# FINANCIAL CALCULATIONS Essay Example

Financial Calculations

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

(Cengage Learning, 2010)

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

Therefore,

Degree of Financial Leverage (DFL)

(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,

(Cengage Learning, 2010)

Question 2

1. 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

The Beta Books should make the investment because it will boost the company’s earnigs

1. 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.

1. 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 Forecast Values Forecast Values Retained Earnings 30.95% of net income Dividends 69.05% of net income 30% of taxable income Liabilities/Equity Current Assets Current Liabilities Creditors Short Term Notes Inventory Non-Current Assets Non-Current Liabilities Debentures Total Assets Owner’s Equity Retained Profits Ordinary Shares

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

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.

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

1. 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 Forecast values Forecast values Retained Earnings Dividends 30% of taxable income Liabilities/Equity Current Assets Current Liabilities Creditors Short Term Notes Inventory Non-Current Assets Non-Current Liabilities Debentures Total Assets Owners’ Equity Retained Profits Ordinary Shares

Sales forecast is 20% increase, which is calculated as;

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

1. Addition to retain earnings is given as:

1. The Sustainable Growth Rate (SGR)

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

1. 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.

2. 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

 Taxable Income Net Profit Current Assets Non-Current Assets Liabilities/Equity

Retained Earnings 150

Dividends 130

1. The total assets-to-sales ratio consistent with a growth in sales of 15%

At sales growth of 15%,

Sales forecast

Current assets as a percentage of sales

Forecast current assets

Non-current assets as a percentage of sales

Forecast non-current assets

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

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

Debt as a percentage of sales

Forecast debt

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

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

Cost as a percentage of sales

Forecast costs

Net forecast sales

Tax as a percentage of taxable income

Forecast tax

Question 6

1. 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,

1. 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.

1. The value of a right to buy 1 new share

The number of rights needed is calculated first.

1. The ex-rights share price

The ex-rights shares for the stockholder will be

Therefore,

1. 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.

 Debenture Term to Maturity (Years) Coupon Rate (%)

The current market interest rate is 9 per cent.

1. The price of these bonds at 9%

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

1. 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

1. The price of these debentures would be if the market interest rate increased to 12 percent.

1. The capital gain or loss on each debenture

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

1. 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

1. The findings

The interest rates have direct effect on the bond prices, as the interest increases, the bond prices reduces.

The duration of the bond is also affected by the market interest rates. As the interest rate increases, the duration reduces slightly.

Question 9

Debenture Face Value \$2000

Coupon Rate 11%

35% probability that rates will fall to 9%

65% probability that rates will increase to 12%

Par value \$1900

1. Calculate the Market Price of the Non-Callable Debenture

1. What would the coupon rate need to be for the debentures to sell at par?

For callable debentures,

1. The cost of the call provision

Question 10

Face value \$400000

Yielding 10.25% per annum

180 days to maturity

1. At no interest rate, the maturity value equals the face value, which is \$400000.00.

The price of the note (P) will be at a discounted price,

Where S=maturity value, r=yielding rate, t=period in years

Therefore,

1. The interest for 180 days will be the difference between the face value and the price of the note

Where I=interest, P=price of the note, t=time in years

The interest rate equals the yielding rate.

Question 11

The Miller-Orr Model

Target cash balance (Z)

Where TC=transaction costs of buying or selling, v=standard deviation, r=daily rate, L=Lower limit

Upper limit for the cash account (H)

Where Z=target cash balance, L=lower limit

Question 12

Quantity=80000 liters per year

Ordering cost=\$220 per order

Cost of carrying the inventory=\$1.20 per liter per year

1. The economic order quantity (EOQ)

1. The order cost

1. The ordering days

Taking 365 days in a year,

1. The holding cost

1. The annual total cost

Question 13

Annual demand=20000 units

Ordering cost=\$2 per unit

Carrying cost=\$0.50 per unit

The cost per unit=\$10

Question 14

Calculate the Black—Scholes price for a call option with the following features: share price \$24.00, exercise price \$23.00, term to expiry 1 year, risk-free interest rate 5.25 per cent per annum (compounding annually) and volatility (variance) 0.07 per annum.

The Black-Scholes Model: European options formula

C= theoretical call value

S =current stock price

N= cumulative normal standard distribution

K=option strike price

r=risk free interest

v=the volatility

S=\$24, K=\$23, r=0.0525, v=0.07

Calculating terms in the formula

Substituting N(d1) and N(d2) in the original formula

Question 15

Determining the profit and/or loss to the following:

1. Call Options- Buyer/Holder and Seller/Writer

 Market Price Exercise Price Call Premium

When the holder exercise the right to buy,

The holder will make a profit of \$0.25.

1. Put Options- Buyer/Holder and Seller/Writer

 Market Price Exercise Price Call Premium

When the holder exercise the right to sell,

The holder will make a profit of \$0.70.

Question 16

 Cash Price per Unit Variable Cost per Unit Current Quantity Sold per Month Quantity Sold under New Policy Monthly Required Return

The company is planning to switch from a cash basis to offering credit terms.

1. The cost of switching using both the One Shot Approach and the Accounts Receivable Approach.

One Shot Approach

The cost of the switch=current revenue + the cost of producing extra 180 units under the new policy

1. If the new Credit price was set at \$64 per Unit and 2% of sales were uncollectable, the NPV of the switch is calculated as follows;

There is a discount rate (d) of

Since 2% (u) will not be collected, the amount collected will be

Where P-cash price, P’-credit price, Q-current quantity, Q’-quantity under new policy

1. The default rate that makes NPV equal to zero.

Rearranging the equation gives

The default rate (u) would be

1. The NPV associated with a One-Time Sale.

Where: v = variable cost per unit

u = probability of default

P = Current Price

r = Monthly requiredreturn

1. The percentage chance the company would have of collecting given the one time sale extension of credit.

The percentage chance is one minus the probability of the default at one-time sale. Hence,

1. The NPV associated with a repeat sale

Question 17

1. The gain from the merger

The annual savings from the merger is \$270000 per year.

1. The net cost of the cash offer

The cash offer is \$5.9 million

The combined value of the two companies

50% holding will be

1. The net cost of the share alternative

This amount is similar to the net cost of the cash offer, which is \$850000

1. The NPV of the acquisition under:

The cash offer

NPV=850000/0.01=\$85000000

The share offer

Similarly, NPV=850000/0.01=\$85000000

Question 18

1. The gain from the takeover; and

1. The maximum price that Endeavour should be prepared to pay for Beard’s shares.

The maximum would be the total share price minus the gain= (\$5million×2)-270000=\$9730000

References