Finance 1 (for premasters)
Formula chapter 1 - 13
2018 - 2019
,Chapter 2
Net Working Capital
𝑁𝑒𝑡 𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = NWC = current assets − current liablities
Book Value of Equity; Stockholder’s Equity
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 = Book Value of Assets − Book Value of Liabilities
Market Value of Equity; Market Capitalization
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 = Market Price per Share ∗ Number of Shares outstanding
Market-to-Book Ratio; Price-to-Book Ratio
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
𝑀𝑎𝑟𝑘𝑒𝑡 − 𝑡𝑜 − 𝐵𝑜𝑜𝑘 𝑅𝑎𝑡𝑖𝑜 =
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
Value Stocks Low Market-to-Book Ratios (<1)
Growth Stocks High Market-to-Book Ratios (>1)
Income Statement
EBIT
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐵𝑒𝑓𝑜𝑟𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑎𝑛𝑑 𝑇𝑎𝑥𝑒𝑠
EBITDA (= bedrijfsresultaat voor afschrijvingen)
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐵𝑒𝑓𝑜𝑟𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡, 𝑇𝑎𝑥𝑒𝑠, 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑛 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛
Income Statement: measuring Net Income (“bottom line” literally)
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 = 𝑃𝑟𝑒 − 𝑇𝑎𝑥 𝐼𝑛𝑐𝑜𝑚𝑒 − 𝑇𝑎𝑥𝑒𝑠
Earnings per Share
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝐸𝑃𝑆 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
,Diluted Earnings per Share
Value of earnings per share if all securities that can be converted into stock would be converted N of
shares goes up, EPS goes down (dilution)
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝐷𝐸𝑃𝑆 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 + 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑖𝑒𝑠
=
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝐷𝐸𝑃𝑆 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 + 𝑆𝑡𝑜𝑐𝑘 𝑂𝑝𝑡𝑖𝑜𝑛𝑠 + 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝐵𝑜𝑛𝑑𝑠
Chapter 3
Interest Rate; Exchange Rate Across Time
The rate at which we can exchange money today for money in the future is determined by the current
interest rate.
Risk–Free Interest Rate; Discount Rate = 𝑟𝑓
The interest rate at which money can be lent without risk.
Express in values one year from now: multiply current value by interest rate factor
Express in current values: divide future value by discount factor
– Interest Rate Factor = 1 + 𝑟𝑓
– Discount Factor = 1 / (1 + 𝑟𝑓 )
Present Value: discount
The value expressed in terms of dollars today is called the present value (PV) of the investment.
Memory aid: discounting involves dividing by, compounding involves multiplying with
𝐶1
𝑃𝑉 =
(1 + 𝑟𝑓 )𝑛
𝐶1 = 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 1 𝑟 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑𝑠
, Future Value: compound
The value expressed in terms of dollars in the future is called the future value (FV) of the investment.
Memory aid: discounting involves dividing by, compounding involves multiplying with
𝐹𝑉 = 𝐶0 × (1 + 𝑟𝑓 )𝑛
𝐶0 = 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 0 𝑟 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑𝑠
Net Present Value
The net present value (NPV) of a project or investment is the difference between the present value of its
benefits and the present value of its costs.
𝑁𝑃𝑉 = 𝑃𝑉(Benefits) − 𝑃𝑉 (Costs)
𝑁𝑃𝑉 = 𝑃𝑉 (All project cash flows)
Rules:
- Reject projects with negative NPV
- Choose the alternative with the highest NPV, if you can only choose one
No Arbitrage Price of a Security
𝑃𝑟𝑖𝑐𝑒 (Security) = 𝑃𝑉 (All cash flows paid by the security)
Risk-free interest 𝒓𝒇
𝑟𝑖𝑠𝑘 − 𝑓𝑟𝑒𝑒 𝑏𝑜𝑛𝑑 𝑡ℎ𝑎𝑡 𝑝𝑎𝑦𝑠 𝑥
1 + 𝑟𝑓 =
𝑐𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑖𝑣𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒
= 1 + 𝑟𝑓 − 1
= 𝑟𝑓
Valuation with risk
When cash flows are risky, we must discount them at a rate equal to the risk-free interest rate plus an
appropriate risk premium. If an investment has much more variable returns, it must pay investors a
higher risk premium.
𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 → 𝑑𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 (1 + 𝑟𝑓 + 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚)
Formula chapter 1 - 13
2018 - 2019
,Chapter 2
Net Working Capital
𝑁𝑒𝑡 𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = NWC = current assets − current liablities
Book Value of Equity; Stockholder’s Equity
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 = Book Value of Assets − Book Value of Liabilities
Market Value of Equity; Market Capitalization
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 = Market Price per Share ∗ Number of Shares outstanding
Market-to-Book Ratio; Price-to-Book Ratio
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
𝑀𝑎𝑟𝑘𝑒𝑡 − 𝑡𝑜 − 𝐵𝑜𝑜𝑘 𝑅𝑎𝑡𝑖𝑜 =
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
Value Stocks Low Market-to-Book Ratios (<1)
Growth Stocks High Market-to-Book Ratios (>1)
Income Statement
EBIT
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐵𝑒𝑓𝑜𝑟𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑎𝑛𝑑 𝑇𝑎𝑥𝑒𝑠
EBITDA (= bedrijfsresultaat voor afschrijvingen)
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐵𝑒𝑓𝑜𝑟𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡, 𝑇𝑎𝑥𝑒𝑠, 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑛 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛
Income Statement: measuring Net Income (“bottom line” literally)
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 = 𝑃𝑟𝑒 − 𝑇𝑎𝑥 𝐼𝑛𝑐𝑜𝑚𝑒 − 𝑇𝑎𝑥𝑒𝑠
Earnings per Share
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝐸𝑃𝑆 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
,Diluted Earnings per Share
Value of earnings per share if all securities that can be converted into stock would be converted N of
shares goes up, EPS goes down (dilution)
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝐷𝐸𝑃𝑆 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 + 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑖𝑒𝑠
=
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝐷𝐸𝑃𝑆 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 + 𝑆𝑡𝑜𝑐𝑘 𝑂𝑝𝑡𝑖𝑜𝑛𝑠 + 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝐵𝑜𝑛𝑑𝑠
Chapter 3
Interest Rate; Exchange Rate Across Time
The rate at which we can exchange money today for money in the future is determined by the current
interest rate.
Risk–Free Interest Rate; Discount Rate = 𝑟𝑓
The interest rate at which money can be lent without risk.
Express in values one year from now: multiply current value by interest rate factor
Express in current values: divide future value by discount factor
– Interest Rate Factor = 1 + 𝑟𝑓
– Discount Factor = 1 / (1 + 𝑟𝑓 )
Present Value: discount
The value expressed in terms of dollars today is called the present value (PV) of the investment.
Memory aid: discounting involves dividing by, compounding involves multiplying with
𝐶1
𝑃𝑉 =
(1 + 𝑟𝑓 )𝑛
𝐶1 = 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 1 𝑟 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑𝑠
, Future Value: compound
The value expressed in terms of dollars in the future is called the future value (FV) of the investment.
Memory aid: discounting involves dividing by, compounding involves multiplying with
𝐹𝑉 = 𝐶0 × (1 + 𝑟𝑓 )𝑛
𝐶0 = 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 0 𝑟 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑𝑠
Net Present Value
The net present value (NPV) of a project or investment is the difference between the present value of its
benefits and the present value of its costs.
𝑁𝑃𝑉 = 𝑃𝑉(Benefits) − 𝑃𝑉 (Costs)
𝑁𝑃𝑉 = 𝑃𝑉 (All project cash flows)
Rules:
- Reject projects with negative NPV
- Choose the alternative with the highest NPV, if you can only choose one
No Arbitrage Price of a Security
𝑃𝑟𝑖𝑐𝑒 (Security) = 𝑃𝑉 (All cash flows paid by the security)
Risk-free interest 𝒓𝒇
𝑟𝑖𝑠𝑘 − 𝑓𝑟𝑒𝑒 𝑏𝑜𝑛𝑑 𝑡ℎ𝑎𝑡 𝑝𝑎𝑦𝑠 𝑥
1 + 𝑟𝑓 =
𝑐𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑖𝑣𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒
= 1 + 𝑟𝑓 − 1
= 𝑟𝑓
Valuation with risk
When cash flows are risky, we must discount them at a rate equal to the risk-free interest rate plus an
appropriate risk premium. If an investment has much more variable returns, it must pay investors a
higher risk premium.
𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 → 𝑑𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 (1 + 𝑟𝑓 + 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚)
