Formulas For Final Exam Spring 03

Current Ratio = Current Assets/Current Liabilities Quick Ratio = (Current Assets - Inventories)/Current Liabilities Inventory Turnover = Sales/Inventories Days Sales Outstanding = Receivables/(Annual Sales/360) Fixed Asset Turnover = Sales/Net Fixed Asset Total Asset Turnover = Sales/Total Assets Total Debt to Total Assets (Debt Ratio) = Total Debt/Total Assets Times-Interest-Earned = Earnings Before Interest and Taxes/Interest Profit Margin on Sales = Net Income/Sales Return on Total Assets = Net Income/Total Assets Return on Common Equity = Net Income/Common Equity Price/Earnings = Price per Share/Earnings per Share Earnings Per Share = Net Income/Number of Common Stock Shares Outstanding Price/Cash Flow = Price Per Share/Cash Flow per Share Cash Flow Per Share = (Net Income + Depreciation)/Number of Common Stock Shares Outstanding Market/Book = Market Price Per Share/Book Value per Share Book Value Per Share = Common Equity/Number of Common Stock Shares Outstanding Return on Equity = (Net Income/Sales) X (Sales/Total Assets) X (Total Assets/Common Equity)

k=

k 1 + k 2 + ... + k n n

Estimated σ (or S)

=

(k 1 − k) 2 + (k 2 − k) 2 + ... + (k n − k) 2 n −1

σ = σ2 σ CV = k n

b p = w 1 b1 + w 2 b 2 + ... + w n b n = ∑ w i b i i =1

k i = k RF + (k M − k RF )b i

FV = PV (1 + i )n = PV(FVIF i, n)

FV (1 + i) n

PV =

= FV(PVIF i, n)

FVA = PMT(FVIFA i, n)

PVA = PMT(PVIFA i, n) PV =

PMT i

EAR = (1 +

i nominal m ) −1 m

PV = PMT(PVIFA k d , N ) + FV(PVIFk d , N ) PV =

PMT (PVIFA k d /2 , N(2) ) + FV(PVIFk d /2 , N(2) ) 2

D1 = D0 (1 + g)

Pˆ0 =

D0 (1 + g) D1 = ks − g ks − g

D kˆ s = 1 + g P0 D Pˆp = p kp D kˆ p = p Pp ks =

D1 +g P0

ke =

D1 +g Pn

Breakpoint = Retained Earnings available for investment wc WACC1 = wdkd(1 - T)+ wpkp + wcks WACC2 = wdkd(1 - T)+ wpkp + wcke Payback Period = number of years required to recover the cost of the project

CF1 CF2 CFn + + ... + 1 2 (1 + k) (1 + k) (1 + k) n CF1 CF2 CFn CF0 + + + ... + =0 1 2 (1 + IRR) (1 + IRR) (1 + IRR) n NPV = CF0 +

I. Capital Investment or Initial Outlay (CF0)- cash flows associated with the investment in the project + +

A. B. C. D. E.

Cost of Project (Machinery/Plant/Equipment/Land) Installation/Modification Costs Initial Investment in Working Capital Selling Price of Old Equipment (replacement analysis only) Change in Taxes Due to Sale of Old Equipment (replacement analysis only) (Selling Price - Book Value)(-Tax Rate)

Note: The cost of the Machinery/Plant/Equipment and installation/modification costs comprises the depreciable value for the project. Depreciation per year is calculated as depreciable value divided by depreciable life. II. Operating Cash Flows (CF1, CF2, …, CFn) - cash flows received over the life of the project CFt = (Rt - Ot - Dt)(1 - T) + Dt or

CFt = (Rt - Ot )(1 - T) + Dt T Rt = Revenues in time period t Ot = Operating Expenses in time period t Dt = Depreciation in time period t T = Marginal Tax Rate

Note: Remember that all cash flows (including depreciation) should be incremental cash flows. In other words, only the new cash flows (depreciation) the project will bring to the firm should be considered. If the project generates annual cost savings, the annual savings amount replaces Rt - Ot in the above formulas. III. Terminal Cash Flow (CFn) - additional cash flows associated with the end of the project + + +

A. Salvage Value (Selling Price) of the Machinery/Plant/Equipment/Land at end of project’s life B. Tax Effect due to Sale of the Machinery/Plant/Equipment/Land (Selling Price - Book Value)(-Tax Rate) C. Recovery of Working Capital Investment

Note: The sale or value of land at the end of the project may also be included in the terminal cash flow. However, land is not a depreciable asset. Land is recorded on the firm’s books at its

cost and is not depreciated over the life of the project. Its book value will be the original cost of the land.