝑟𝑖𝑐𝑒) = 𝐶𝑙𝑒𝑎𝑛 𝑃𝑟𝑖𝑐𝑒 + 𝐴𝑐𝑐𝑟𝑢𝑒𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
394
Appendix A: Formula Sheet
395
25. Accrued Interest
𝐴𝑐𝑐𝑟𝑢𝑒𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 =
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝑃𝑒𝑟𝑖𝑜𝑑𝑠 𝑎𝑐𝑐𝑟𝑢𝑒𝑑 𝑓𝑟𝑜𝑚 𝑙𝑎𝑠𝑡 𝑝𝑎𝑦𝑚𝑒𝑛𝑡
×
𝑃𝑎𝑦𝑚𝑒𝑛𝑡𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
𝑃𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 𝑎 𝑝𝑎𝑦𝑚𝑒𝑛𝑡
26. Stock Valuation
Zero Growth
𝑃𝑡 =
𝐷𝑡
𝑅
Constant Growth
𝑃𝑡 =
𝐷𝑡+1
(𝑅−𝑔)
Differential Growth
𝑃0 = ∑𝑇𝑡=1
Benchmarking
𝑃0 = 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑃𝐸 𝑅𝑎𝑡𝑖𝑜 × 𝐸𝑃𝑆
𝑆𝑡𝑜𝑐𝑘 𝑃𝑟𝑖𝑐𝑒
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝑊ℎ𝑒𝑟𝑒 𝑃𝐸 =
& 𝐸𝑃𝑆 =
𝐸𝑃𝑆
𝑆ℎ𝑎𝑟𝑒𝑠
=
𝐷𝑡 (1+𝑔)
(𝑅−𝑔)
𝐷(1+𝑔1 )𝑡
(1+𝑅)𝑡
𝐷
1
𝑡+1
+ (𝑅−𝑔
× (1+𝑅)𝑇
)
2
27. Growth Rate
𝑔 = 𝑅𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 × 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 (𝑅𝑂𝐸)
28. Rate of Return
𝑅 = 𝐷𝑖𝑣𝑒𝑑𝑒𝑛𝑑 𝑌𝑖𝑒𝑙𝑑 + 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐺𝑎𝑖𝑛𝑠 𝑌𝑖𝑒𝑙𝑑 =
𝐷1 𝑃1 − 𝑃0
𝐷1
+
=
+𝑔
𝑃0
𝑃0
𝑃0
29. Dividend per Share
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 × 𝑃𝑎𝑦𝑜𝑢𝑡 𝑅𝑎𝑡𝑖𝑜
𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
30. Risk Premium
𝑅 − 𝑅𝑓
31. Terminal Value
𝑇𝑉 𝑡 =
𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 (𝐶𝐹𝑡+1 )
𝐶𝐹𝑡 × (1 + 𝑔)
=
(𝑅 − 𝑔)
(𝑅 − 𝑔)
32. Holding Period Return
[(1 + 𝑅1 ) + (1 + 𝑅2 ) + (1 + 𝑅3 ) + … (1 + 𝑅𝑇 )] − 1
33. Athematic Average Return
𝑅1 + 𝑅2 + 𝑅3 + … 𝑅𝑁
𝑁
Appendix A: Formula Sheet
34. Geometric Average Return
1
[(1 + 𝑅1 ) + (1 + 𝑅2 ) + (1 + 𝑅3 ) + … (1 + 𝑅𝑇 )]𝑇 − 1
35. Variance (σ2) for equal weights
𝑁
1
∑ (𝑅𝑖 − 𝑅̅ )2
𝑁−1
𝑖=1
36. Standard Deviation (σ)
√𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
37. Expected Return
𝐸(𝑅𝑋 ) = ∑ 𝑆𝑡𝑎𝑡𝑒 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 × 𝑅𝑋 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑠𝑡𝑎𝑡𝑒
38. Variance for un-equal weights
σ𝑥 2 = ∑ 𝑆𝑡𝑎𝑡𝑒 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 × (𝑅𝑋 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑠𝑡𝑎𝑡𝑒 − 𝐸(𝑅𝑋 ))2
39. Expected Return of Portfolio
𝐸(𝑅𝑃 )𝑆𝑡𝑎𝑡𝑒 1 (𝑆1) = 𝑊𝑋 𝑅𝑋,𝑆1 + 𝑊𝑌 𝑅𝑌,𝑆1 …
𝐸(𝑅𝑃 )𝑆𝑡𝑎𝑡𝑒 2 (𝑆2) = 𝑊𝑋 𝑅𝑋,𝑆2 + 𝑊𝑌 𝑅𝑌,𝑆2 …
.
.
