Financial Calculations (Math Problem Sample)

Financial Calculations
Student’s Name
Institutional Affiliation
Financial Calculations
Question 1
Units sales at $180 each (P)
Number of units 9000 (Q)
Variable cost per unit $95 (V)
Fixed operating cost $550000 per annum (F)
Outstanding debt of $1500000 at an interest cost of 8% per annum
50000 ordinary shares (N)
Interim dividend at $1 per share
Tax at 30%
10% increase in sales
Degree of Operating Leverage
 QUOTE

(Cengage Learning, 2010)
Where Q(P-V)-F= Earnings before interest and tax (EBIT) (Cengage Learning, 2010)
Therefore,




Degree of Financial Leverage (DFL)
 QUOTE

 (Cengage Learning, 2010)
Where EPS is earnings per share and I is interest paid. Hence,






Combining degree of operating leverage (DOL) and degree of financial leverage (DFL) give degree of total leverage (DTL). Therefore,
 QUOTE

 (Cengage Learning, 2010)


Question 2
Beta Books new investment
Let state 1 be when share price is $10.25 and state 2 when share price is $11.25.




The average payment to old shareholders will be  QUOTE




The Beta Books should make the investment because it will boost the company’s earnigs
The time to make the investment
The investment should be made before the share market learns the true value of the company existing assets to allow the company raise more money when it becomes known.
Given a choice the new investment should be made by issuing shares and foregoing debt. It will be self-financing without external obligations.
Question 3
Previous Years% SalesForecast Values % SalesForecast Values Sales1500-1725Retained Earnings13030.95% of net income149.5Costs90060%1035Dividends29069.05% of net income333.5Tax rate0.330% of taxable income207AssetsLiabilities/EquityCurrent AssetsCurrent LiabilitiesCash16010.67%184Creditors30020%345Debtors44029.33%506Short Term Notes100N/A100Inventory60040%690Non-Current AssetsNon-Current LiabilitiesPP&E1800120%2070Debentures800N/A800Total Assets30003450Owner’s EquityRetained Profits 1000N/A1149.50Ordinary Shares800N/A800Total 30003195
Calculations for various entries are done below;
Sales forecast is 15% increase
Percentage sales are calculated by dividing values that affected by sales by the current sales. For example, cost as a percentage of sales QUOTE


The percentage for tax rate is determined using the taxable income, which gives 30%.
Retained earnings and dividends respective percentages are determined by using net income.
External financing required (EFN) is the forecasted total assets minus forecasted total liability/equity


 QUOTE


At a capacity of 85%


S0 = Current Sales,
S1 = Forecasted Sales
g = the forecasted growth rate is Sales,
A*0 = Assets (at time 0) which vary directly with Sales,
L*0 = Liabilities (at time 0) which vary directly with Sales,
PM = Profit Margin = (Net Income)/(Sales), and
b = Retention Ratio = (Addition to Retained Earnings)/(Net Income).


Since SFC is greater than the forecast sales, the above formula is used, but only the total current assets are used in the calculations.


Extra funding not needed in this case.
Question 4
Previous years% SalesForecast values% SalesForecast valuesSales520120%624Retained Earnings6273.81%74.4Costs40076.92%480Dividends2226.19%26.4Tax rate0.330% of taxable income43.20AssetsLiabilities/EquityCurrent AssetsCurrent LiabilitiesCash20038.46%240CreditorsDebtorsShort Term NotesInventoryNon-Current AssetsNon-Current LiabilitiesPP&E30057.69360Debentures250N/A250Total Assets500600Owners’ EquityRetained Profits 250N/A324.4Ordinary Shares 500574.4
Sales forecast is 20% increase, which is calculated as;












External financing required (EFN) is the forecasted total assets minus forecasted total liability/equity


Addition to retain earnings is given as:


The Sustainable Growth Rate (SGR)


Where d-dividend payout ratio and ROE-return on equity








The sustainable growth rate has been calculated with values considering sales growth of 20%. Therefore, external funding needed is equal to that needed at a sales forecast of 20% increase, which is $25.6.
At the growth rate where no external funding is required, the total assets will equal the total liability/equity. Given that before a growth rate, Total assets equals total liability/equity. Therefore, external funding will not be required at no growth rate or at zero (0) rate.
Question 5
Sales900Costs500Taxable Income400Tax120Net Profit280AssetsCurrent Assets500Non-Current Assets6001100Liabilities/EquityDebt700Equity4001100Retained Earnings 150
Dividends 130
The total assets-to-sales ratio consistent with a growth in sales of 15%
At sales growth of 15%,
Sales forecast  QUOTE


