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# Financial Calculations (Math Problem Sample)

Instructions:

SOLVING MULTIPLE FINANCIAL CALCULATIONS

source..Content:

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.

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