𝐸(𝑅𝑃 )𝑂𝑣𝑒𝑟𝑎𝑙𝑙 = 𝑃(𝑆1) × 𝐸(𝑅𝑃 )𝑆1 + 𝑃(𝑆2) × 𝐸(𝑅𝑃 )𝑆2 …
40. Variance (σ2) of Portfolio
σ𝑃 2 = 𝑃(𝑆1) × [𝐸(𝑅𝑃 )𝑆1 − 𝐸(𝑅𝑃 )𝑂𝑣𝑒𝑟𝑎𝑙𝑙 ]2 + 𝑃(𝑆2) × [𝐸(𝑅𝑃 )𝑆2 − 𝐸(𝑅𝑃 )𝑂𝑣𝑒𝑟𝑎𝑙𝑙 ]2 …
41. Beta of Portfolio
𝛽𝑃 = 𝑊𝑋 𝛽𝑋 + 𝑊𝑌 𝛽𝑌 …
42. Capital Asset Pricing Model (CAPM)
𝐸(𝑅𝑋 ) = 𝑅𝑓 + 𝛽𝑋 × 𝑀𝑅𝑃 = 𝑅𝑓 + 𝛽𝑋 [𝐸(𝑅𝑚 ) − 𝑅𝑓 ]
43. Reward-to-Risk Ratio
𝐸(𝑅𝑋 ) − 𝑅𝑓
𝛽𝑋
396
Appendix A: Formula Sheet
44. Covariance 1
𝐶𝑜𝑣(𝑋, 𝑌) = 𝑃(𝑆1) × [𝑅𝑋,𝑆1 − 𝐸(𝑅𝑋 )] × [𝑅𝑌,𝑆1 − 𝐸(𝑅𝑌 )]
+ 𝑃(𝑆2) × [𝑅𝑋,𝑆2 − 𝐸(𝑅𝑋 )] × [𝑅𝑌,𝑆2 − 𝐸(𝑅𝑌 )]
.
.
45. Covariance 2
2
𝜎 𝑋,𝑌
= (𝑤𝑋 𝜎𝑋 )2 + (𝑤𝑌 𝜎𝑌 )2 + 2(𝑤𝑋 𝜎𝑋 )(𝑤𝑌 𝜎𝑌 )𝜌𝑋𝑌
46. Correlation (ρ)
𝜌𝑋,𝑌 =
𝐶𝑜𝑣(𝑋, 𝑌)
σ𝑋 σ𝑌
47. Capital Market Line (CML) Slope
𝑆𝑙𝑜𝑝𝑒𝐶𝑀𝐿 =
[𝐸(𝑅𝑚 ) − 𝑅𝑓 ]
𝑅𝑖𝑠𝑒
𝐼𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛
𝑜𝑟
=
σ𝑀
𝑅𝑢𝑛 𝐼𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
48. Beta
𝛽𝑋 =
𝜌𝑋,𝑀 × σ𝑋
σ𝑀
49. Cost of Equity (RS) using CAPM
𝑅𝑆 = 𝑅𝑓 + 𝛽𝑋 × 𝑀𝑅𝑃 = 𝑅𝑓 + 𝛽𝑆 [𝐸(𝑅𝑚 ) − 𝑅𝑓 ]
50. Cost of Equity (RS) using DDM
𝑅𝑆 =
𝐷1
+𝑔
𝑃0
51. Equity (S)
𝑆ℎ𝑎𝑟𝑒𝑠 × 𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑆ℎ𝑎𝑟𝑒
52. Cost of Debt (RB)
𝑅𝐵 = 𝑌𝑖𝑒𝑙𝑑 𝑡𝑜 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦
53. Book Value of Debt (BVB)
𝐵𝑉𝐵 = 𝑆𝑢𝑚 𝑜𝑓 𝐴𝑙𝑙 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒
54. Market Value of Debt (B)
𝐵 = 𝑄𝑜𝑢𝑡𝑒𝑑 𝑃𝑟𝑖𝑐𝑒 % 𝑜𝑓 𝐵𝑜𝑛𝑑 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒 × 𝐷𝑒𝑏𝑡 𝑓𝑟𝑜𝑚 𝐵𝑜𝑛𝑑
397
Appendix A: Formula Sheet
55. Weighted Average Cost of Capital (RWACC)
𝑅𝑊𝐴𝐶𝐶 =
𝑆
𝐵
× 𝑅𝑆 +
× 𝑅𝐵 × (1 − 𝑇𝑎𝑥 𝑅𝑎𝑡𝑒)
𝑆+𝐵
𝑆+𝐵
56. Weighted Average Flotation Cost (f)
𝑓𝑋 =
𝑆
𝐵
× 𝑓𝑆 +
× 𝑓𝐵
𝑆+𝐵
𝑆+𝐵
57. Amount needed after flotation costs
Amount needed after flotation costs = 𝐴𝑚𝑜𝑢𝑛𝑡 𝑅𝑎𝑖𝑠𝑒𝑑 × (1 − 𝑓𝑋 )
398