Question

A local company presented you with the following financial data: A & B firm reported that its sales for 2018 was $125,000 with total costs of $100,000 and there was no taxes. The owner also reported $15,000 in cash, $20,000 in inventory and $30,000 of accounts payable. Also there was $70,000 in net fixed assets with $15,000 in accounts receivables. It included that there was $40,000 in long term debt. The Company also pay 25 percent of the net income as cash dividend.

1. Compute the firm's internal growth rate. Compute the substainable growth rate. If you deposit $1200 in bank that pay 15% annual rate, what will this money be worth in five years? What is the present value of $45,000 that you will receive six years from today if the discount rate is 12%? What is the annual interest rate you must earn if you wish to turn a $5,000 deposit in an account for seven years into $8,250?

Answer 1

i) Internal growth rate = Retention ratio * Return on assets

Here,

a) Retention ratio = 1 - dividend payout ratio @ 25% or 0.25

Retention ratio = 1 - 0.25 = 0.75

b) Return on assets = Net income / Total assets

Net income = Sales - Total cost - Tax

Net income = $1,25,000 - $1,00,000 - 0 = $25,000

Total assets = Cash + Inventory + Net fixed assets + Accounts receivables

Total assets = $15,000 + $20,000 + $70,000 + $15,000 = $1,20,000

Now,

Return on assets = $25,000 / $1,20,000 = 0.2083

Put the values into internal growth rate formula,

Internal growth rate = 0.75 * 0.2083

Internal growth rate = 0.1562 or 15.62%

ii) Sustainable growth rate = Retention ratio * Return on equity

Here,

a) Retention ratio = 1 - dividend payout ratio

Retention ratio = 1 - 0.25 = 0.75

b) Return on equity = Net income available to equity shareholders / Equity

Net income to equity holder = Net income - dividend @ 25%

Net income to equity holder = $25,000 - ($25,000 * 25%)

Net income to equity holder = $25,000 - $6,250

Net income to equity holder = $18,750

Equity = Total assets - Total liabilities

Equity = (Cash + Inventory + Net fixed assets + Accounts receivables) - (Accounts payable + Long term debt)

Equity = ($15,000 + $20,000 + $70,000 + $15,000) - ($30,000 + $40,000)

Equity = $50,000

Now,

Return on equity = $18,750 / $50,000

Return on equity = 0.375

Put the values into sustainable growth rate formula,

Sustainable growth rate = 0.75 * 0.375

Sustainable growth rate = 0.2813 or 28.13%

iii) Future value of money = Amount * ((1 + i)^n)

i (rate of interest) = 15% or 0.15

n (years) = 5

Amount = $1,200 deposited

Future value of money = $1,200 * ((1 + 0.15)^5)

Future value of money = $1,200 * 2.0114

Future value of money = $2,413.68

iv) Present value of money = Amount * (1/(1 + i) ^n)

i (Interest rate) = 12% or 0.12

n (years) = 6

Amount = $45,000

Present value of money = $45,000 * (1 / (1 + 0.12)^6)

Present value of money = $45,000 * 0.5066

Present value of money = $22,797

v) Annual interest rate = ((Future value / Present value)^1/n) - 1

n (years) = 7 years

Annual interest rate = (($8,250 / $5,000)^1/7) - 1

Annual interest rate = (1.65)^1/7 - 1

Annual interest rate = 1.0742 - 1

Annual interest rate = 0.742 or 7.42%

Note : Rate calculation on calculator -

Step 1 : Take 1.65 & press √ (root sign) 12 times

Step 2 : Minus 1 & press equals to (=) sign

Step 3 : Divide by 7 & add 1 press (=) sign

Step 4 : Press (➗ & =) sign 12 times