ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.35 : A voluntary accountant is performing Du Pont Analysis for a charitable engineering organization. References for 3-step Du Pont formula are : (ROE) = (Net Income $) / (Equity $), where ROE is Return On Equity. (ROS) = (Net Income $) / (Sales $), where ROS is Return On Sales. (Asset Turnover) = (Sales $) / (Assets $). (Leverage) = (Assets $) / (Equity $). From the balance sheet and income statement, the company has Assets of $3753.19 this year and $3216.86 last year. Sales for this year is $2292.34. Let ROE = 0.37 and ROS = 0.21. (a) Calculate the Asset Turnover of the organization. (b) Find the value of the organizational Leverage. (c) Calculate the Net Income $ of the organization.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.35 : (a) (Assets $) = [ (Assets of this year) + (Assets of last year) ] / 2 = ($3753.19 + $3216.86) / 2 = $3485.025. Asset Turnover = (Sales $) / (Assets $) = ($2292.34) / ($3485.025) = 0.658. (b) From 3-step Du Pont formula, (Net Income $) = (ROE) (Equity $) = (ROS) (Sales $). Then (Equity $) = (ROS) (Sales $) / (ROE) = (0.21) ($2292.34) / (0.37) = $1301.0578. From answer (a), (Assets $) = $3485.025. (Leverage) = (Assets $) / (Equity $) = ($3485.025) / ($1301.0578) = 2.6786. (c) From 3-step Du Pont formula, (Net Income $) = (ROS) (Sales $) = (0.21) ($2292.34) = $481.3914. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.10 : Let D be the random outcome of rolling a dice once. A new dice has values of D* = D - 3.5. There is a total of n rolls of a dice. (a) Find the variance for D* by using the formula 6 V = [ D* (D = 1) ] [ D* (D = 1) ] + [ D* (D = 2) ] [ D* (D = 2) ] + [ D* (D = 3) ] [ D* (D = 3) ] + [ D* (D = 4) ] [ D* (D = 4) ] + [ D* (D = 5) ] [ D* (D = 5) ] + [ D* (D = 6) ] [ D* (D = 6) ]. (b) Calculate the standard deviation of D* as a square root of V. (c) Another new dice has values of D** = kD*. (i) Find the value of k so that D** has a standard deviation of 1. (ii) Find the values of D** for each outcome of D = 1, 2, 3, 4, 5 and 6, when the standard deviation is 1. (iii) Given that the average score of a dice is 3.5, find the equivalent, new and improved model of a dice, Sn in term of n and D**. (iv) Find the expected value of D** as the average of D**.
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