Current assets as a percentage of sales


Forecast current assets QUOTE


Non-current assets as a percentage of sales


Forecast non-current assets QUOTE


Forecast total assets=575+690=$1265
The total assets-to-sales ratio consistent with a growth in sales of 15%




The total assets-to-sales ratio=1.22
The debt/equity ratio consistent with a growth in sales of 15%
Debt as a percentage of sales  QUOTE


Forecast debt QUOTE


The debt/equity ratio consistent with a growth in sales of 15%


The net profit margin ratio consistent with a growth in sales of 15%


Cost as a percentage of sales  QUOTE


Forecast costs  QUOTE


Net forecast sales QUOTE


Tax as a percentage of taxable income  QUOTE


Forecast tax  QUOTE










Question 6
The lease payment
Lease amount (PV) is assumed to be the cost of purchase of the equipment at $1000000.
The residual payment (FV)=$70000


Where N=period in years, i=interest on income, Pyr=yearly lease payments
Rearranging the equation,


Therefore, 



The company to either purchase or lease the asset
Cost purchasing the equipment by acquiring the loan




Interest (I) charged on the loan for five years






It is cheaper to buy the new equipment than to lease one. Therefore, the company should purchase the equipment.
Question 7
Ben owns 800 shares in Black Enterprises whose current share price (cum rights) is $3 per share. Black Enterprises wishes to raise $3 million through a rights issue at a subscription price of $2.40. They currently have issued 10 million shares.
The value of a right to buy 1 new share
The number of rights needed is calculated first.








The ex-rights share price
The ex-rights shares for the stockholder will be  QUOTE


Therefore,


The value of the investment cum rights and ex-rights
Before the right issues the value Ben investment was


After the issue, the prices will fall but Ben will hold the rights and his investment become


Question 8
Calculate the current price and the duration of the following debentures, each of which has a face value of $1000. Assume that coupon payments are made at the end of each year.
DebentureTerm to Maturity (Years)Coupon Rate (%)A312B210C49D511E813F714The current market interest rate is 9 per cent.
The price of these bonds at 9%




Where
c coupon rate, F face value, r prevailing market rate, t time period over the term of the bond
Price of bond is given as
Present value of interest payments + present value of face value of a bond


Bond A




Bond B


Bond C


Bond D


Bond E


Bond F


The duration of these bonds at 9%
Assuming the bonds was issued on 01/01/2015. The calculations are done using excel formula. The calculations are for Macaulay Duration.
Duration for Bond A
=DURATION("01/01/2015","01/01/2018",0.12,0.09,1,1)=2.701
Duration for Bond B
=DURATION("01/01/2015","01/01/2017",0.1,0.09,1,1)=1.910
Duration for Bond C
=DURATION("01/01/2015","01/01/2019",0.09,0.09,1,1)=3.531
Duration for Bond D
=DURATION("01/01/2015","01/01/2020",0.11,0.09,1,1)=4.138
Duration for Bond E
=DURATION("01/01/2015","01/01/2023",0.13,0.09,1,1)=5.674
Duration for Bond F
=DURATION("01/01/2015","01/01/2022",0.14,0.09,1,1)=5.118
The price of these debentures would be if the market interest rate increased to 12 percent.
Bond A


Bond B


Bond C


Bond D


Bond E


Bond F


The capital gain or loss on each debenture


Where Po initial stock price and P1 stock price after interest changes












The duration of these bonds at 11%
Assuming the bonds was issued on 01/01/2015. The calculations are done using excel formula. The calculations are for Macaulay Duration.
Duration for Bond A
=DURATION("01/01/2015","01/01/2018",0.12,0.11,1,1)=2.694
Duration for Bond B
=DURATION("01/01/2015","01/01/2017",0.1,0.11,1,1)=1.908
Duration for Bond C
=DURATION("01/01/2015","01/01/2019",0.09,0.11,1,1)=3.515
Duration for Bond D
=DURATION("01/01/2015","01/01/2020",0.11,0.11,1,1)=4.102
Duration for Bond E
=DURATION("01/01/2015","01/01/2023",0.13,0.11,1,1)=5.549
Duration for Bond F
=DURATION("01/01/2015","01/01/2022",0.14,0.11,1,1)=5.027
The findings
The interest rates have direct effect on the bond prices, as the interest increases, the bond prices reduces.